Observation of Near-Inertial Oscillations Induced by Energy Transformation During Typhoons

energies

Article Observation of Near-Inertial Oscillations Induced by Energy Transformation during Typhoons

Huaqian Hou 1,2, Fei Yu 1,*, Feng Nan 1, Bing Yang 1, Shoude Guan 1 and Yuanzhi Zhang 3,*

1 Key Laboratory of Ocean Circulation and Wave Studies, Institute of Oceanology, Chinese Academy of Sciences, Qingdao 266071, China; [email protected] (H.H.); [email protected] (F.N.); [email protected] (B.Y.); [email protected] (S.G.) 2 University of Chinese Academy of Sciences, Beijing 100049, China 3 Nanjing University of Information Science and Technology, Nanjing 210044, China * Correspondence: [email protected] (F.Y.); [email protected] (Y.Z.); Tel.: +86-186-5328-0417 (F.Y.)

Received: 19 October 2018; Accepted: 25 December 2018; Published: 29 December 2018

Abstract: Three typhoon events were selected to examine the impact of energy transformation on near-inertial oscillations (NIOs) using observations from a subsurface mooring, which was deployed at 125◦ E and 18◦ N on 26 September 2014 and recovered on 11 January 2016. Almost 16 months of continuous observations were undertaken, and three energetic NIO events were recorded, all generated by passing typhoons. The peak frequencies of these NIOs, 0.91 times of the local inertial frequency f, were all lower than the local inertial frequency f. The estimated vertical −1 group velocities (Cgz) of the three NIO events were 11.9, 7.4, and 23.0 m d , and were relatively small compared with observations from other oceans (i.e., 100 m d−1). The directions of the horizontal near-inertial currents changed four or five times between the depths of 40 and 800 m in all three NIO events, implying that typhoons in the northwest Pacific usually generate high-mode NIOs. The NIO currents were further decomposed by performing an empirical orthogonal function (EOF) analysis. The first and second EOF modes dominated the NIOs during each typhoon, accounting for more than 50% of the total variance. The peak frequencies of the first two EOF modes were less than f, but those of the third and fourth modes were higher than f. The frequencies of all the modes during non-typhoon periods were more than f. Our analysis indicates that the relatively small downward group velocity was caused by the frequent direction changes of the near-inertial currents with depth.

Keywords: Near-inertial kinetic energy; vertical group velocity; near-inertial oscillations; energy transformation

1. Introduction Free-propagating internal waves in the ocean usually have frequencies lower than the buoyancy frequency N and higher than the inertial frequency f [1,2]. Near-inertial oscillations (NIOs) are internal waves with frequencies close to the local inertial frequency f. NIOs have been observed in all ocean basins and the entire ocean column [3–5]. The breaking of near-inertial waves can cause ocean mixing, which inﬂuences pollutant dispersal and marine productivity [3,6,7], maintains ocean thermohaline circulation, and modulates the climate [8]. Alford presented spatial maps of wind–NIO energy ﬂuxes [8] between 50◦ S and 50◦ N, which showed that the energy supplied to NIOs by wind is of the same order of magnitude as that provided to baroclinic tides by their barotropic counterparts. NIOs are strongly intermittent or highly temporally variable [9] and have high wavenumber aspects [10–12]. NIOs may play an important role in upper-ocean mixing, potentially affecting various processes, including the biogeochemical variety and those affecting the climate [13].

Energies 2019, 12, 99; doi:10.3390/en12010099 www.mdpi.com/journal/energies Energies 2019, 12, 99 2 of 19

Near-inertial waves are largely generated by transient strong wind systems, such as mid-latitude storms and tropical cyclones, while NIOs have been observed in all ocean basins [14–16]. Strong winds supply kinetic energy to the mixed layer of the ocean, generating strong currents. Near-inertial internal waves form after several Rossby adjustment cycles [17,18]. Strong vertical shear in a near-inertial horizontal current can cause intense turbulent mixing at the base of the mixed layer through shear instability, which can entrain subsurface cold water, bringing it to the sea surface and markedly cooling the latter under a typhoon [7,19,20]. This cooling can further decrease or even eliminate surface enthalpy fluxes from the ocean to the atmosphere, significantly affecting typhoon evolution and intensity changes. Fluctuations in tropical cyclones, that is, negative feedback from the ocean, can therefore occur [21]. Clockwise-rotating energy peaks at near-inertial frequencies for records from all current meter mooring accompanying the passage of atmospheric fronts was found by Chen in the Texas-Louisiana shelf [22]. Studies of typhoon-generated NIOs have been focused on observations made under high wind conditions to allow forecasting of the typhoon’s intensity to be improved, for example, in the Gulf of Mexico [23,24] and the Atlantic [16]. Near-inertial kinetic energy (NIKE) is generated in the surface mixed layer before being preferentially propagated from thence to the deep ocean [25–28], providing the energy for thermohaline circulation to occur [29]. NIOs propagate downward decay because of turbulent dissipation. Alford and Whitmont [30] examined 2,480 historical current-meter records and found that NIKE decreased by a factor of 4–5 between depths of 500 and 3,500 m in winter. Eugene found that wind-generated, near-inertial, internal waves reach a depth of 1200 m (where many current meters were located) in a few days after the hurricane passes the region [31]. Meanwhile, Alford et al. [32] found that 12%–33% of the surface NIKE could reach a depth of 800 m at the Papa station in the northeast Pacific Ocean. The vertical group velocity Cgz of an NIO depends theoretically on the vertical wave number m and becomes extremely small when the NIO has a large m, resulting in sizable differences between the group velocities Cgz of NIOs, as has been found in numerous previous studies (see Table1).

Table 1. Summary of vertical group velocity (Cg) values found in previous studies.

−1 Reference Cg (m d ) Method Price, 1983 [19] 100 MODEL 7–39 FASTEST* Qi et al., 1995 [18] CURRENT METER 4–20 SLOWEST* Kim et al., 2013 [33] 39.7 ADCP Yang et al., 2015 [5] 240 ADCP Yang et al., 2015 [34] 233 ADCP Pallàs et al., 2016 [35] 56 ± 7 ADCP Note that: ADCP means acoustic Doppler current proﬁlers.

As shown in Table1, vertical propagation of NIKE was examined using in situ observations or numerical simulation in previous studies [18,19]. Qi et al. [18] used the observations of two moorings in the northeast Pacific Ocean to calculate the vertical group velocity in different months. The fastest was in October by mooring Cl; the slowest was in March by mooring NP. The Pacific is the largest ocean in the world. Many studies have focused on NIO events therein, including Alford [3], who estimated that the north Pacific receives an annual mean energy input of 65 ± 10 GW from wind over the box of calculation (13% of the total energy input from wind for all the oceans). Energetic NIOs have been observed at all depths in the eastern Pacific, radiating both upward and downward in abrupt ridges/steps, with near-inertial shear exceeding internal tide shear by a factor of 2–4 at all depths [12]. Furthermore, shallow ocean near-inertial wave responses to three typhoons in the north-western South China Sea were examined using temperature and current profiles observed at moorings in 2005 [5]. Kim et al. [33] found that an anti-cyclonic eddy trapped near-inertial energy between two layers at Energies 2019, 12, 99 3 of 19 depths of 120–210 m in the northwest Pacific. This region suffers more frequent and intense typhoons than any other oceanic zone and features highly complex current systems, such as the Kuroshio and the Northern Equatorial Currents [36,37], although few in-situ observations of NIOs have been conducted in the locality. This lack of long-term observations has caused a dearth of reporting of NIO characteristics. Nonetheless, three typhoons passed a mooring we had deployed in the northwest Pacific between September 2014 and January 2016, allowing us to record three energetic NIO events. This offered a rare opportunity to examine typhoon-generated NIOs using continuous current profiles measured by a mooring. We first examined the general characteristics of NIOs in the area, focusing mainly on the high-mode vertical structure based on observations and further theoretical analysis. The temporal and vertical structure of NIKE was studied in depth via such an analysis. The mooring observations and the three typhoons are described in Section2, the theoretical analysis for the vertical distributions of the group velocities are in Section3, the results of general characteristics of the three observed NIO events are presented in Section4, and the discussion and conclusion are in Sections5 and6.

2. Data The mooring was deployed at 125◦ E and 18◦ N on 26 September 2014 and recovered on 11 January 2016, giving a total of 473 days (Figure1A). The water depth at the mooring station was 4714 m. The main float was 400 m deep and had two 75 kHz Teledyne RDI acoustic Doppler current profilers (ADCPs), one upward-looking and the other downward-looking, to monitor ocean currents at depths of 40 and 800 m. The temporal and vertical sampling resolutions of the ADCPs were 1 h and 8 m, respectively. The velocity and temperature data were interpolated linearly to uniform levels at 5 m intervals. Three typhoons passed the mooring during the observation period, with three corresponding energetic NIO events being recorded. The tracks of the three typhoons were obtained from the Japan Meteorological Agency as shown in Figure1A, and the temporal evolutions of the maximum wind speed and distances between the typhoons and the mooring are displayed in Figure1C. The first typhoon, named Fung-Wong, formed on 17 September 2014 near 135.0◦ E and 12.6◦ N, and dissipated on 25 October 2014 near 138.5◦ E and 37.5◦ N. Fung-Wong was 177.1 km from the mooring on 17 September and passed southwest of it with a maximum sustained wind speed of 23 m s−1 and a radius (with an average wind velocity more than 15 m s−1, which was also used later) of 500 km. The mooring, which was deployed on 26 September 2014, captured part of the NIO induced by Fung-Wong. The second typhoon was Maysak, which formed on 26 March 2015 near 159.9◦ E and 6.7◦ N, and was closest to the mooring on 5 April 2015. The maximum wind speed sustained was 18 m s−1. The closest the typhoon center got to the mooring was 285.9 km, which exceeded its radius of 150 km. The large distance between the typhoon center and the mooring, as well as the low maximum wind speed probably made the NIO event associated with Maysak less energetic than that associated with Fung-Wong. The third typhoon, Noul, formed on 2 May 2015 near 144.1◦ E and 7.4◦ N, and dissipated as a tropical storm on 16 May 2015 at 178.1◦ E and 48.7◦ N. Noul was closest to the mooring on 10 May, and the smallest distance between its center and the mooring was 211.8 km. The maximum sustained wind speed was 55 m s−1 and the maximum wind speed radius was about 280 km. Argo is a global array of about 3800 freely drifting buoys that measure temperature and salinity profiles in the top 2000 m of the oceans. It has been used in many studies on global changes and regional effects [38]. In this study, Argo data for a radius of 100 km from the typhoon centers as the storm passed were used. No Argo data were available during Fung-Wong, three Argo profiles were available during Maysak, and five profiles were available during Noul. The positions of the Argo buoys that provided the data are shown in Figure1. Energies 2018, 11, x FOR PEER REVIEW 4 of 20 Energies 2019, 12, 99 4 of 19

30 60 FUNG-WONG MAYSAK (B) 50 (A) NOUL

40 25 ) -1 30

7th s (m 11th 20 20 Mooring and Argo 10 FUNG-WONG 20th MAYSAK

Maximum Wind Speed NOUL 0 Apr. 4th, 2015 0 2 4 6 8 10 12 15 Time (day) 20 Sep. 17th, 2014 3000 FUNG-WONG 19.5 (C) MAYSAK Latitude (°N) Latitude 1st 2500 NOUL 10 19 May. 8th, 2015 2000 18.5 5th 1500 18 5 1000 17.5 Distance (km) 500 17 124 125 0 0 115 120 125 130 135 140 0 2 4 6 8 10 12 Longitude (°E) Time (day)

FigureFigure 1. 1. ((AA)) Best Best tracks tracks of of typhoon typhoon Fung-Wong Fung-Wong (No. (No. 16) 16) in in 2014, 2014, typhoon typhoon Maysak Maysak (No. (No. 4) 4) in in 2015, 2015, andand typhoon typhoon NoulNoul (No. 6) in 2015.2015. TheThe magentamagenta asterisk asterisk indicates indicates the the location location of of the the mooring, mooring, and and the ◦ theplus plus signs signs are are the locationsthe locations of the of Argothe Argo buoys. buoys. The horizontalThe horizontal axis ofaxis (A )of is e longitude Figure 1( withA) is thelongitude unit E. ◦ withThe verticalthe unit axis°E. The is latitude vertical with axis theis latitude unit N. with Locations the unit of °N the. Locations Argo proﬁles of the were Argo labeled profiles with were the labeleddifferent with colors the corresponding different colors to differentcorresponding typhoon to passages.different (typhoonB) Maximum passages. wind ( speedB) Maximum over time wind from speedwhen over each time typhoon from was when generated. each typhoonThe horizontal was generated.axis of The (B) ishorizontal time with axis the of unit Figure day. 1(TheB) is vertical time −1 withaxis isthe maximum unit day. windThe vertical speed with axis theis maximum unit ms wind.(C) Distancespeed with between the unit each ms typhoon-1. (C) Distance and the between mooring eachover typhoon time from and when the mooring each typhoon over time was generated.from when The each horizontal typhoon was axis generated. of (C) is time The with horizontal the unit axis day. ofThe Figure vertical 1(C axis) is time is distance with the with unit the day. unit Th km.e vertical All these axis three is distance ﬁgures with in Figure the unit1 have km. the All same these legend. three 3. Theoreticalfigures in Figure Analysis 1 have the same legend.

3. TheoreticalFrom the Analysis basic dynamics theory of oceanic internal waves, the dispersion relationship for a propagating inertial wave could be written as Equation (1) [1], From the basic dynamics theory of oceanic internal waves, the dispersion relationship for a propagating inertial wave could be written as Equationk 2(1)+ [1],l2 ω2 = f 2 + N2 (1) m2 ()kl22+ ω 22=fN+ 2 (1) where (k, l, m) is a three-dimensional wave number, ω ism the2 wave frequency, f is the inertial frequency and N is the buoyancy frequency. whereThe (k, l Boussinesq, m) is a three-dimensional approximation wave was appliednumber, in ω theis thef plane, wave frequency, implying the f is changethe inertial in frequency frequencyf andwith N latitude is the buoyancy could be frequency. neglected. This simpliﬁcation is achievable for this single mooring position. TheThe displacement Boussinesq of approximation the mooring position was applied is much in smaller the f plane, than theimplying change the of fchangewith latitude. in frequency f with latitudeThe vertical could group be neglected. velocity C Thisgz can simplification therefore be writtenis achievable as: for this single mooring position. The displacement of the mooring position is much smaller than the change of f with latitude. 2 2 2 The vertical group velocity Cgz can therefore∂ω be written−N as:k + l Cgz = = q (2) ∂m N2 m3 f 2222+ (k2 + l2) ∂ω −Nkl()m2+ C == gz ∂ 2 m CN m (2) where the relationship between vertical groupmf velocity32+ gz and() kl 22+ can be calculated by: m2 3 ∂Cgz − 2 = Am−3 m2 f 2 + A 2m2 f 2 + 2A + m2 ≥ 0 (3) Where the relationship∂m between vertical group velocity Cgz and m can be calculated by:

Energies 2019, 12, 99 5 of 19 where A = N2(k2 + l2) to simplify the equation. The border limitations mean that velocity and pressure can be written as the product of the vertical mode item and the horizontal item, as shown in Equation (4).

u(x, y, z, t) = Ψ(z)U(x, y, t) v(x, y, z, t) = Ψ(z)V(x, y, t) (4) w(x, y, z, t) = Ψ(z)W(x, y, t) p(x, y, z, t) = Ψ(z)P(x, y, t) where Ψ(z) is the vertical mode of velocity and pressure. U, V, W, and P are the horizontal structure of velocity and pressure. As the vertical velocity at the surface and seabed is zero. Thus, the boundary conditions are expressed as:

dΨ = dz 0 z=0 (5) dΨ = 0 dz z=−H where H is the water depth. The solution of the vertical mode is shown in Equation (6) [39]. To solve the equation, we assume that the water body is of uniform stratification, which means that the Buoyancy frequency is constant. With this simplification, Ψ(z) can be solved in the following Equation (7). nπ Ψ(z) = cos( z), (n = 1, 2, 3, . . .) (6) H Here n is the mode number, which is a positive integer, like n = 1, 2, 3. This means that Ψ(z) changes in the horizontal current direction as a function of depth. The larger is n in Equation (6), then Ψ(z) has more zero solutions under the same conditions. They have more times of horizontal current direction changes at the same times. Meanwhile, the vertical wave vector m = nπ/H so that the vertical wave number m is proportional to the number of modes n, m ∝ n. In the case where the Buoyancy frequency N is not a constant, Ψ(z) will have different forms of solution, such as in Zervakis et al. in 1995 [40]. The good news is the conclusion that m and n are in a relatively increasing relationship and can still be obtained [40,41]. From Equations (3) and (6), it can be seen that the more the velocity changes with depth, the more NIKE propagates downward. The group velocity was downward; therefore, the vertical group velocity Cgz is less than zero. A larger vertical wave number m would make Cgz smaller. Considering that vertical wave number m is proportional to the number of modes n, a larger n will give a smaller Cgz. Even though we have no idea of velocity at full depth, the direction-changing times of the velocity at the known depth can also be used to describe the complexity of the velocity. The more times the vertical velocity changes with depth, the larger will be the n produced. Thus, if vertical velocity changed more times in the unit depth, a smaller Cgz would exist. This is similar to previous studies, such as [2,40,41] To study the relationship between the vertical group velocity Cgz and the vertical stratification, Equation (7) can be derived from Equation (2). Based on these assumptions, the absolute group velocity (–Cgz) is an increasing function related to the buoyancy frequency N as below:

dC (N) k2 + l2 2Nm2 f 2 + N3k2 + l2 gz = − · < 2 3 0 (7) dN m [m2 f 2 + N2(k2 + l2)] 2

4. Results for Typhoon-Generated NIOs

4.1. Near-Inertial Responses Frequency bands are selected to suit local NIO characteristics. For example, Shay et al. [42] used 0.8 f –1.2 f for the Gulf of Mexico, Chen et al. [43] used 0.85 f –1.15 f for the South China Sea, Energies 2018, 11, x FOR PEER REVIEW 6 of 20

dC() N ()kl22+2 NmfNkl 22+ 3() 22 + gz =− ⋅ <0 dN m2 3 (7) 22+ 2() 2 2 2 mf N k+ l

4. Results for Typhoon-Generated NIOs

4.1. Near-Inertial Responses

EnergiesFrequency2019, 12, 99 bands are selected to suit local NIO characteristics. For example, Shay et al. [42] used6 of 19 0.8 f–1.2 f for the Gulf of Mexico, Chen et al. [43] used 0.85 f–1.15 f for the South China Sea, and Pallàs et al. [35] used 0.9 f–1.15 f for the Gulf of Mexico. In this study, the passband was based on 1/e (the and Pallàs et al. [35] used 0.9 f –1.15 f for the Gulf of Mexico. In this study, the passband was based reciprocal Euler’s number) of the power spectrum maximum for the average depth. This method on 1/e (the reciprocal Euler’s number) of the power spectrum maximum for the average depth. prevented the main NIO signal information from being lost when the velocity spectrum was This method prevented the main NIO signal information from being lost when the velocity spectrum significant in a wider spectral band. The selected passband frequency for the NIOs was 0.7 f–1.2 f (see was signiﬁcant in a wider spectral band. The selected passband frequency for the NIOs was 0.7 f –1.2 f Figure 2). (see Figure2).

Figure 2. The power spectra of the first near-inertial oscillation (NIO) event is shown in (A ,D). The second is shown in (B,E). The third is shown in (C,F). The horizontal axis of the figure is frequency Figure 2. The power spectra of the first near-inertial oscillation (NIO) event is shown in A and D. The with the unit cpd. The vertical axis is water depth with the unit m. Power spectra of the (A–C) eastward second is shown in B and E. The third is shown in C and F. The horizontal axis of the figure is and (D–F) northward components of the horizontal currents at 40–800 m deep for the three NIOs. frequency with the unit cpd. The vertical axis is water depth with the unit m. Power spectra of the (A, The dashed lines indicate local frequencies f, 0.7 f, and 1.2 f. Note that the different color-bars represent B, and C) eastward and (D, E, and F) northward components of the horizontal currents at 40–800 m the three typhoon events. deep for the three NIOs. The dashed lines indicate local frequencies f, 0.7 f, and 1.2 f. Note that the differentThe power color-bars spectra represen of thet the horizontal three typhoon currents events. are at average depth (from 50 to 800 m), while the typhoons influencing the conditions (21 days) are shown in Figure3. The inertial signal was the clearest signal during each event. Velocity spectra for the three NIO events are shown in Figure2. The maximum spectral density of the first, second, and third NIOs were 0.172 m2 s−2 Hz−1 at 140 m, 0.049 m2 s−2 Hz−1 at 115 m, and 0.115 m2 s−2 Hz−1 at 145 m, respectively. The maximum inertial energy peaks were all deeper than 100 m, meaning that the most energetic NIOs did not appear at the surface. The peaks in the NIO frequency spectra were all clearly red-shifted and were all at 0.91 f (i.e., lower than the local inertial frequency f ). The strongest red-shift was about 0.91 f and was between 100 and 300 m deep.

Energies 2019, 12, 99 7 of 19 Energies 2018, 11, x FOR PEER REVIEW 7 of 20

-1 10 FUNG-WONG MAYSAK

) NOUL -1 -2 10 cpd -2 s 2

-3 10

-4 10 Spectral Density (m Density Spectral

-5 f k1 m2 10 -1 0 1 10 10 10 Frequency(cpd) √2 2 Figure 3.FigureAverage 3. Average power power spectra spectra for allfor theall the depths depths (from (from 50 50 toto 800800 m) velocities velocities U U= √=(u +( uv2) +atv the2) at the mooring.mooring. The The horizontal horizontal axis axis of of the th figuree figure is is the the frequency frequency withwith the unit cpd. cpd. The The vertical vertical axis axis is is spectral density with the unit m2 s−2 cpd−1. The three different lines are the average power spectra of spectral density with the unit m2 s−2 cpd−1. The three different lines are the average power spectra of velocity after the three typhoons (Fung-Wong, Maysak, and Noul). The dotted lines indicate the local velocity after the three typhoons (Fung-Wong, Maysak, and Noul). The dotted lines indicate the local inertial frequency f, the frequency of the k1 tide, and the frequency of the m2 tide. This figure has the 2 inertial frequencysame legendf, as the Figure frequency 1. of the k1 tide, and the frequency of the m tide. This figure has the same legend as Figure1. The power spectra of the horizontal currents are at average depth (from 50 to 800 m), while the 4.2. Near-Inertial Horizontal Current typhoons influencing the conditions (21 days) are shown in Figure 3. The inertial signal was the Theclearest horizontal signal current during timeeach seriesevent. wasVelocity band-filtered spectra for (fromthe three 0.7 NIOf to 1.2eventsf ) to are allow shown the in near-inertial Figure 2. 2 −2 −1 featuresThe to be maximum analyzed. spectral As mentioned density of earlier,the first, the second, first typhoon and third was NIOs closest were to0.172 the m mooring s Hz locationat 140 m, on 0.049 m2 s−2 Hz−1 at 115 m, and 0.115 m2 s−2 Hz−1 at 145 m, respectively. The maximum inertial energy 19 September 2014, seven days before the mooring was deployed. As shown in Figure4, the maximum peaks were all deeper than 100 m, meaning that the most energetic NIOs did not appear at the surface. zonal velocity was 0.51 m s−1 and the maximum meridional velocity was 0.58 m s−1, both at The peaks in the NIO frequency spectra were all clearly red-shifted and were all at 0.91 f (i.e., lower 135 m deepthan. the The local second inertial NIO frequency event f). was The thestrongest weakest red-shift of the was three about because0.91 f and the was distance between 100 from and the second typhoon’s300 m deep. center to the mooring site was further than for the other two typhoons, and its radius was smaller. The maximum zonal and meridional near-inertial velocities were 0.30 and 0.32 m s−1, respectively,4.2. Near-Inertial both at a depthHorizontal of 145 Current m. The third near-inertial event had a maximum zonal velocity of −1 −1 0.47 m s atThe 215 horizontal m deep andcurrent a maximum time series meridionalwas band-filtered velocity (from of 0.7 0.45 f to m 1.2 s f) toat allow 175 m. the near-inertial Thefeatures directions to be of analyzed. the horizontal As mentioned currents earlier, changed the first four typhoon or five timeswas closest between to the 40 mooring and 800 location m during the threeon NIO 19 September events. Pall 2014,às etseven al. [ 35days] observed before the near-inertial mooring was horizontal deployed. currentsAs shown with in Figure two direction 4, the changesmaximum between zonal the surface velocity and was depth 0.51 m of s− 1,4001 and mthe in maximum the Gulf meridional of Mexico. velocity Meanwhile, was 0.58 Shay m s et−1, al.both [42 ] observedat NIOs135 m indeep. the The Gulf second of Mexico NIO event by examining was the weakest airborne of the expendable three because current the distance profiles, from and the the horizontalsecond current typhoon’s directions center alsoto the changed mooring twicesite was between further thethan surface for the other and 800two m.typhoons, Kim et and al. its [33 ], radius was smaller. The maximum zonal and meridional near-inertial velocities were 0.30 and 0.32 for their part, found that near-inertial horizontal current directions changed twice between the surface m s−1, respectively, both at a depth of 145 m. The third near-inertial event had a maximum zonal and 500 m in the northwest Pacific, nearly 2,000 km east of our mooring. All these researchers observed velocity of 0.47 m s−1 at 215 m deep and a maximum meridional velocity of 0.45 m s−1 at 175 m. the baroclinic structure of the first near-inertial baroclinic mode, where surface horizontal currents are 180 degrees out of phase in respect to horizontal currents at depth. The horizontal currents changed more frequently in our observations than in those of our predecessors, implying that the NIOs at the mooring had higher modes and more complex vertical structures than those in the previous studies [33,35,39]. Energies 2019, 12, 99 8 of 19 Energies 2018, 11, x FOR PEER REVIEW 8 of 20

Figure 4. Time evolution of the cross-track component of the band-pass filtered (σ ∈ [0.7, 1.2] f)(A,C,E) Figure 4. Time evolution of the cross-track component of the band-pass filtered (σ∈[0.7,1.2] f) (A, C, eastward and (B,D,F) northward ocean currents (m s-1) at 40–800 m deep. The first near inertial current and E) eastward and (B, D, and F) northward ocean currents (m s-1) at 40–800 m deep. The first near is shown in (A,B). The second is shown in (C,D). The third is shown in (E,F). The horizontal axis of the inertial current is shown in A and B. The second is shown in C and D. The third is shown in E and F. figureThe is time. horizontal The vertical axis of the axis figure is the is watertime. The depth vertical with axis the is unit the m.water The depth black with circles the indicateunit m. The the black times the typhoonscircles were indicate closest the totimes the mooring.the typhoon Notes were that closest the different to the mooring. color-bars Note are that for the the different three typhoon color-bars events. are for the three typhoon events. As shown in Figure1, the first typhoon (FUNG-WONG) was closest to the Mooring, so it stimulated a strong near-inertialThe directions internal of the horizontal wave. The currents second changed typhoon four (MAYSAK) or five times had between the smallest 40 and 800 wind m during speed and the farthestthe three distance, NIO events. and Pallàs the near-inertial et al. [35] observed internal near-inertial wave excited horizontal was the currents smallest. with Although two direction the third typhoonchanges (NOUL) between was the far surface away (similar and depth to theof 1,400 second m in one), the Gulf the intensityof Mexico. of Meanwhile, the typhoon Shay was et large, al. [42] so the intensityobserved of the NIOs near-inertial in the Gulf internal of Mexico wave by was examin alsoing relatively airborne large, expendable which current is close profiles, to the first and event.the horizontal current directions also changed twice between the surface and 800 m. Kim et al. [33], for 4.3. Verticaltheir part, Propagation found that of near-inertia Near-Inertiall horizontal Kinetic Energy current directions changed twice between the surface and 500 m in the northwest Pacific, nearly 2,000 km east of our mooring. All these researchers Afterobserved the threethe baroclinic typhoons structure passed, of NIKE the first was near-inertial concentrated baroclinic in the uppermode, 400where m ofsurface the water horizontal (Figure 5), − wherecurrents the density are 180 was degrees 1.025 out× 10 of3 kgphase m in3 (the respect average to horizontal ocean-water currents density). at depth. NIKE The belowhorizontal 400 m is not showncurrents in changed this section more because frequently it wasin our not observatio strong enough.ns than in The those black of our lines predecessors, in Figure5 implying indicate the maximumthat the NIKE NIOs divided at the mooring by e, to had indicate higher the modese-folding and more time. complex Inside the vertical observation structures area, than the those maximum in NIKEthe per previous unit mass studies (unit: [33,35,39]. kg, as in following) after the ﬁrst typhoon was 163.64 J near depth of 135 m at 07:00 on 28 September 2014. The maximum NIKE per unit mass after the second typhoon was 51.83 J near depth of 130 m at 14:00 on 15 April 2015. The maximum NIKE per unit mass after the third typhoon was 113.60 J near depth of 195 m at 14:00 on 20 May 2015. Energies 2018, 11, x FOR PEER REVIEW 9 of 20

As shown in Figure 1, the first typhoon (FUNG-WONG) was closest to the Mooring, so it stimulated a strong near-inertial internal wave. The second typhoon (MAYSAK) had the smallest wind speed and the farthest distance, and the near-inertial internal wave excited was the smallest. Although the third typhoon (NOUL) was far away (similar to the second one), the intensity of the typhoon was large, so the intensity of the near-inertial internal wave was also relatively large, which is close to the first event.

4.3. Vertical Propagation of Near-Inertial Kinetic Energy After the three typhoons passed, NIKE was concentrated in the upper 400 m of the water (Figure 5), where the density was 1.025 × 103 kg m−3 (the average ocean-water density). NIKE below 400 m is not shown in this section because it was not strong enough. The black lines in Figure 5 indicate the maximum NIKE divided by e, to indicate the e-folding time. Inside the observation area, the maximum NIKE per unit mass (unit: kg, as in following) after the first typhoon was 163.64 J near depth of 135 m at 07:00 on 28 September 2014. The maximum NIKE per unit mass after the second typhoon was 51.83 J near depth of 130 m at 14:00 on 15 April 2015. The maximum NIKE per unit mass after the third typhoon was 113.60 J near depth of 195 m at 14:00 on 20 May 2015. The outline in Figure 5 is the contour of the maxima NIKE divided by e. Because the first NIO was not the full NIO event, its e-folding time had to be estimated based on the second and third events. From the outline, the e-folding times for the second and third NIOs were 7 and 13 days, respectively. The mooring was deployed seven days after typhoon Fung-Wong had passed the mooring site. Meanwhile, the initial calculation time of the second NIO events is eight days after the typhoon coming, and the initial calculation time of the second NIO events is two days. So, for the first NIO events, the time between the occurrence of the first typhoon and the occurrence of first NIO takes the average of the second and third times. It is estimated that for the first NIO events, the initial calculation time is five days. So the e-folding time of the first NIO was estimated to be 16 days. Interestingly, all the NIKE maxima were deeper than 100 m rather than in the surface layer, consistent Energies 2019, 12, 99 9 of 19 with the near-inertial currents.

FigureFigure 5.5. TimeTime evolutionevolution ofof thethe band-pass band-pass ( σ(σ∈∈[0.7,[0.7,1.2] 1.2] f)) filtered filtered near-inertia near-inertiall kinetic energy (NIKE)(NIKE) (in(in J).J). TheThe horizontalhorizontal axisaxis ofof thethe figurefigure isis time.time. TheThe vertical axis is thethe waterwater depthdepth with the unit m. TheThe thickthickblack black lineslines areare 1/ 1/ee ofof thethe maximamaxima NIKE.NIKE. TheThe blackblack circlescircles indicateindicate thethe timestimes thethe typhoonstyphoons werewere closestclosest toto thethe mooring.mooring. NIKENIKE belowbelow 400400 mm waswas tootoo weakweak andand notnot shownshown inin thisthis figure.figure. ForFor thethe threethree picturespictures toto bebe presentable,presentable, the the three three colorbars colorbars are are different. different.

The outline in Figure5 is the contour of the maxima NIKE divided by e. Because the first NIO was not the full NIO event, its e-folding time had to be estimated based on the second and third events. From the outline, the e-folding times for the second and third NIOs were 7 and 13 days, respectively. The mooring was deployed seven days after typhoon Fung-Wong had passed the mooring site. Meanwhile, the initial calculation time of the second NIO events is eight days after the typhoon coming, and the initial calculation time of the second NIO events is two days. So, for the first NIO events, the time between the occurrence of the first typhoon and the occurrence of first NIO takes the average of the second and third times. It is estimated that for the first NIO events, the initial calculation time is five days. So the e-folding time of the first NIO was estimated to be 16 days. Interestingly, all the NIKE maxima were deeper than 100 m rather than in the surface layer, consistent with the near-inertial currents. From Figure5, we can see that the estimated vertical group velocities of the first, second, and third NIOs were 11.9, 7.4, and 23.0 m d−1, respectively. The second typhoon gave a correspondingly weak NIO response, and the NIKE could barely propagate downward. The maximum NIKE for the third NIO was at 175 m deep. The group velocities were fairly small compared with those found in other studies (Table1). This observed slow downward propagation was examined via a theoretical analysis in the previous section (based on Equations (3) and (6)).

4.4. Vertical Structure of the Buoyancy Frequency and Background Current during Typhoon-Generated NIOs The cruise conductivity temperature depth (CTD) and ARGO data are combined in Figure6. The N values for the said data were averaged inside an area of 150 km around the mooring location. The depth of N decreased sharply from 100 to 175 m during the ﬁrst NIO (Figure6A), based on the CTD data, and the maximum NIKE was 135 m deep. In the second NIO, N decreased sharply from 100 to 130 m (Figure6B), and the maximum NIKE was at 127 m, based on the ARGO data. In the third NIO, N decreased sharply at three depths between 155 and 180 m (Figure6C), and the maximum NIKE was at 175 m. Energies 2018, 11, x FOR PEER REVIEW 10 of 20

From Figure 5, we can see that the estimated vertical group velocities of the first, second, and third NIOs were 11.9, 7.4, and 23.0 m d−1, respectively. The second typhoon gave a correspondingly weak NIO response, and the NIKE could barely propagate downward. The maximum NIKE for the third NIO was at 175 m deep. The group velocities were fairly small compared with those found in other studies (Table 1). This observed slow downward propagation was examined via a theoretical analysis in the previous section (based on Equations (3) and (6)).

4.4. Vertical Structure of the Buoyancy Frequency and Background Current during Typhoon-Generated NIOs The cruise conductivity temperature depth (CTD) and ARGO data are combined in Figure 6. The N values for the said data were averaged inside an area of 150 km around the mooring location. The depth of N decreased sharply from 100 to 175 m during the first NIO (Figure 6A), based on the CTD data, and the maximum NIKE was 135 m deep. In the second NIO, N decreased sharply from 100 to 130 m (Figure 6B), and the maximum NIKE was at 127 m, based on the ARGO data. In the third

NIO,Energies N2019 decreased, 12, 99 sharply at three depths between 155 and 180 m (Figure 6C), and the maximum10 of 19 NIKE was at 175 m.

Sep. 2014 Apr. 2015 May. 2015 0 0 0 (A) (B) (C) -50 -50 -50

-100 -100 -100

-150 -150 -150

-200 -200 -200

-250 -250 -250

-300 -300 -300

-350 -350 -350

NCTDm NWOD NWOD -400 -400 -400 0 500 1000 1500 0 500 1000 1500 0 500 1000 1500 N (cpd) N (cpd) N (cpd)

Figure 6. Regional average buoyancy frequency N calculated from the ARGO profiles (blue lines) Figure 6. Regional average buoyancy frequency N calculated from the ARGO profiles (blue lines) and and cruise conductivity temperature depth (CTD) profile (green line) during (A) the first NIO cruise conductivity temperature depth (CTD) profile (green line) during (A) the first NIO (in (in September 2014), (B) the second NIO (in April 2015), and (C) the third NIO (in May 2015). September 2014), (B) the second NIO (in April 2015), and (C) the third NIO (in May 2015). The The horizontal axis of the figure is the Buoyancy frequency with the unit cpd. The vertical axis horizontal axis of the figure is the Buoyancy frequency with the unit cpd. The vertical axis is water is water depth with the unit m. The red circle is the maximum NIKE depth. The selected sea area for depth with the unit m. The red circle is the maximum NIKE depth. The selected sea area for the second the second and third NIOs was 100 km around the mooring location. No ARGO data were available and third NIOs was 100 km around the mooring location. No ARGO data were available for within for within 100 km of the mooring for the first NIO. 100 km of the mooring for the first NIO. Figure7 describes the mean flow characteristics at the mooring array. During the first NIO, the zonal current field was westward upper of approximately 600 meters, and the maximum westward velocity was 0.27 ms−1. The meridional current fields are all northward. The maximum northward velocity is 0.59 ms−1. The flow during the second NIO is southwestward for the first six days. Then it changed to northeastward afterwards. The maximum eastward velocity was 0.47 ms−1, and the maximum westward velocity was 0.33 ms−1. During the third NIO, the flow field direction remains in the southeast direction. The maximum eastward velocity was 0.76 ms−1, and the maximum westward velocity was 0.52 ms−1.

Figure 7. Time evolution of the cross-track component of the low-pass ﬁltered (σ smaller than 1/72 h−1) (A,C,E) eastward and (B,D,F) northward ocean currents (m s−1) at 40–800 m deep. The background current is shown in (A,B). The second is shown in (C,D). The third is shown in (E,F). The horizontal axis of the ﬁgure is time. The vertical axis is the water depth with the unit m. The black circles indicate the times the typhoons were closest to the mooring.

Energies 2019, 12, 99 11 of 19 Energies 2018, 11, x FOR PEER REVIEW 12 of 20 these4.5.Vertical two modes Structure may of thehave Typhoon-Generated been caused by NIOs something other than the typhoon. The average contributions of the first, second, third, and fourth modes to the total NIKE were 30.8%, 25.1%, 12.3%, and 10.1%,Bandpass respectively. filtering allows us to get the results of the near-inertial current. Meanwhile, in order to analyzeThe thecomplete vertical evolution structure ofof the the near third inertial NIO current, was captured empirical by orthogonal the mooring function (Figure (EOF) 10). analysis The amplitudewas used intrends this study.in the time This series method for is the widely first tw usedo modes in the were study the of verticalsame as structuresfor the total of energy. near inertial The maximumwaves and amplitudes internal tides, of the like time Xu etseries al. in for 2013 the [ 44third] and and Yang fourth et al. modes in 2015 were [5]. Forearlier the than first NIOthe maximum(Figure8), amplitude the first two of modesthe total dominated energy. The the first near-inertial mode had waves five nodes and contributed and contributed more 30.6% than 80%of the of totalthe totalNIKE; NIKE. the second The first mode mode had contributed four nodes about and co 43.7%ntributed of the 24.0% total, andof the the total second NIKE; mode the aboutthird and 39% . theThe fourth vertical modes modes contributed indicate that 12.2% both and components 10.2%, resp changedectively, five of the times total between NIKE; the third surface and layer fourth and modesdepth of of the 800 third m. The NIO third event and contributed fourth modes little to contributed the total NIKE. only 7.5% and 5.2%, respectively, of the totalThe NIKE. EOF The analysis strongest can signal decompose of the first the and overall second ne modesar-inertial came atcurrent the same into time different as the strongestcurrent modalities,NIO signal. giving The strongest us the spatial signal distribution of the third andand fourth time series modes of was each found modal earlier near-inertial than the strongestcurrent. Meanwhile,NIO signal. the time series of each modal near-inertial current has its own unique frequency. AlthoughThe secondthe frequency NIO event of each had current only half is theclose amplitude to the inertial of the frequency, first (Figure the9). frequency As for the peaks NIKE are pattern still different.(Figure5 A),The the spectra first andof the second time series modes were gained analyzed their maximum to allow the amplitudes frequencies on of 15 the April modes 2015 to and be assessedchanged (Figure four times 11). over The the most observed interesting depth finding range. Thewas third that mode’sthe peak maximum first and spatial second amplitude mode frequenciesoccurred earlier for all than three the NIOs maximum were ofred-shifted the total NIO(i.e., event,were smaller while the than fourth f) while mode’s the maximum peak third spatial and fourthamplitude mode occurred frequencies later were than blue-shifted the maximum (bigger of the than total f), NIOexcept event. for the This zonal indicates velocity that of the fourth signals modeof these for the two first modes NIO. may Taking have the been vertical caused structur by somethinges of the NIOs other into than consideration, the typhoon. we The found average that thecontributions first and second of the first,modes second, followed third, a pattern and fourth of ha modesving tofour the or total five NIKE node weres, which 30.8%, means 25.1%, that 12.3%, the verticaland 10.1%, structures respectively. of these two modes changed four or five times from a depth of 50 to 800 m.

0 0.15 (B) (A) 0.1 -200 0.05

-400 0 U

-0.05 Depth(m) -600 -0.1 1st 45.4% 2nd 37.98% -800

0 0.15 (D) (C) 0.1 -200 0.05

-400 0 V

-0.05 Depth(m) -600 -0.1 1st 41.96% 2nd 39.81% -800 -4000 -2000 0 2000 4000 27-Sep-2014 03-Oct-2014 08-Oct-2014 13-Oct-2014

0 0.15 (F) (E) 0.1 -200 0.05

-400 0 U

-0.05 Depth(m) -600 -0.1 3rd 7.58% 4th 5.07% -800

0 0.15 (H) (G) 0.1 -200 0.05

-400 0 V

-0.05 Depth(m) -600 -0.1 3rd 7.65% 4th 5.35% -800 -4000 -2000 0 2000 4000 27-Sep-2014 03-Oct-2014 08-Oct-2014 13-Oct-2014

FigureFigure 8. 8. VerticalVertical profiles profiles of thethe ((AA, Eand) eastward E) eastward and ( Cand,G) ( northwardC and G) northward components components of the near-inertial of the near-inertialcurrent and thecurrent corresponding and the corresponding (B,F) eastward (B and and ( DF), Heastward) northward and time(D and series H) bynorthward empirical time orthogonal series byfunction empirical (EOF) orthogonal analysis. functi The firston (EOF) and second analysis. modes The first are shownand second in (A –modesD). Meanwhile, are shown the in thirdA, B, andC, andfourth D. Meanwhile, modes are shown the third in (andE–H fo).urth The NIOmodes event are occurredshown in inE, September F, G, and H 2014.. The NIO event occurred in September 2014. The complete evolution of the third NIO was captured by the mooring (Figure 10). The amplitude trends in the time series for the first two modes were the same as for the total energy. The maximum amplitudes of the time series for the third and fourth modes were earlier than the maximum amplitude of the total energy. The first mode had five nodes and contributed 30.6% of the total NIKE; the second mode had four nodes and contributed 24.0% of the total NIKE; the third and the fourth modes

Energies 2019, 12, 99 12 of 19

contributed 12.2% and 10.2%, respectively, of the total NIKE; the third and fourth modes of the third EnergiesEnergiesNIO event 20182018,, 1111 contributed,, xx FORFOR PEERPEER REVIEW littleREVIEW to the total NIKE. 1313 ofof 2020

00 0.150.15 (A) (B)(B) (A) 0.10.1 -200-200 0.050.05

-400 0 U -400 0 U

-0.05 Depth(m) -0.05 Depth(m) -600-600 -0.1 -0.1 1st1st 30% 30% 2nd2nd 24.22% 24.22% -800-800

00 0.150.15 (C) (D)(D) (C) 0.10.1 -200-200 0.050.05

-400 0 V -400 0 V

-0.05 Depth(m) -0.05 Depth(m) -600-600 -0.1 -0.1 1st1st 30.85% 30.85% 2nd2nd 25.34% 25.34% -800-800 -4000-4000 -2000-2000 00 20002000 40004000 10-Apr-201510-Apr-2015 16-Apr-201516-Apr-2015 21-Apr-201521-Apr-2015 26-Apr-201526-Apr-2015 01-May-201501-May-2015 00 0.150.15 (E) (F)(F) (E) 0.10.1 -200-200 0.050.05

-400 0 U -400 0 U

-0.05 Depth(m) -0.05 Depth(m) -600-600 -0.1 -0.1 3rd3rd 12.94% 12.94% 4th4th 10.52% 10.52% -800-800

00 0.150.15 (G) (H)(H) (G) 0.10.1 -200-200 0.050.05

-400 0 V -400 0 V

-0.05 Depth(m) -0.05 Depth(m) -600-600 -0.1 -0.1 3rd3rd 11.95% 11.95% 4th4th 9.36% 9.36% -800-800 -4000-4000 -2000-2000 00 20002000 40004000 10-Apr-201510-Apr-2015 16-Apr-201516-Apr-2015 21-Apr-201521-Apr-2015 26-Apr-201526-Apr-2015 01-May-201501-May-2015

FigureFigureFigure 9.9. 9. AsAsAs forfor for FigureFigure Figure 88 8 butbut but forfor for thethe the NIONIO NIO eventevent event inin in AprilApril April 2015.2015. 2015.

00 0.150.15 (A) (B)(B) (A) 0.10.1 -200-200 0.050.05

-400 0 U -400 0 U

-0.05 Depth(m) -0.05 Depth(m) -600-600 -0.1 -0.1 1st1st 30.32% 30.32% 2nd2nd 24.94% 24.94% -800-800

00 0.150.15 (C) (D)(D) (C) 0.10.1 -200-200 0.050.05

-400 0 V -400 0 V

-0.05 Depth(m) -0.05 Depth(m) -600-600 -0.1 -0.1 1st1st 30.7% 30.7% 2nd2nd 22.82% 22.82% -800-800 -4000-4000 -2000-2000 00 20002000 40004000 09-May-201509-May-2015 15-May-201515-May-2015 20-May-201520-May-2015 25-May-201525-May-2015 30-May-201530-May-2015 00 0.150.15 (E) (F)(F) (E) 0.10.1 -200-200 0.050.05

-400 0 U -400 0 U

-0.05 Depth(m) -0.05 Depth(m) -600-600 -0.1 -0.1 3rd3rd 12.19% 12.19% 4th4th 10.01% 10.01% -800-800

00 0.150.15 (G) (H)(H) (G) 0.10.1 -200-200 0.050.05

-400 0 V -400 0 V

-0.05 Depth(m) -0.05 Depth(m) -600-600 -0.1 -0.1 3rd3rd 12.22% 12.22% 4th4th 11.66% 11.66% -800-800 -4000-4000 -2000-2000 00 20002000 40004000 09-May-201509-May-2015 15-May-201515-May-2015 20-May-201520-May-2015 25-May-201525-May-2015 30-May-201530-May-2015 FigureFigureFigure 10.10. 10. AsAsAs forfor for FigureFigure Figure 88 8 butbut but forfor for thethe the NIONIO NIO eventevent event inin in MayMay May 2015.2015. 2015.

The EOF analysis can decompose the overall near-inertial current into different current modalities, giving us the spatial distribution and time series of each modal near-inertial current. Meanwhile, the time series of each modal near-inertial current has its own unique frequency. Although the frequency of each current is close to the inertial frequency, the frequency peaks are still different. The spectra of the time series were analyzed to allow the frequencies of the modes to be assessed

Energies 2019, 12, 99 13 of 19

(Figure 11). The most interesting finding was that the peak first and second mode frequencies for all three NIOs were red-shifted (i.e., were smaller than f ) while the peak third and fourth mode frequencies were blue-shifted (bigger than f ), except for the zonal velocity of the fourth mode for the first NIO. Taking the vertical structures of the NIOs into consideration, we found that the first and second modes followed a pattern of having four or five nodes, which means that the vertical structures of these two Energies 2018, 11, x FOR PEER REVIEW 14 of 20 modes changed four or five times from a depth of 50 to 800 m.

-3 σ -3 σ x 10 /f x 10 /f

8 f 8 f (A) first mode (B) first mode second mode second mode 6 6 third mode third mode forth mode forth mode 4 4

2 2 2014.9.27-10.16 0 0

0 -3 0.5 1 1.5 2 0 -3 0.5 1 1.5 2 x 10 x 10

8 f 8 f (C) first mode (D) first mode second mode second mode 6 6 third mode third mode forth mode forth mode 4 4

2 2 2015.4.10-5.1

0 0

0 -3 0.5 1 1.5 2 0 -3 0.5 1 1.5 2 x 10 x 10

8 f 8 f (E) first mode (F) first mode second mode second mode 6 6 third mode third mode forth mode forth mode 4 4

2 2 2015.5.10-6.1

0 0

0 0.5 1 1.5 2 0 0.5 1 1.5 2

Figure 11. Power spectra of the (A,C,E) eastward and (B,D,F) northward time series of the near-inertial Figure 11. Power spectra of the (A, C, and E) eastward and (B, D, and F) northward time series of the currents in the three NIOs by EOF analyses results. The power spectra of the first NIO event is shown near-inertial currents in the three NIOs by EOF analyses results. The power spectra of the first NIO in (A,B). The second is shown in (C,D). The third is shown in (E,F). The horizontal axis of the figure event is shown in A and B. The second is shown in C and D. The third is shown in E and F. The is the relative frequency of the Coriolis frequency f. The vertical axis is spectral density with the unit horizontal axis of the figure is the relative frequency of the Coriolis frequency f. The vertical axis is m2s−2cpd−1. Each picture has the time series result of the first four modes by EOF analyses. spectral density with the unit m2s−2cpd−1. Each picture has the time series result of the first four modes byThe EOF EOF analyses. results for the three NIO events exhibited many similarities. First, the contributions of the first two modes to the total NIKE were similar and around twice those of the third and fourth. The EOF results for the three NIO events exhibited many similarities. First, the contributions of Second, the time series and vertical modes of the first two modes were regular. The vertical modes the first two modes to the total NIKE were similar and around twice those of the third and fourth. changed four or five times along the observed depth, and the time series frequencies were

Energies 2019, 12, 99 14 of 19 Energies 2018, 11, x FOR PEER REVIEW 15 of 20

0 0.15 (B) (A) 0.1 -200 0.05

-400 0 U

-0.05 Depth(m) -600 -0.1 1st 32.41% 2nd 25.36% -800

0 0.15 (D) (C) 0.1 -200 0.05

-400 0 V

-0.05 Depth(m) -600 -0.1 1st 34.3% 2nd 24.69% -800 -4000 -2000 0 2000 4000 01-Jan-2015 07-Jan-2015 12-Jan-2015 17-Jan-2015 22-Jan-2015 27-Jan-2015 01-Feb-2015 0 0.15 (F) (E) 0.1 -200 0.05

-400 0 U

-0.05 Depth(m) -600 -0.1 3rd 15.14% 4th 9.45% -800

0 0.15 (H) (G) 0.1 -200 0.05

-400 0 V

-0.05 Depth(m) -600 -0.1 3rd 13.83% 4th 10.48% -800 -4000 -2000 0 2000 4000 01-Jan-2015 07-Jan-2015 12-Jan-2015 17-Jan-2015 22-Jan-2015 27-Jan-2015 01-Feb-2015

-3 σ x 10 /f 8 f 6 (I) 1st mode 2nd mode 4 3rd mode 4th mode 2

-2 -3 0x 10 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 8 f 6 (J) 1st mode 2nd mode 4 3rd mode 4th mode 2

-2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 FigureFigure 12.12.Vertical Vertical profiles profiles of of the the (A (,AE) and eastward E) eastward and (C ,andG) northward (C and G) components northward ofcomponents the near-inertial of the currentnear-inertial and the current corresponding and the corresponding (B,F) eastward ( andB and (D ,FH) )eastward northward and time (D seriesand H by) northward empirical orthogonaltime series functionby empirical (EOF) orthogonal analysis. Thefuncti firston and(EOF) second analysis. modes The are first shown and second in (A–D modes). Meanwhile, are shown the in third A, B and, C, fourthand D. modes Meanwhile, are shown the third in (E –andH). fo Powerurth modes spectra are of theshown (I) eastwardin E, F, G and, and (J H) northward. Power spectra time seriesof the of(I) theeastward near-inertial and (J) currents northward in the time three series NIOs of the by near-inertial EOF analyses currents result. Thein the horizontal three NIOs axis by of EOF the figureanalyses is theresult. relative The horizontal frequency ofaxis the of Coriolis the figure frequency is the relativef. The frequency vertical axis of the is spectral Coriolis density frequency with f. theThe unit vertical m2 saxis−2 cpd is spectral−1.(I,J) density have the with time the series unit results m2 s−2 cpd of the−1. I first and four J have modes the time by EOF series analyses. results Theof the NIO first signal four occurredmodes by in EOF January analyses. 2015. The NIO signal occurred in January 2015.

Energies 2019, 12, 99 15 of 19 Energies 2018, 11, x FOR PEER REVIEW 16 of 20

0 0.15 (B) (A) 0.1 -200 0.05

-400 0 U

-0.05 Depth(m) -600 -0.1 1st 33.65% 2nd 22.64% -800

0 0.15 (D) (C) 0.1 -200 0.05

-400 0 V

-0.05 Depth(m) -600 -0.1 1st 34.94% 2nd 23.34% -800 -4000 -2000 0 2000 4000 01-Sep-2015 07-Sep-2015 12-Sep-2015 17-Sep-2015 22-Sep-2015 27-Sep-2015 0 0.15 (F) (E) 0.1 -200 0.05

-400 0 U

-0.05 Depth(m) -600 -0.1 3rd 12.07% 4th 9.88% -800

0 0.15 (H) (G) 0.1 -200 0.05

-400 0 V

-0.05 Depth(m) -600 -0.1 3rd 12.6% 4th 8.5% -800 -4000 -2000 0 2000 4000 01-Sep-2015 07-Sep-2015 12-Sep-2015 17-Sep-2015 22-Sep-2015 27-Sep-2015 -3 σ x 10 /f 8 f 6 (I) 1st mode 2nd mode 4 3rd mode 4th mode 2

-2 -3 0x 10 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 8 f 6 (J) 1st mode 2nd mode 4 3rd mode 4th mode 2

-2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

Figure 13. As for Figure 10 but the NIO signal occurred in September 2015. Figure 13. As for Figs. 10 but the NIO signal occurred in September 2015. 5. Discussion 5. DiscussionAs mentioned earlier, the structures we found were more complex than those that have been found in previous studies, such as Pallàs et al. [35] in the Gulf of Mexico, Chen et al. [43] in the As mentioned earlier, the structures we found were more complex than those that have been South China Sea, and Kim et al. [33] to the east of our mooring. This explains the much smaller C found in previous studies, such as Pallàs et al. [35] in the Gulf of Mexico, Chen et al. [43] in the South gz in our study than in previous studies. Given the e-folding time and slow vertical group velocity, China Sea, and Kim et al. [33] to the east of our mooring. This explains the much smaller Cgz in our the typhoon-induced internal waves in this region were less likely to inﬂuence the deeper sea than study than in previous studies. Given the e-folding time and slow vertical group velocity, the was the case in previous studies. The observer may note from Figure5 that the e-folding scales of the typhoon-induced internal waves in this region were less likely to influence the deeper sea than was the case in previous studies. The observer may note from Figure 5 that the e-folding scales of the three

Energies 2019, 12, 99 16 of 19 three NIOs we studied were less than 400 m. The NIKE weakened to 0.1 times the maximum more than 400 m depth, and the NIOs could only exert a clear influence at smaller than 400 m (Figure5), which is much shallower than the 1,500 m found in the Gulf of Mexico [35]. As shown in Figure5, the maximum NIKEs in the observation area for the first, second, and third NIOs were found at 135, 127, and 175 m, respectively. This mirrors many previous studies, in which none of the maximum NIKEs were at the surface [35]. Some researchers have explained this using a region termed inertial chimneys, which is created by anticyclonic eddies [45,46]. However, strong circulation and widely varying characteristics in our study area mean that anticyclonic eddies would not have persisted. The buoyancy frequency distribution should therefore be taken into consideration. To study the relationship between energy transfer and water stratification, some simplifications are needed. We assumed that in one NIO event, although the wave number k was not determined, the change in wave numbers (k, l, m) could be neglected for downward energy transmission. As shown in Equation (2), the group velocity Cg is a function of the buoyancy frequency N when the wave number (k, l, m) is stable. The NIKE distribution can be simplified as a distribution of N (see Equation (7)). Using Equation (7), we can calculate the downward group velocity (–Cgz) and the buoyancy frequency N in a monotonically increasing relationship. Here NIO can more easily be transmitted downward in an area with a larger N. In other words, NIKE will accumulate where N decreases sharply with depth. The maximum NIKE can be found at the depth at which Cg is large in the upper layer or small in the lower layer. The most obvious feature of the NIOs influenced by typhoons is shown in Figures8–10. For the three NIO events the first mode explained greater than 30% of the variance and the second mode explained no smaller than 24%. The different modes did not make significantly different contributions during periods untroubled by typhoons. The amplitudes of the vertical structures were much stronger at less than 300 m deep than at deeper than 300 m when the typhoons were exerting their influences. The vertical distributions of the eastward and northward velocities alternated four or five times during this period. The amplitudes varied to be of lesser degree, and the vertical structures changed irregularly in periods unaffected by typhoons. The most interesting aspect was the time series when a typhoon was exerting its influence. The peak frequencies of the first two modes were smaller than f, and the frequencies of the third and fourth modes were bigger than f. The frequency of almost every mode in periods unaffected by typhoons was bigger than f, so the first and second modes may have been typhoon-induced signals in the cases when typhoons occurred. The results of this study provide useful and intriguing insights into NIOs in the northwest Pacific. However, as shown in Equation (2), the vertical group velocity depends largely on the change of buoyancy frequency N, vertical wave number m, and horizontal wave numbers k and l. The complexity of the ocean means that wave numbers may change during the propagation process, weakening the correlation between Cg and N. Although Qi et al. presented a method for calculating the vertical wave number for a mooring [18], we could not obtain 4D data for the wave number. We are currently exploring the relationship between Cg and N using the marine model. Therefore, it still needs to be refined in future study.

6. Conclusions Three energetic typhoon-generated NIO events were examined based on subsurface mooring observations lasting over 16 months (473 days) in the northwest Pacific Ocean. Compared to previous studies, a relatively wider band of the NIO energy concentrating at 0.7 f –1.2 f and stronger redshift of the NIO signals were reported in this study. The maximum amplitudes of the observed near-inertial currents during three typhoon passages were 0.58, 0.32, and 0.47 m s−1, respectively, with current directions changing four or five times from the surface to a depth of 800 m. Group velocities of the first, second, and third NIO were 11.9, 7.4, and 23.0 m d−1, respectively, which were lower than those reported by previous studies. The e-folding times of the first, second, and third NIO events were 16, 7, and 13 days, respectively. Energies 2019, 12, 99 17 of 19

The EOF analysis indicated high mode vertical structures of the three NIO events, with energy mostly concentrating at the first two modes. Contributions from the first two modes were comparative and were more than twice larger than that from the third and fourth modes. Peak energy frequencies of the first two modes were less than f, but that of the third and fourth modes were mostly higher than f. Furthermore, non-typhoon-period NIO signals had frequencies more than f, suggesting a possibility that the third and fourth modes of the three NIO signals were not directly generated by the passages of typhoons. Theoretical analyses demonstrated that the vertical group velocity of NIOs decreased with the increasing vertical wave numbers. The more times the velocity direction changes within a unit of length, the higher the vertical wave number will be, and the harder it will be to transmit energy downward. By considering the high mode vertical structure of the observed NIOs here, it can partially explain why the group velocity was relatively small in this study. However, it still needs to be refined in detail in future studies.

Author Contributions: Conceptualization, H.H. and F.Y.; Methodology, F.Y.; Software, F.N.; Validation, B.Y., S.G. and Y.Z.; Formal Analysis, H.H.; Investigation, F.Y.; Resources, F.Y.; Data Curation, H.H.; Writing-Original Draft Preparation, H.H.; Writing-Review & Editing, Y.Z.; Visualization, B.Y.; Supervision, Y.Z.; Project Administration, F.Y.; Funding Acquisition, F.Y. Funding: This research is jointly supported by the National Key R&D Program of China (No. 2017YFC1403400 and 2016YFC1402003), the National Natural Science Foundation of China (No. U1406401, No. 41421005), and Global Change and Air Sea Interaction Project (No. GASI-02-PAC-STMSspr). Acknowledgments: This research was jointly supported by the National Key R&D Program of China (No. 2017YFC1403400 and 2016YFC1402003), the National Natural Science Foundation of China (No. U1406401, No. 41421005), and Global Change and Air Sea Interaction Project (No. GASI-02-PAC-STMSspr). We also thank Qiang Ren and Chuanjie Wei for helping data collection. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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