AUGUST 2020 T A M I Z I A N D Y O U N G 2123 The Spatial Distribution of Ocean Waves in Tropical Cyclones ALI TAMIZI AND IAN R. YOUNG Department of Infrastructure Engineering, University of Melbourne, Melbourne, Australia (Manuscript received 27 January 2020, in final form 28 May 2020) ABSTRACT The spatial structure of both the wind and wave fields within tropical cyclones is investigated using two large databases. The first of these was compiled from global overpasses of tropical cyclones by satellite altimeters. The second dataset consists of an extensive collection of North American buoy measurements during the passage of tropical cyclones (hurricanes). The combined datasets confirm the vortex structure of the tropical cyclone wind field with the strongest winds to the right (Northern Hemisphere) of the storm. The wave field largely mirrors the wind field but with greater right–left asymmetry that results from the extended fetch to the right of the translating tropical cyclone. The extensive in situ buoy database confirms previous studies indi- cating that the one-dimensional spectra are generally unimodal. The directional spectra are, however, di- rectionally skewed, consisting of remotely generated waves radiating out from the center of the storm and locally generated wind sea. The one-dimensional wave spectra have many similarities to fetch-limited cases, although for a given peak frequency the spectra contain less energy than for a fetch-limited case. This result is consistent with the fact that much of the wave field is dominated by remotely generated waves. 1. Introduction This paper attempts to build an extensive database of observations of tropical cyclone wave conditions In tropical and subtropical regions, tropical cyclones from a number of sources. These sources include a (TCs; hurricanes or typhoons) represent the major global database of satellite altimeter observations extreme meteorological systems. The strong winds as- from 13 satellite missions across a period of 33 years sociated with the moving tropical cyclone vortex gen- together with 37 years of in situ data from the National erate extreme waves which critically impact processes Data Buoy Center (NDBC) buoy network around the such as: coastal and offshore engineering design, ship- United States. The combined dataset includes altim- ping, coastal beach erosion and coastal inundation. The 2 eter data from 2730 tropical cyclones worldwide and extreme winds (in excess of 40 m s 1), the rapidly in situ data from 353 tropical cyclones (hurricanes) in turning nature of the vortex, and its translation are a the North American region. This combined dataset is demanding test for our understanding of wind gener- analyzed to provide an overview of the spatial distri- ation physics. The situation is exacerbated by the butions of significant wave height and wind speed, as paucity of quality wind and wave data during intense well as details of the directional wave spectrum gen- tropical cyclones. The relatively small geographic size erated in tropical cyclones. of tropical cyclones means a dense network of obser- The arrangement of this paper is as follows. Following vations is required to ensure that extreme conditions this introduction, section 2 provided a brief overview of will be captured. When they are, the conditions are previous observations and computations of the tropical such that failure of in situ measurement systems is not cyclone wave field, and section 3 describes the data uncommon. Therefore, the observational database of sources used to construct the present tropical cyclone wave conditions under tropical cyclone forcing is still databases. The details of the altimeter observations are relatively small, meaning that a comprehensive un- provided in section 4, followed by the in situ buoy ob- derstanding of the wave fields generated by such sys- servations in section 5. In addition to the distribution of tems is still limited. significant wave height, the in situ buoy data provide a comprehensive view of the directional wave spectrum. Corresponding author: Ian R. Young, ian.young@unimelb. The one-dimensional (1D) energy density spectrum is edu.au described in section 6, followed by the directional DOI: 10.1175/JPO-D-20-0020.1 Ó 2020 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses). Unauthenticated | Downloaded 09/29/21 05:32 AM UTC 2124 JOURNAL OF PHYSICAL OCEANOGRAPHY VOLUME 50 properties of the spectrum in section 7. Conclusions and the center of the storm. The directional properties ob- discussion appear in section 8. tained from the buoys showed strong directional skew, with remotely generated waves and wind sea often 8 2. Observations of tropical cyclone wave fields propagating in directions separated by more than 90 . The directional properties indicated that the wave The earliest attempts to model/describe the tropical systems (remotely generated waves and wind sea) did cyclone wave field assumed that it would mirror the not completely decouple and there was a continuum of wind field (Bretschneider 1959, 1972; USACE 1977; energy between the systems. As a result, the 1D spectra Ross 1976). However, the first limited observations from generally remained unimodal. In addition, these 1D in situ instruments (Patterson 1974; Whalen and Ochi spectra had many of the attributes previously observed 1978; Black 1979; Ochi and Chiu 1982; Ochi 1993; Young for fetch-limited wind seas. The nondimensional en- 5 2 4 1998; Young 2006) and remote sensing observations, ergy g Etot/U10 and nondimensional peak frequency largely using aircraft-based synthetic aperture radar and n 5 fpU10/g were approximately related by the same orbiting altimeter data (Elachi et al. 1977; King and power law as observed for fetch-limited wind seas. In Shemdin 1978; Gonzalez et al. 1982; McLeish and Ross these relations, Etot is the total energy of the waves, fp is 1983; Holt and Gonzalez 1986; Beal et al. 1986; Young the spectral peak frequency, U10 is the wind speed, and and Burchell 1996; Wright et al. 2001; Black et al. 2007) g is gravitational acceleration. The high-frequency face 2 showed a more complex structure. These measurements of the spectrum decayed at ;f 4,wheref is frequency, indicated that, ahead of the tropical cyclone vortex, the and the energy level of this region of the spectrum was wave field was composed of locally generated wind seas similar to fetch-limited spectra. The peak frequency (aligned with the local wind direction) and remotely values were, however, such that these waves were generated waves which had been generated in the in- propagating faster than the local wind. This is consis- tense wind regions of the storm and then propagated tent with these waves being generated in other parts of ahead of the storm. These observations have also been the storm and then propagating to the observation site. augmented with model simulations of tropical cyclone Young (2006) concluded that these observed spectral conditions (SWAMP Group 1985; Young 1988; The shapes were consistent with an energy balance in which WAMDI Group 1988). nonlinear wave–wave interactions played a dominant These measurements and modeling led to the con- role (Young and van Vledder 1993). clusion that the forward motion of the storm was an Hu and Chen (2011) considered directional spectra important variable in understanding wave generation recorded at 12 buoys in the Gulf of Mexico during within tropical cyclones. As a result, the concept of an the passage of seven tropical cyclones (hurricanes). ‘‘extended’’ or ‘‘trapped’’ fetch was developed (Young Consistent with Young (2006), they found the 1D 1988; Young and Burchell 1996; Bowyer and MacAfee spectra were generally unimodal with the exception of 2005; Young and Vinoth 2013). In this representation, spectra far from the tropical cyclone center (r . 6Rm, waves generated to the right (Northern Hemisphere) of where Rm is the radius to maximum winds) and spec- the storm center propagate forward with the storm and tra to the left of the storm center. Esquivel-Trava et al. hence stay in the strong wind region for an extended (2015) considered spectra from four buoys in the period of the time (the extended fetch). Hence, both the Gulf of Mexico and Caribbean during the passage of velocity of forward movement and the maximum wind 14 tropical cyclones (hurricanes). Again, they found speed in the storm are important in determining the that the 1D spectra were unimodal. However, their wave field. results indicated that the energy in the high-frequency A number of studies have aggregated data from tail of the spectrum was lower than proposed by multiple tropical cyclones to provide information on the Young (2006). spatial distribution of tropical cyclone waves. Young Collins et al. (2018) reported on observations from (1998, 2006) considered data from directional wave two Taiwanese buoys during the passage of three trop- buoys off the northwest coast of Australia during the ical cyclones (typhoons) plus a tropical storm. They passage of nine tropical cyclones. To aggregate the data confirmed that the spectra were commonly directionally from the multiple storms, a frame of reference moving skewed. However, in contrast to the previous measure- with the tropical cyclone was adopted. The analysis ments, they found that a significant percentage of the 1D confirmed the conclusions from the remote sensing data spectra were bimodal. that, ahead of the storm, the wave field was composed of In a more recent series of papers (Hwang 2016; locally generated wind sea and remotely generated Hwang and Fan 2017; Hwang et al. 2017; Hwang and waves radiating out from the intense wind regions near Walsh 2016, 2018a,b), scanning radar altimeter data Unauthenticated | Downloaded 09/29/21 05:32 AM UTC AUGUST 2020 T A M I Z I A N D Y O U N G 2125 were used to examine directional properties of waves In the present analysis, data after 1980 have been from six North American hurricanes.