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BY R. DWI SUSANTO, LEONID MITNIK, AND QUANAN ZHENG ted in teaching to copy thisand research. for use Repu article e Oceanography Society, PO Box 1931, Rockville, MD 20849-1931, USA. 1931, Rockville, Box PO Society, e Oceanography blication, systemmatic reproduction,

80 Oceanography Vol. 18, No. 4, Dec. 2005 @ESA1996 THE INDONESIAN SEAS, with to describe solitary behavior, which ward and upward from this depth. Tid- their complex coastline geometry and is when Korteweg and de Vries (1895) ally generated internal waves are usually , narrow passages, stratifi ed coined the phrase “ theory” (the nonlinear and occur often in the form waters, and strong tidal currents, are Korteweg-de Vries, or K-dV, equation). of wave packets. The amplitude and dis- favorable places for the generation of Since their pioneer publication, hun- tance between waves in a intensive internal waves. Internal dreds of papers dealing with soliton the- decreases from the front to the rear. waves, which occur within the subsurface ory and its applications have been pub- Since the launching of Seasat in 1978, layers of the ocean where density strati- lished. Zabusky and Kruskal (1965) were Almaz-1 in 1991, and European Remote fi cation is strong, are generated when the fi rst people to use a computer to sim- Sensing Satellite (ERS-1) in 1991 with the interface between layers is disturbed. ulate the K-dV equation to demonstrate a synthetic aperture radar (SAR) on Disturbances are often caused by tidal the collision of two solitary waves. They board, a large number of the surface fl ow passing over shallow underwater concluded that the waves retained their imprints of the small-, meso- and sub- obstacles such as a sill or a shallow ridge. shape and propagation speed after colli- synoptic-scale oceanic and atmospheric Internal waves are commonly observed sion. In the current era of satellite obser- phenomena have been detected on SAR in the , one of the outfl ow vations, some space images of the ocean images of the surface. Oceanic in- straits of the Indonesian throughfl ow surface show that solitary internal waves ternal vertically displace the (ITF) (see Gordon, this issue), which indeed retain their shape after collision, and cause internal currents, transports water from the Pacifi c to the confi rming these simulation results. For with near-surface fl ow convergence and . a comprehensive review of divergence (Gargett and Hughes, 1972). , in the 19th century, theory as well as their observation in the The latter effects can modulate the sea- was the fi rst to observe internal waves , see Osborne and Burch surface roughness on small length scales (Russell, 1838, 1844). He reported the (1980); a brief discussion of internal [O (1–10 cm)], which can be imaged by formation of a single unchanging hump wave theory is provided in Box 1. radar such as satellite-borne SAR (Alp- or mound in the shallow waters of the Disturbances, such as those caused by ers, 1985). SAR images of the sea surface Scottish Canal, which was generated tidal fl ow of stratifi ed water over shal- can delineate oceanic phenomena such when a towed barge was brought to a low sills, can generate internal waves as surface waves, internal waves, ed- sharp halt. Since ancient times, mariners that propagate along density surfaces. dies, fronts, , shallow bottom sailing the world’s observed inter- These internal waves are a signifi cant nal-wave activity, which manifests itself mechanism for the transport of mo- R. Dwi Susanto ([email protected]. in the form of bands with increased sea- mentum and energy within the ocean edu) is Senior Staff Associate and Director, surface roughness and intensive foaming (Maxworthy, 1979; Osborne and Burch, Indonesian Research Coordination, Lamont- due to wave breaking (rips). Fedorov and 1980; Helfrich and Melville, 1986; Lamb, Doherty Earth Observatory of Columbia Ginzburg (1992) summarized evidence 1994). Ocean internal waves typically University, Palisades, NY, USA. Leonid of internal waves from different sources, have from hundreds of me- Mitnik is Head, Satellite Oceanography including papers from Marine Weather ters to tens of kilometers and periods Department, V.I. Il’ichev Pacifi c Oceanologi- Log. Horsburgh (Maury, 1861) and Perry from several minutes to several hours. cal Institute, Far Eastern Branch, Russian and Schimke (1965) described observa- Their amplitudes (peak to trough) often Academy of Sciences, Vladivostok, Russia. tions of internal waves near the northern exceed 100 m. Orbital motions of the Quanan Zheng is Senior Research Scientist, tip of (Andaman Sea). However, water particles associated with internal Department of Atmospheric and Oceanic it took more than half a century to estab- waves have the largest radius at the pyc- Science, University of Maryland, College lish the model differential equation used nocline depth, which decreases down- Park, MD, USA.

Oceanography Vol. 18, No. 4, Dec. 2005 81 BOX 1. INTERNAL WAVE THEORY IN BRIEF

Vertical stratifi cation in the Lombok topography, island wakes, river plumes, of ocean internal solitons (Zheng et al., Strait can be modeled by a two-layer biogenic and oil slicks, and atmospheric 2001a, 2001b, 2002) as well as to esti- ocean characterized by a shoaling phenomena such as convective rolls and mate the ocean mixed layer depth (Li et thermocline. For a two-layer ocean, cells, atmospheric internal waves, land- al., 2000). SAR-image time series have an oceanic internal wave can be de- sea breezes, katabatic , and rain been used to analyze internal-wave evo- scribed with a dimensional form of cells (Jackson and Apel, 2004). Table 1 lution (Liu et al., 1998). the K-dV equation (Osborne and provides an overview of SAR satellites In general, SAR signatures caused by Burch, 1980) beginning with the ERS-1. dynamic phenomena in the tropical and Detection of ocean internal waves subtropical ocean are more easily identi- ∂η ∂η ∂η ∂ 3η + C +αη + β = 0, ∂t ∂x ∂x ∂x 3 [1] on airborne and space-borne SAR im- fi ed than those in mid- and high-latitude ages can be traced back to the earliest waters. In the mid and high latitudes, where η(x, t) is the interface displace- stage of the technology (Elachi and Apel, surface waters are exposed to greater ment between the two layers from 1976; Apel and Gonzalez, 1983; Fu and average speeds than in the tropics the unperturbed level, C is the linear Holt, 1982, 1984). From SAR images, and subtropics, which tend to mask the phase speed, α is a nonlinear coef- one can directly determine the location sea-surface expression of internal waves. fi cient, and β is the coef- and time, , or separation dis- Thus, SAR images are particularly useful fi cient. Under certain conditions, the tance between two consecutive waves; for studying the tropical Indonesian seas. nonlinear term (αηηx) and the dis- the length of a crest line; the number of persive term (βηxxx) balance. When solitons in a wave packet; the distance LOMBOK STRAIT these terms balance, the result is a sta- between two consecutive wave packets; The Lombok Strait (Figure 1) separates ble confi guration of a solitary wave, and the propagation direction. SAR im- the Indonesian islands of and Lom- which is a special solution of the K- ages can also be used to determine the bok and is an important pathway for dV equation and has the analytical characteristic half width and amplitude Pacifi c Ocean water to fl ow into Indian solution in the form of

⎡()x −Vt ⎤ η = η sec h 2 , 0 ⎣⎢ ∆ ⎦⎥ [2]

Table 1. An overview of Synthetic Aperture Radar (SAR) satellites. where ηo is the maximum soliton am- plitude, V is the soliton phase speed, Satellite ERS-1 and ERS-2 RADARSAT ENVISAT and ∆ is the characteristic length or Sensor SAR SAR ASAR half width. Jul 17, 1991 If we know the ocean stratifi cation Launch Date(s) Nov 4, 1995 Mar 1, 2002 Apr 20, 1995 in the generation and propagation areas, we can calculate the propaga- Frequency 5.3 GHz 5.3 GHz 5.3 GHz tion phase speed, soliton amplitude in Wavelength 5.6 cm 5.6 cm 5.6 cm the interface, characteristic half width, Polarization1 VV HH VV, HH, VH, HV and horizontal velocity of the water Incidence Angle 20-26° 10-59° 15-45° particles of soliton in the upper and lower layers. The amplitudes of the Swath Width 100 km 50-500 km 100-405 km horizontal velocities in both layers do 25 x 25 m Ground Resolution 25 x 25 m 8 x 100 m not decay with depth, but that veloci- 150 x 150 m ties in the lower layer are opposite in 1V and H are vertical and horizontal polarization of SAR signal, respectively. Th e fi rst letter denotes direction to those in the upper layer polarization of transmitting signal. Th e second letter represents polarization of receiving signal. (Osborne and Burch, 1980).

82 Oceanography Vol. 18, No. 4, Dec. 2005 Ocean as part of the ITF. In the northern and central strait, there is a deep chan- nel with water depth up to 1400 m. At 7°S the southern outlet, Island Kangean divides the strait into two channels. The

00 -100 -1 -250 western channel, Bandung Strait, is shal- -750

-500 -500 0 -1000 5 lower. Its water depth is less than 100 m. -2 The eastern channel is deeper and has

0 5 -1 000 an east-west running sill along its bot- -7 0 tom. The channel serves as a major pas- -75 sage for water exchange from the Indian 0 0 -5 -10 Ocean into the strait. The latest measure- 8°S -75000 -100 -500

-250 ment carried out during the 2005 Indo- -250 nesian throughfl ow cruise showed that Bali Lombok St. the sill-crest depth is about 250 m. SPGA SPGA

The northern part of the Lombok -100 -10

00

-100 50 Strait has mixed that have a pre- -7 Lombok 0 -100 -2 -500 50 -25 dominantly diurnal cycle (Chong et -500 NP -750 Lembar al., 2000). However, the at the sill -250 -250 0 -100 0 5 -1 -50 region is predominantly semi-diurnal; -1000 0 -750 9°S 0 -1-100 50 00 -1750 20 0 tidal velocity there can exceed 3.5 m/s - -1750 - 3 -2500 0 -2000 0 (Murray and Arief, 1988; Murray et al., 0 -25 00 1990). Nonlinear interactions between -4000 0 0 -30 5 -3 3 00 50 the semi-diurnal and diurnal tidal com- - 0

ponents induce a strong tide with a pe- -4000 riod close to 14 days (Ffi eld and Gordon, -4000 1996; Susanto et al., 2000). Because of the presence of stratifi ed Indian Ocean water, rough topography, and strong 10°S 115°E 116°E tidal currents, the Lombok Strait is Figure 1. Bathymetry of the Lombok Strait superimposed with the locations of characterized by intensive internal-wave ERS-1/2 SAR images for descending track 418 (solid box). White stars are the generation. These waves are detected locations of shallow pressure gauges (SPGA). Th e white circle is a in on ERS-1/2 and RADARSAT SAR and Lembar (Lombok). NP is Nusa Penida Island. ENVISAT advanced SAR images. Cress- well and Tildesly (1998) showed the ex- istence of internal-wave features in the southern Lombok Strait on the RADAR- by tidal currents in the sill area between ent patterns: southward only, northward SAT SAR images taken on July 14 and the islands of Lombok and Nusa Penida only, and in both directions. They con- August 7, 1997. Mitnik et al. (2000) and and that their estimated propagation cluded that background current associ- Mitnik and Alpers (2000) observed non- velocity was 1.8–1.9 m/s. Susanto et ated with the ITF, stratifi cation, and tid- linear internal wave packets using ERS- al. (submitted) suggested that internal al conditions control the internal-wave 1/2 SAR images. They suggested that the waves generated in the sill area of the generation and propagation direction in nonlinear solitary waves were generated Lombok Strait propagate in three differ- this region.

Oceanography Vol. 18, No. 4, Dec. 2005 83 Figure 2. SAR images of the Lombok Strait taken at 02:32 UTC on April 23, 1996 by ERS- 1 (a) and on April 24, 1996 by ERS-2 (b). Packets of internal solitary waves propagating both northward and south- Kangean ward are clearly seen (circular Kangean bright/dark patterns) in both images. Images © the Euro- pean Space Agency. (a) Th e northward-propagating inter- nal solitary wave packet con- tains more than 25 solitons. Wave-packet width is approxi- mately 85 km. Th e length of crest line of the leading wave exceeds 100 km. Within the wave packet, the wavelengths appear to be monotonically decreasing, from about 5 km in front to 2 km in rear. Th ree light bands of the second northward propagating packet are clearly seen at middle right. Th e leading soliton of this packet intrudes the rear of fi rst packet. (b) Th is image shows radar signature pattern of solitary waves similar to the pattern visible in (a). Th e crests of the fi rst two solitons are observed within the whole swath width. Th e wavelength of the fi rst soliton is about Bali Bali 7 km, decreasing to 2 km at the last soliton. Th e eastern part of the second packet of the northward-propagating Nusa Nusa solitons has the larger radar Penida Penida contrast due to the decreased brightness of the background within the area of Lombok Island wake (dark northwest- ward oriented cone area).

@ESA 1996 @ESA 1996

84 Oceanography Vol. 18, No. 4, Dec. 2005 INTERNAL WAVE SIGNATURE Table 2. Dynamical parameter of northward-propagating ON ERS1/2 SAR IMAGES internal waves in the Lombok Strait. Simultaneous airborne or space-borne Northward Waves April 23, 1996 April 24, 1996 SAR sensing and in situ measurements can be used to determine generation Solitons in a Packet 25 23 conditions and propagation direction of Average Wavelength (Range) 3.10 (2.00–5.00) km 3.80 (2.00–7.25) km internal waves as well as to calculate their Half Width 1.99 ± 0.025 km 2.75 ± 0.025 km dynamic parameters. To estimate charac- Mean Phase Speed 1.97 ± 0.2 m/s 1.96 ± 0.2 m/s teristics of internal waves in the Lombok Strait, we chose two consecutive images First Crest Line Length > 100 km > 100 km taken during the ERS-1/2 tandem mis- sion (Figure 2). The fi rst image (Figure 2a) was taken by ERS-1 on April 23, 1996 at 02:32 UTC and the second image (Fig- ure 2b) was taken 24 hours later by ERS- summarized in Table 2. On the second image, taken on the next 2 on April 24. Packets of internal solitary On the SAR image taken on April 23 day (Figure 2b), radar contrast of the waves propagating both northward and (Figure 2a), the leading soliton located southward-propagating internal waves southward are clearly seen in both im- at the distance of about 180 km from decreased even more. However, the loca- ages. Visibility of solitons (their radar the sill reached the shallow region near tion of the leading soliton can be deter- contrast against a background) depends the Kangean Island. On the image taken mined reasonably well on both images. on non-uniformity of sea surface wind on April 24 (Figure 2b), the distance be- Assuming that the southward propagat- conditions, particularly those caused by tween the leading soliton and the coral ing packet was generated at the same the interaction of airfl ow with the high reefs of Kangean Island at the top of the time as the second northward propagat- mountains in Bali and Lombok. image is 8 km. The difference is mainly ing packet, its speed was approximately The observed internal waves were due to the fact that the solitons were a half of the speed of the northward generated by the interaction of succes- observed at an earlier phase of the tidal propagating packet. This slower speed sive tidal fl ows with the sill between cycle (after two consecutive semidiurnal indicates that Indian Ocean stratifi cation islands of Nusa Penida and Lombok. tides, which is approximately 50 minutes was different (less intense) from that of Based on current measurements using earlier). After accounting for this tidal the northern Lombok Strait. moorings deployed near to the sill, the factor, the leading solitons should have The SAR images (Figure 2) were tidal fl ow is predominantly semidiurnal reached 6 km from the Kangean Island. taken after the maximum spring tide. (Murray et al., 1990). Hence, by know- Other factors such as changes in the The presence of this tide is evident from ing the distance between successive average background current, tidal con- analyses of data from shallow pressure- wave packets and their distances to the ditions, and stratifi cation, which affect gauge arrays deployed at both sides of sill, we can calculate the average wave wave-propagation speed, are responsible the strait (Figure 1) and also tide-gauge speed. The distance between packets on for the 2-km difference. data from Lembar (Figure 3). Mixed the image taken on April 23 is 88.1 km. The southward-propagating (semidiurnal and diurnal tides) and Meanwhile, on the image taken on April waves have weaker radar signatures than strong fortnightly tide modulation are 24, the distance between the consecu- those propagating northward. About 10 clearly seen in Figure 3. tive wave packets is 87.6 km. Thus, the crests are seen on the SAR image (Figure More accurate calculation of dynamic average propagation velocity is 1.97 m/s 2a). Their wavelength decreases from parameters of the solitons requires fi eld and 1.96 m/s, respectively. Dynamical about 3 km to 1 km from the front to the observations of the stratifi cation, back- parameters of these internal waves are rear (from the open water to the strait). ground currents, and wind and tidal

Oceanography Vol. 18, No. 4, Dec. 2005 85 3.5 conditions collected simultaneously with

Image taken on April Image taken on April satellite SAR sensing. Figure 4 provides 23 24 an example of internal solitary waves 3 propagating northward that was re- corded by the ship’s echosounder in the Lombok Strait (115.75°E, 8.47°S) during 2.5 the June/July 2005 INSTANT Indone- sian throughfl ow cruise (see Gordon, this issue). For solitary internal waves, Height (m) 2 horizontal velocities in the lower layer are opposite in direction to those in the upper layer. Large vertical displacements

1.5 SPGA in Bali side of water masses (Figure 4) caused by internal waves are important to vertical SPGA in Lombok side transport and mixing of biogenic and Lembar tide gauge 1 non-biogenic components in the water 04/21/1996 04/28/1996 05/05/1996 column that move nutrients and phy- Figure 3. Tidal conditions in the Lombok Strait from April 14 to May 8, 1996. Tidal height was toplankton into or out of the euphotic derived from shallow pressure gauges in the Bali side (red) and Lombok side (blue) and from layer (Weidemann et al., 1996). Intense the tidal gauge in Lembar (green). Solid vertical lines mark the time when the images shown in Figure 2 were taken. Mixed tide (semidiurnal and diurnal tides) and strong fortnightly internal-wave activity, as observed in the tide modulation are clearly seen. Shallow pressure gauge data are courtesy of Janet Sprintall, Lombok Strait, infl uences acoustic fi eld Scripps Institution of Oceanography, La Jolla, CA. properties and undersea navigation.

SUMMARY Lombok Strait is one of the straits in the Indonesian seas where high-amplitude internal solitary waves are observed. The waves are generated in stratifi ed water by interaction among strong tidal fl ows, background current (i.e., Indonesian throughfl ow), and rough bottom to- pography. Analyses of two consecutive satellite SAR images acquired on April 23 and 24, 1996 have shown that internal waves were generated by interaction of successive semidiurnal tidal fl ows with the sill south of the Lombok Strait. The average propagation speed was 1.96 m/s.

Figure 4. A spectacular echogram of the obtained by an EK500 Echosounder Stratifi cation plays an important role in operating at frequency of 38 kHz during the 2005 INSTANT Indonesian throughfl ow cruise. determining the phase speed and ampli- Th e echogram clearly shows the internal waves in the Lombok Strait. Th e ship was on standby tude of internal solitary waves. A combi- when waves with a wavelength of ~1.8 km passed under the ship with a speed of ~1.5 m/s. Th e wave amplitude (peak to trough) exceeds 100 m. Higher backscatter values indicate high- nation of satellite SAR sensing and fi eld er plankton concentration or large schools of fi sh. Vertical axis is depth in meters. Horizontal measurements is needed to determine axis is time. Colors represent relative backscatter strength in decibels.

86 Oceanography Vol. 18, No. 4, Dec. 2005 the detailed characteristics and dynamics Gargett, A.E., and B.A Hughes. 1972. On the in- numerical model results. Pp. 3–23 in The of internal waves and other submesocale teraction of surface and internal waves. Jour- of Straits, L.J. Pratt, nal of Fluid Mechanics 52(1):179–191. ed. Kluwer Academic Publishers, Norwell, features in the Lombok Strait. Jackson, C.R., and J.R. Apel. 2004. Synthetic Ap- MA, USA. erture Radar Marine User’s Manual, NOAA/ Osborne, A.R., and T.L. Burch. 1980. Inter- ACKNOWLEDGEMENTS NESDIS, Silver Spring, MD, USA, 427 pp. nal solitons in the Andaman Sea. Science Helfrich, K.R., and W.K. Melville. 1986. On 208(4443):451–460. This research is funded by the Offi ce long nonlinear internal waves over slope Perry, R.B., and G.R. Schimke. 1965. Large of Naval Research (ONR) under grant shelf topography. Journal of Fluid Mechanics amplitude internal waves observed off the 167:285–308. northwest coast of Sumatra. 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