• Adams, J. K., and V. T. Buchwald, 1969: The generation of continental shelf waves. J. Fluid Mech., 35, 815826, https://doi.org/10.1017/S0022112069001455.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Brink, K. H., 1991: Coastal-trapped waves and wind-driven currents over the continental shelf. Annu. Rev. Fluid Mech., 23, 389412, https://doi.org/10.1146/annurev.fl.23.010191.002133.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Brink, K. H., and D. C. Chapman, 1985: Programs for computing properties of coastal-trapped waves and wind-driven motions over the continental shelf and slope. Woods Hole Oceanographic Institution Tech. Rep. WHOI-85-17, 99 pp., https://doi.org/10.1575/1912/5363.

    • Crossref
    • Export Citation
  • Church, J. A., H. J. Freeland, and R. L. Smith, 1986: Coastal-trapped waves on the east Australian continental shelf—Part I: Propagation of modes. J. Phys. Oceanogr., 16, 19291943, https://doi.org/10.1175/1520-0485(1986)016<1929:CTWOTE>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Clarke, A. J., 1977: Observational and numerical evidence for wind-forced coastal trapped long waves. J. Phys. Oceanogr., 7, 231247, https://doi.org/10.1175/1520-0485(1977)007<0231:OANEFW>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Craig, P. D., and P. E. Holloway, 1993: The influence of coastally trapped waves on the circulation in Jervis Bay, New South Wales. Dynamics and Exchanges in Estuaries and the Coastal Zone, D. Prandle, Ed., Coastal and Estuarine Studies, Vol. 40, Amer. Geophys. Union, 9–33, https://doi.org/10.1029/CE040p0009.

    • Crossref
    • Export Citation
  • Csanady, G. T., 1967: Large‐scale motion in the Great Lakes. J. Geophys. Res., 72, 41514162, https://doi.org/10.1029/JZ072i016p04151.

  • Dee, D. P., and et al. , 2011: The ERA-Interim reanalysis: Configuration and performance of the data assimilation system. Quart. J. Roy. Meteor. Soc., 137, 553597, https://doi.org/10.1002/qj.828.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Ding, Y., X. Bao, and M. Shi, 2012: Characteristics of coastal trapped waves along the northern coast of the South China Sea during year 1990. Ocean Dyn., 62, 12591285, https://doi.org/10.1007/s10236-012-0563-3.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Freeland, H. J., and et al. , 1986: The Australian Coastal Experiment: A search for coastal-trapped waves. J. Phys. Oceanogr., 16, 12301249, https://doi.org/10.1175/1520-0485(1986)016<1230:TACEAS>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gill, A. E., and A. J. Clarke, 1974: Wind-induced upwelling, coastal currents and sea-level changes. Deep-Sea Res. Oceanogr. Abstr., 21, 325345, https://doi.org/10.1016/0011-7471(74)90038-2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Huthnance, J. M., 1975: On trapped waves over a continental shelf. J. Fluid Mech., 69, 689704, https://doi.org/10.1017/S0022112075001632.

  • Huthnance, J. M., 1978: On coastal trapped waves: Analysis and numerical calculation by inverse iteration. J. Phys. Oceanogr., 8, 7492, https://doi.org/10.1175/1520-0485(1978)008<0074:OCTWAA>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Igeta, Y., T. Watanabe, H. Yamada, K. Takayama, and O. Katoh, 2011: Coastal currents caused by superposition of coastal-trapped waves and near-inertial oscillations observed near the Noto Peninsula, Japan. Cont. Shelf Res., 31, 17391749, https://doi.org/10.1016/j.csr.2011.07.014.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Koch, K. R., 2014: Robust estimations for the nonlinear Gauss Helmert model by the expectation maximization algorithm. J. Geod., 88, 263271, https://doi.org/10.1007/s00190-013-0681-9.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Liao, F., and X. H. Wang, 2018: A study of low-frequency, wind-driven, coastal-trapped waves along the southeast coast of Australia. J. Phys. Oceanogr., 48, 301316, https://doi.org/10.1175/JPO-D-17-0046.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Mellor, G. L., 2004: User’s guide for a three-dimensional, primitive equation, numerical ocean model. Princeton University Rep., 56 pp.

  • Middleton, J. F., 1994: The baroclinic response of straits and bays to coastal-trapped wave scattering. J. Phys. Oceanogr., 24, 521539, https://doi.org/10.1175/1520-0485(1994)024<0521:TBROSA>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Mortimer, C. H., 1963: Frontiers in physical limnology with particular reference to long waves in rotating basins. Proc. Sixth Conf. Great Lakes Research, Ann Arbor, Michigan, University of Michigan and American Society of Limnology and Oceanography, 9–42.

  • Mysak, L. A., 1980: Topographically trapped waves. Annu. Rev. Fluid Mech., 12, 4576, https://doi.org/10.1146/annurev.fl.12.010180.000401.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Oey, L. Y., and P. Chen, 1992: A model simulation of circulation in the northeast Atlantic shelves and seas. J. Geophys. Res., 97, 20 08720 115, https://doi.org/10.1029/92JC01990.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Schumann, E. H., and K. H. Brink, 1990: Coastal-trapped waves off the coast of South Africa: Generation, propagation and current structures. J. Phys. Oceanogr., 20, 12061218, https://doi.org/10.1175/1520-0485(1990)020<1206:CTWOTC>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Smith, R. L., 1978: Poleward propagating perturbations in currents and sea levels along the Peru coast. J. Geophys. Res., 83, 60836092, https://doi.org/10.1029/JC083iC12p06083.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sun, Y.-J., I. Jalón-Rojas, X. H. Wang, and D. Jiang, 2018: Coastal upwelling by wind-driven forcing in Jervis Bay, New South Wales: A numerical study for 2011. Estuarine Coastal Shelf Sci., 206, 101115, https://doi.org/10.1016/j.ecss.2017.11.022.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wang, D.-P., and C. N. K. Mooers, 1976: Coastal-trapped waves in a continuously stratified ocean. J. Phys. Oceanogr., 6, 853863, https://doi.org/10.1175/1520-0485(1976)006<0853:CTWIAC>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wang, X. H., and X. L. Wang, 2003: A numerical study of water circulation in a thermally stratified embayment. J. Ocean Univ. Qingdao (Engl. Ed.), 2, 2434, https://doi.org/10.1007/s11802-003-0022-3.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • View in gallery

    (a) JB bathymetry (from Wang and Wang 2003), (b) the grid of JBOM, and (c) the five coastal stations used in this paper. In (a), stations with current-meter moorings are denoted with solid triangles and tide gauge moorings with solid circles. The stations are Northwest (NW), Northeast (NE), South-Central (SC), and Creswell Naval Base (CW). The red star shows the sites A–C, the green dashed line is a north–south cross section used in Figs. 7 and 10, and the purple dashed box indicates the area D where the wind stress was applied in case g in section 3b. In (c), the five coastal stations are Eden (ED), Bateman’s Marine Park (BMP), JB, Port Kembla (PK), and Fort Denison (FD; in Sydney Harbor).

  • View in gallery

    Initial temperature profile in the vertical water column from Wang and Wang (2003). The temperature for water depth shallower than 25 m was measured inside the bay, and for water deeper than 25 m, the temperature was measured on the shelf. The temperature for water deeper than 120 m was approximated based on the temperature gradient at 120 m.

  • View in gallery

    Heat fluxes at the ocean surface from 1 December 1988 to 1 February 1989. (a) Surface net downward shortwave flux, (b) surface net upward longwave flux, (c) surface upward sensible heat flux, (d) surface upward latent heat flux, and (e) net heat flux.

  • View in gallery

    Structures of the first three CTW modes of the alongshore velocity under typical summer temperature stratification. Mode 1 is on the left. The colorbar scales for the three panels are different for a better visualization.

  • View in gallery

    Comparisons of periods of modeled current in the N/S direction and periods of the corresponding forcings for three sites inside Jervis Bay. From left to right, the sites are A–C.

  • View in gallery

    Time–depth contours of temperature at site A in JB for the three CTW modes. Mode 1 is on the left. From left to right, they are cases a–c.

  • View in gallery

    (top) Amplitude and (bottom) phase distributions of the temperature component at a period of 10 days along the N/S cross section for the three CTW modes. Mode 1 is on the left. The N and S on the top of [a(1)] denote the north and south sides of JB, respectively. From left to right, they are cases a–c. The colorbar scale in [b(1)] is different than in [a(1)] and [c(1)] for a better visualization.

  • View in gallery

    Distributions of (top) temperature, (middle) phase, and (bottom) current component υ of period 10 days at a depth of 10 m for (from left to right) cases a–c. The colorbar scales for panels in each row are different for a better visualization.

  • View in gallery

    Time–depth contours of temperature at coastal site A in JB for (from left to right) cases d–g. The colorbar scale in (g) is different than in (d)–(f) for a better visualization.

  • View in gallery

    (top) Amplitude and (bottom) phase distribution of the temperature component of period 10 days along an N/S cross section for (from left to right) cases d–g. The N and S on the top of [d(1)] denote the northern and southern sides of JB, respectively. The colorbar scale for panels in each row is different for a better visualization.

  • View in gallery

    Distributions of (top) temperature, (middle) phase, and (bottom) current component υ of period 10 days at a depth of 10 m for (from left to right) cases d–g. The colorbar scale for panels in each row is different for a better visualization.

  • View in gallery

    Detection of CTWs propagating along the Australian east coast. (a) Low-pass filtered SLA time series at ED (black) and FD (red) from 1 December 1988 to 1 March 1989, (b) PSD of the SLAs at these two coastal stations, (c) coherence squared between the two SLA time series, and (d) phase delay between the two SLA time series.

  • View in gallery

    Wind in JB from 20 Nov 1998 to 20 Jan 1989. Wind component (a) in the E/W direction, (b) in the N/S direction, and (c) the PSDs of the wind component in the E/W (black line) and the N/S direction (blue line). The arrow in (c) shows the period of the local PSD peak of the oscillations in the wind.

  • View in gallery

    Comparisons of (top) temperature anomalies and (bottom) the corresponding spectral analyses from both observations and model results for (from left to right) cases h–j at depth 18.5 m at station SC. The top row indicates the confidence interval (CI) of the correlation coefficient.

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 72 72 4
PDF Downloads 71 71 1

A Numerical Study of Coastal-Trapped Waves in Jervis Bay, Australia

View More View Less
  • 1 Sino-Australian Research Centre for Coastal Management, and School of Physical, Environmental and Mathematical Sciences, University of New South Wales, Canberra, Australian Capital Territory, Australia
© Get Permissions
Full access

Abstract

Coastal-trapped waves (CTWs) in Jervis Bay were investigated using a Jervis Bay Ocean Model (JBOM), based on the Princeton Ocean Model. Under the typical temperature stratification in Jervis Bay in summer, the first three modes of external CTWs can scatter into the bay. The wind stress inside Jervis Bay can generate CTWs, and the wind stress on the adjacent shelf can also generate CTWs in the bay by oscillations at the bay's opening, which are associated with temperature fluctuations there. The actual subinertial CTWs in Jervis Bay are a result of the interference of these CTWs. The amplitudes of the first three CTW modes were calculated from the observed sea level data. Three numerical experiments were designed to identify the major forcing for the observed subinertial temperature oscillations in Jervis Bay during an observational program in the summer of 1988/89. It was found that the local wind stress was the major contributor to the observed oscillations.

© 2018 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Fanglou Liao, fanglou.liao@student.unsw.edu.au

Abstract

Coastal-trapped waves (CTWs) in Jervis Bay were investigated using a Jervis Bay Ocean Model (JBOM), based on the Princeton Ocean Model. Under the typical temperature stratification in Jervis Bay in summer, the first three modes of external CTWs can scatter into the bay. The wind stress inside Jervis Bay can generate CTWs, and the wind stress on the adjacent shelf can also generate CTWs in the bay by oscillations at the bay's opening, which are associated with temperature fluctuations there. The actual subinertial CTWs in Jervis Bay are a result of the interference of these CTWs. The amplitudes of the first three CTW modes were calculated from the observed sea level data. Three numerical experiments were designed to identify the major forcing for the observed subinertial temperature oscillations in Jervis Bay during an observational program in the summer of 1988/89. It was found that the local wind stress was the major contributor to the observed oscillations.

© 2018 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Fanglou Liao, fanglou.liao@student.unsw.edu.au

1. Introduction

Propagating low-frequency fluctuations are commonly seen in coastal waters, with some of them being responses to the weather patterns that are moving alongshore and some being waves with periods ranging from several days to several weeks. Some of these waves exist in the form of coastal-trapped waves (CTWs), a type of subinertial wave widely studied along most of the continental shelves and slopes around the world (Clarke 1977; Smith 1978; Igeta et al. 2011). CTWs are important in coastal oceanic variabilities on time scales between the local inertial period and atmospheric weather changes over the continental margins (Brink 1991; Ding et al. 2012), as they are generally excited by the alongshore wind stress (Adams and Buchwald 1969). Assuming no stratification and a variable shelf bottom, the low-frequency wind-forced coastal responses generally exist as continental shelf waves (CSWs), whereas in a stratified ocean with a flat shelf bottom and a lateral boundary, internal Kelvin waves (IKWs) are the dominant coastal-trapped subinertial waves (Wang and Mooers 1976). As stratification and variable bathymetry commonly coexist in most continental shelves, the actual low-frequency coastal-trapped waves are a hybrid between CSWs and IKWs, and were called “coastal trapped waves” by Gill and Clarke (1974). CTWs propagate with the coast on the right (left) in the Northern (Southern) Hemisphere, as theoretically explained by Huthnance (1975, 1978).

Waves trapped over a sloping shelf also include edge waves. Edge waves can be thought of as long gravity waves that are trapped near the coast because of refraction (Mysak 1980). Unlike CTWs, edge waves generally have periods ranging from minutes to hours and belong to superinertial waves. Because of the relatively high frequency, edge waves depend weakly upon Earth’s rotation and can travel in both directions along the shelf. It is also necessary to mention Rossby waves here to differentiate them from the three other waves above. Rossby waves result from the variations in the Coriolis parameter with latitude. They have long wavelengths and persistently westward phase speeds to conserve the potential vorticity. In contrast to CTWs and edge waves, Rossby waves can exist far away from the coast and are not coastally trapped.

Although CTWs are large-scale waves and are common on continental shelves, previous studies revealed that they can also be found in lakes and semiclosed coastal bays (Mortimer 1963; Csanady 1967; Clarke 1977). A typical semiclosed embayment is Jervis Bay (JB), located on the east coast of Australia. This part of the Australian coast is known for the northward-propagating CTWs found during the Australian Coastal Experiment (ACE) in 1983/84 (Church et al. 1986; Freeland et al. 1986). Jervis Bay has an area of around 124 km2 and is approximately 15 km long in the north–south (N/S) direction and 8 km wide in the east–west (E/W) direction. It connects with the adjacent continental shelf through its 3.5-km-wide opening. The bathymetry of Jervis Bay is shown in Fig. 1a and its location in the inset. From Fig. 1, it can be seen that Jervis Bay is a shallow embayment, with a maximum depth of 50 m at the opening and a mean depth inside the bay of around 15 m (Craig and Holloway 1993).

Fig. 1.
Fig. 1.

(a) JB bathymetry (from Wang and Wang 2003), (b) the grid of JBOM, and (c) the five coastal stations used in this paper. In (a), stations with current-meter moorings are denoted with solid triangles and tide gauge moorings with solid circles. The stations are Northwest (NW), Northeast (NE), South-Central (SC), and Creswell Naval Base (CW). The red star shows the sites A–C, the green dashed line is a north–south cross section used in Figs. 7 and 10, and the purple dashed box indicates the area D where the wind stress was applied in case g in section 3b. In (c), the five coastal stations are Eden (ED), Bateman’s Marine Park (BMP), JB, Port Kembla (PK), and Fort Denison (FD; in Sydney Harbor).

Citation: Journal of Physical Oceanography 48, 11; 10.1175/JPO-D-18-0106.1

From 6 December 1988 to 11 January 1989, a field measurement program was conducted in Jervis Bay to investigate the bay’s dynamics (Craig and Holloway 1993). It was argued that baroclinic CTWs existed in Jervis Bay. By applying a simple quasi-geostrophic model, Craig and Holloway (1993) inferred that the CTWs in the bay were generated by the oscillations at the bay’s opening as a response to the large-scale baroclinic motions over the adjacent shelf and slope. A numerical study of summertime circulation in Jervis Bay was conducted by Wang and Wang (2003). The local wind stress was found to be able to generate wind-forced IKWs inside the bay but to make only a minor contribution to the observed CTWs. Consistent with Craig and Holloway (1993), the authors concluded that the dominant forcing came from the external CTWs on the open shelf through a process of scattering. This agreed with the theoretical argument that baroclinic CTWs could scatter into Jervis Bay (Middleton 1994).

However, our analysis of recent acoustic Doppler current profiler (ADCP) observations inside Jervis Bay showed that the low-frequency current was strongly related to the local wind stress. In addition, both Craig and Holloway (1993) and Wang and Wang (2003) failed to detect the propagation of CTWs along the Australian east coast over the period they investigated, a premise for their conclusions. The condition of constant density in Craig and Holloway’s model may influence the model’s performance.

Despite a high correlation between model results and observations in Wang and Wang (2003), the oversimplified and idealized IKW structure they used as the boundary condition across the cross-shore boundaries may be significantly different from the actual wave modal structures. Their simple model domain and the closure of the eastern boundary may have influenced the numerical model’s accuracy, leading to the poor correlation between the observations and the model results when the local wind stress was the forcing. Jervis Bay is generally strongly stratified during the summertime, mainly because of the extensive heat fluxes through the ocean surface. Neglect of these thermal inputs may also influence the model results, especially for the cases with wind stress forcing, which can mix the water column thoroughly and weaken the stratification unless external heat fluxes are included to keep the temperature structure in the water column.

Another reason encouraging us to study the subinertial dynamics of Jervis Bay is the fact that there are numerous semiclosed bays of similar scale around the world. As mentioned above, CTWs propagate along most continental shelves. These CTWs may generate subinertial circulations in the small semiclosed bays they pass during propagation and may have some impacts on the hydrodynamic environment of the bays and their exchange process with the open shelf. Therefore, it is vital to understand the response of a small semiclosed bay to the external CTWs on the adjacent shelf.

In this paper, a three-dimensional (3D) numerical ocean model based on the Princeton Ocean Model (POM) was developed, with high-resolution bathymetry data, and called Jervis Bay Ocean Model (JBOM) here. The model domain and grid are shown in Fig. 1.

The response of Jervis Bay to idealized forcings was investigated as a first step to understand CTW generation inside the bay. JBOM was driven either by idealized CTWs along the southern boundary of the model domain or by idealized wind stress in the N/S direction. Middleton (1994) found theoretically that baroclinic CTWs were more effective in scattering into Jervis Bay than barotropic CTWs. Stratification largely determines the CTW structures, so that it is an important consideration in the scattering of CTWs into Jervis Bay. According to the stratification and bathymetry given in Wang and Wang (2003), the barotropic and first-mode baroclinic Rossby radius of deformation for a typical summer period in Jervis Bay are 350 and 5 km, respectively. The Rossby radius of deformation represents the length scale at which rotational effects play an important role, as buoyancy and gravity wave effects do. When comparing the Rossby radius of deformation with the size of Jervis Bay, we can assume that baroclinic CTWs are much more important than barotropic CTWs in scattering into Jervis Bay.

In this paper, the structures of the first three CTW modes of the alongshore velocity were calculated given the bathymetry and stratification along the southern boundary, following Brink and Chapman (1985). These were combined with a modal amplitude of period 10 days to produce the idealized alongshore current on the southern boundary of JBOM; JBOM was then run with these boundary conditions to see if CTWs could be generated in the bay as a response.

Next, to understand the response of Jervis Bay to the local wind stress forcing, JBOM was run with an idealized wind stress of period 10 days. The maximum wind speed in the model domain was chosen to be 7 m s−1, based on the observed low-pass filtered wind speed in Jervis Bay during the summer of 1988/89 (Craig and Holloway 1993).

Finally, the model was run for the period from December 1988 to January 1989, the period of the observational program in Wang and Wang (2003), to investigate the dynamic response of Jervis Bay to the actual forcings and to identify the relative contributions of the local wind stress and the external CTWs.

In section 2, the JBOM model configuration is described, and the observational program in Jervis Bay during the summer of 1988/89 is introduced. This section also describes the reanalyzed data from the European Centre for Medium-Range Weather Forecasts (ECMWF). The investigation of the response of Jervis Bay to different idealized forcings is in section 3. Section 4 gives a least squares method for decomposing CTW modal amplitudes and a case study to identify the dominant forcing for the observed subinertial oscillations in the observation program conducted in the summer of 1988/89.

2. The numerical ocean model and datasets

a. Model configuration

In JBOM, the horizontal grid size in the E/W direction is 450 m near Jervis Bay, increasing to 2000 m on the eastern side of the model domain (Fig. 1). The grid size in the N/S direction is 500 m near Jervis Bay, increasing to 2500 m on the northern side of the domain. There are 100 grid points in the E/W direction and 111 grid points in the N/S direction. A sigma coordinate is used in the vertical direction, with 21 vertical layers and a logarithmic distribution law near the surface and bottom to resolve the surface and bottom boundary layers (Mellor 2004). The bottom drag coefficient is calculated based on Eq. (14e) in Mellor (2004), with the bottom roughness at 0.01 m and drag coefficient between 0.0025 and 1. It should be noted here that, in order to suppress the computational noise, 5 sponge layers were added along the southern open boundary where the grid boundary is not perpendicular to the coast. As the wavelength of CTWs is generally large (on the scale of 1000 km), much larger compared to the alongshore distance of the 5 sponge layers, the addition of these sponge layers produced very minor influence on the phases of the incoming CTWs along the southern boundary.

The internal time step is 12 s and the external time step 0.2 s (Mellor 2004). The northern, southern, and eastern boundaries are open boundaries, and the western boundary is land. The radiation boundary condition method was applied along the northern and eastern boundaries. For the numerical experiments with CTW forcings, the alongshore current was calculated based on the modal structures from the Brink and Chapman (1985) program and the given idealized sinusoidal modal amplitudes then imposed on the southern boundary. For the numerical experiments forced by the local wind stress, the radiation boundary condition was applied along the southern boundary. The initial temperature structure was from Wang and Wang (2003), as shown in Fig. 2. The water was set to be at rest initially. The topography for the Jervis Bay area used for JBOM was from the high-resolution (100 m × 100 m) bathymetry data measured by the Royal Australian Navy with multibeam sonar and conventional echo sounders (Sun et al. 2018); the topography for the other areas in JBOM was from the bathymetry data of the ETOPO1 global relief model.

Fig. 2.
Fig. 2.

Initial temperature profile in the vertical water column from Wang and Wang (2003). The temperature for water depth shallower than 25 m was measured inside the bay, and for water deeper than 25 m, the temperature was measured on the shelf. The temperature for water deeper than 120 m was approximated based on the temperature gradient at 120 m.

Citation: Journal of Physical Oceanography 48, 11; 10.1175/JPO-D-18-0106.1

The continental shelf around Jervis Bay is around 20 km wide, and CTWs are mainly concentrated on the shelf; the model domain covers this region.

b. Observation data

From 6 December 1988 to 11 January 1989, an observational program was conducted in Jervis Bay as part of a baseline study of the bay’s marine ecology (Craig and Holloway 1993). The program deployed a measurement array of three current stations with eight meters, three tide gauge stations, and a wind station (Fig. 1). The current meters also measured temperature. The four current meters at the South-Central (SC) station (with water depth of 22 m) worked well over the whole deployment period. However, the current meter at 9.5-m depth at the Northwest (NW) station (with water depth of 12 m) only measured the temperature, and the current meter at 5.4-m depth at the Northeast (NE) station (with water depth of 14 m) failed after 8 days; detailed deployment information can be seen in Table 1 of Craig and Holloway (1993). Here, the temperature at 18.5-m depth at SC was used to identify the main forcing for the observed subinertial oscillations in Jervis Bay during the observation period. In addition, tide gauge data from the Australian Bureau of Meteorology were used to detect CTWs along the Australian east coast during the same period, and also used to calculate the modal amplitudes of the first three CTW modes along the southern boundary of the JBOM in order to produce the CTW forcing over the observation program period.

c. ERA-Interim reanalyzed data

ERA-Interim is a dataset of the results of a global climate reanalysis from 1979 (Dee et al. 2011). It uses a fixed version of a numerical weather prediction system [Integrated Forecast System (IFS) Cy31r2] to produce reanalyzed data, with a spatial resolution of 0.125° in both longitude and latitude. Wind data from ERA-Interim were used to calculate the wind stress using Eq. (25) in Oey and Chen (1992), as Eq. (1) here, and the calculated wind stress was then used as the forcing in the numerical experiments h and j to investigate the role played by the wind in generating the subinertial circulations in Jervis Bay in the summer of 1988/89. The sea surface pressures from ERA-Interim were used to adjust the measured sea level to account for the loading effect of barometric pressure on the sea surface height (section 4a). The surface heat fluxes from ERA-Interim were used as surface forcings for all the numerical experiments;
eq1
e1
where is wind stress, is the drag coefficient (multiplied by the ratio of air and seawater densities), and is the wind velocity.

Figure 3 shows the 3-hourly heat flux time series from 1 December 1988 to 1 February 1989. It should be noted that the original 6-hourly heat flux data from ERA-Interim were interpolated to generate the 3-hourly time series in Fig. 3. This period covers that used in the case study in section 4d.

Fig. 3.
Fig. 3.

Heat fluxes at the ocean surface from 1 December 1988 to 1 February 1989. (a) Surface net downward shortwave flux, (b) surface net upward longwave flux, (c) surface upward sensible heat flux, (d) surface upward latent heat flux, and (e) net heat flux.

Citation: Journal of Physical Oceanography 48, 11; 10.1175/JPO-D-18-0106.1

From Fig. 3, it can be seen that net downward shortwave flux is much stronger than the other three, indicating that the water is gaining more heat than it loses. During the summer, this heat flux through the ocean surface is an important mechanism in maintaining the stratification, especially for a small and shallow bay such as Jervis Bay.

3. Dynamic response of Jervis Bay to idealized forcings

Craig and Holloway (1993) inferred that the observed subinertial oscillations in Jervis Bay during the summer of 1988/89 were IKWs and were a response to the large-scale baroclinic motions over the adjacent continental shelf and slope. However, the local wind stress is an important forcing in most cases of CTW generation. In this paper, forcings by idealized external CTWs and by idealized local wind stress were tested to understand the dynamic response of Jervis Bay to these idealized forcings.

a. Dynamic response of Jervis Bay to idealized external CTWs

CTWs propagating along the Australian east coast are mainly generated remotely along the southern coast of Australia rather than by the local wind stress (Church et al. 1986; Freeland et al. 1986; Liao and Wang 2018). To numerically simulate the scattering of the northward CTWs along the Australian east coast into Jervis Bay, the domain of JBOM should be large enough to include the source of these CTWs, but this is computationally far too time consuming. An alternative method is to introduce CTWs along the southern boundary of JBOM. Because of the scarcity of observations, actual CTWs cannot be used for the boundary conditions. However, given the temperature stratification and the bathymetry along the southern boundary of the domain, the relevant CTW modal structures can be calculated following Brink and Chapman (1985).

We used each of the first three CTW modes separately to create the boundary condition in order to investigate the scattering of external CTWs into Jervis Bay. The modal structures are shown in Fig. 4. It should be noted that the modal structure values have been normalized. Each modal structure was combined with a sinusoidal signal of period 10 days to simulate CTWs propagating across the southern boundary of JBOM; here, 10 days was chosen as a typical CTW period. Other period values were also tried and resulted in similar linkages, as shown in Fig. 5. The maximum CTW amplitude value of the alongshore current for all three modes was the same, 0.1 m s−1, which is comparable to the values used in Wang and Wang (2003).

Fig. 4.
Fig. 4.

Structures of the first three CTW modes of the alongshore velocity under typical summer temperature stratification. Mode 1 is on the left. The colorbar scales for the three panels are different for a better visualization.

Citation: Journal of Physical Oceanography 48, 11; 10.1175/JPO-D-18-0106.1

Fig. 5.
Fig. 5.

Comparisons of periods of modeled current in the N/S direction and periods of the corresponding forcings for three sites inside Jervis Bay. From left to right, the sites are A–C.

Citation: Journal of Physical Oceanography 48, 11; 10.1175/JPO-D-18-0106.1

Table 1 shows the settings of the forcing in the numerical experiments, cases a–j, conducted in this paper. In cases a–c, JBOM was forced by each of the three idealized CTW modes along its southern boundary. In cases d–g, JBOM was forced by an idealized N/S wind stress in different areas, aiming at studying the wind-driven circulations. In cases h–j, JBOM was forced by the ECMWF wind in the summer of 1988/89, the calculated CTWs along its southern boundary, and the combination of these two forcings, respectively, in order to identify the major generator of the observed subinertial oscillations. It should be noted here that the surface heat flux shown in Fig. 3 was included in all the cases a–j.

Table 1.

Forcings in cases a–j. An x in the table means the corresponding forcing was not applied. It should be noted here that the surface heat fluxes are included in all the cases.

Table 1.

Site A, shown in Fig. 1 was chosen to represent the vertical temperature structure for runs a–c. From Fig. 6, it can be seen that the temperature oscillates with time, especially at the bottom depths. There is a period of around 10 days in the temperature oscillations from the middle depth to the bottom for all three modes. As the first three CTW modes are similar near the coast, the corresponding scattered CTWs in Jervis Bay are similar.

Fig. 6.
Fig. 6.

Time–depth contours of temperature at site A in JB for the three CTW modes. Mode 1 is on the left. From left to right, they are cases a–c.

Citation: Journal of Physical Oceanography 48, 11; 10.1175/JPO-D-18-0106.1

To investigate the internal structures of the temperature oscillations, a N/S cross section (Fig. 1) was chosen to analyze the temperature component at the period of 10 days.

Figure 7 shows that the temperature oscillations of cases a–c were greatest at the bottom depths for all three CTW modes. It can be seen from the phase distributions that the surface and bottom temperature oscillations were close to being out of phase, indicating that the temperature fluctuations were baroclinic signals. In addition, there was a consistent phase decrease from the south to north in the middle and bottom depths, combined with the phase distribution as shown in Fig. 8, indicating that the temperature oscillations propagated in a clockwise direction around the bay.

Fig. 7.
Fig. 7.

(top) Amplitude and (bottom) phase distributions of the temperature component at a period of 10 days along the N/S cross section for the three CTW modes. Mode 1 is on the left. The N and S on the top of [a(1)] denote the north and south sides of JB, respectively. From left to right, they are cases a–c. The colorbar scale in [b(1)] is different than in [a(1)] and [c(1)] for a better visualization.

Citation: Journal of Physical Oceanography 48, 11; 10.1175/JPO-D-18-0106.1

Fig. 8.
Fig. 8.

Distributions of (top) temperature, (middle) phase, and (bottom) current component υ of period 10 days at a depth of 10 m for (from left to right) cases a–c. The colorbar scales for panels in each row are different for a better visualization.

Citation: Journal of Physical Oceanography 48, 11; 10.1175/JPO-D-18-0106.1

The temperature and current velocity component υ in the N/S direction at a depth of 10 m were chosen to analyze the structures and propagations of the oscillations.

If external CTWs scattered into Jervis Bay and traveled around the bay in a clockwise direction before exiting, the temperature amplitude distribution would be concentric contours, and the phase would decrease along the propagation direction. The amplitude distribution of current component υ would be trapped on the western and eastern sides of the bay and therefore symmetric relative to the bay’s N/S axis. Comparison of these idealized distribution scenarios with those in Fig. 8 shows that the temperature fluctuations in Fig. 8 are indeed stronger close to the coast and weaker in the central bay. The phase distributions also indicate that the waves propagate in a clockwise direction around the bay. The current components υ for modes 1 and 3 are clearly coastal trapped on the western and eastern sides of Jervis Bay, although the coastal trapping for mode 2 is not as clear as the other two modes.

Based on Figs. 68, it can be concluded that under the stratification condition considered in the paper, all three CTW modes can scatter into Jervis Bay and travel around in the bay.

b. Dynamic response of Jervis Bay to an idealized local wind stress

The alongshore wind stress is the main generator of CTWs in a number of coastal waters around the world. In this section, an idealized N/S wind stress with a period of 10 days and a maximum speed at 7 m s−1 was applied in the model domain to have a detailed understanding of wind-forced oscillations inside Jervis Bay.

It can be seen from Fig. 9 that temperature oscillates at a period of 10 days for runs d–g. There are only minor differences between cases d (forced by the idealized wind in the whole model domain) and f (forced by the idealized wind outside Jervis Bay), which indicates that the wind stress on the adjacent shelf was more important in generating oscillations at the same period inside Jervis Bay than the wind stress in the bay. As shown in Fig. 9, case e, wind stress inside the bay also generated temperature oscillations at the period of 10 days, but these oscillations were weaker than those in cases d and f. Case g was designed to understand the mechanism of influence of wind stress on the shelf on the temperature oscillations inside Jervis Bay.

Fig. 9.
Fig. 9.

Time–depth contours of temperature at coastal site A in JB for (from left to right) cases d–g. The colorbar scale in (g) is different than in (d)–(f) for a better visualization.

Citation: Journal of Physical Oceanography 48, 11; 10.1175/JPO-D-18-0106.1

Although wind stress was only applied in the small area D close to the opening of the bay in case g, temperature oscillations were still excited in the bay (Fig. 9g) and were coastal trapped [Fig. 10g(1)]. The consistent phase decrease from the southern side to the northern side in cases f and g indicated again that the oscillations propagated in a clockwise direction around the bay (Fig. 10). Therefore, the shelf wind generated the temperature oscillations in the opening of bay, and these oscillations traveled around the bay as CTWs; the temperature oscillations excited by the local wind stress inside the bay were much stronger on the northern side compared to those on the southern side.

Fig. 10.
Fig. 10.

(top) Amplitude and (bottom) phase distribution of the temperature component of period 10 days along an N/S cross section for (from left to right) cases d–g. The N and S on the top of [d(1)] denote the northern and southern sides of JB, respectively. The colorbar scale for panels in each row is different for a better visualization.

Citation: Journal of Physical Oceanography 48, 11; 10.1175/JPO-D-18-0106.1

The phase distribution shown in Fig. 11e(2) seems to indicate that the CTWs began to be generated on the western side, which is reasonable considering the forcing is the wind stress in the N/S direction, parallel to the western side of the bay but perpendicular to the southern side. That is the reason why the phase distribution shown in Fig. 10e(2), does not decrease from the south to north, as in Fig. 10f(2). The coastal-trapped temperature signal in Fig. 11f(1), the phase distribution in Fig. 11f(2), and the symmetric current distribution indicate that the shelf wind alone can generate the CTWs inside Jervis Bay. Although the temperature oscillations were weaker than in case f, the wind stress in the small rectangular area near the opening of the bay also generated CTWs in the bay [Figs. 11g(1)–g(3)]. In case d, the model-predicted circulation in the bay shows the interference of two wave patterns driven by the local wind stress and the shelf wind stress, respectively, and thus do not behave as typical CTWs [Figs. 11d(1)–d(3)].

Fig. 11.
Fig. 11.

Distributions of (top) temperature, (middle) phase, and (bottom) current component υ of period 10 days at a depth of 10 m for (from left to right) cases d–g. The colorbar scale for panels in each row is different for a better visualization.

Citation: Journal of Physical Oceanography 48, 11; 10.1175/JPO-D-18-0106.1

4. Case study of subinertial dynamics in Jervis Bay in the summer of 1988/89

Sections 3a and 3b showed that CTWs can be generated in Jervis Bay by the scattering of external CTWs, whereas the local wind stress in different areas can generate different types of subinertial fluctuations. Based on the analysis of observations in the bay for one month in the summer of 1988/89, Craig and Holloway (1993, p. 9) inferred that “the dominant sub-inertial dynamics appear to have been a response to the large-scale baroclinic motion over the continental shelf and slope.” Here, we extend their work to gain a clearer understanding of CTWs in Jervis Bay. As the first step, we determine if CTWs could be detected along the Australian east coast using the observed sea level and the sea surface pressure data from ERA-Interim over the period of the observational program.

a. Detection of CTWs along the Australian east coast

Typically, CTWs can be detected from the adjusted sea level fluctuation time series at successive coastal stations (Schumann and Brink 1990); high correlations at a common subinertial period and approximate time delays indicate propagation of CTWs in a cyclonic sense about the deep sea.

In this study, Eden (ED; 37.07°S, 149.90°E) and Fort Denison (FD; 33.85°S, 151.22°E), Australia, were chosen as the two coastal stations for detection of CTWs. The original observed sea level data were provided by the Australian Bureau of Meteorology. The sea surface pressure data from ERA-Interim are 6-hourly sampled, whereas the observed sea level data are hourly, so the sea surface pressure data from ERA-Interim were interpolated to hourly values. The sea surface pressure from ERA-Interim were used to adjust the sea level to account for the loading effect from the barometric pressure using (Schumann and Brink 1990):
e2
where η (cm) is the adjusted sea level height, pa (mbar) is the sea surface pressure variation, and η0 (cm) is the observed sea level height. It should be noted here that the barometric pressure and sea level data have been low-pass filtered with a cutoff period of 40 h.

Figure 12 shows the time series of the sea level anomalies (SLAs) measured at Eden and Fort Denison over a period of three months in 1988/89 and their calculated power spectral densities (PSDs), coherence, and phase difference.

Fig. 12.
Fig. 12.

Detection of CTWs propagating along the Australian east coast. (a) Low-pass filtered SLA time series at ED (black) and FD (red) from 1 December 1988 to 1 March 1989, (b) PSD of the SLAs at these two coastal stations, (c) coherence squared between the two SLA time series, and (d) phase delay between the two SLA time series.

Citation: Journal of Physical Oceanography 48, 11; 10.1175/JPO-D-18-0106.1

It can be seen from Fig. 12 that the SLA time series at the two coastal stations were similar in profile, with the signal at Fort Denison lagging that at Eden by about 32 h. The spectral analysis of these two signals shows that there was a subinertial peak with a period of around 8 days in the SLAs. The coherence at this period indicates that these two subinertial components were highly correlated, and the phase delay shows that the fluctuations propagated from Eden to Fort Denison. Combining these four panels, it can be concluded that CTWs with a period of around 8 days were propagating northward along the Australian east coast over the observed period. The straight-line distance between these two coastal stations is around 377 km, which means that the CTWs were propagating at a phase speed of 3.27 m s−1, and the actual propagation speed was slightly larger. The calculated model phase speeds of modes 1, 2, and 3 at Eden were 6.94, 2.71, and 1.27 m s−1, respectively. As pointed out by Church et al. (1986), the first two modes are the dominant CTW modes in the ACE region, and mode 2 carries more energy than mode 1. The fact that the calculated phase speed from the observations lies between the numerical phase speeds of modes 1 and 2 (from Brink and Chapman’s program) agrees with the previous research (Church et al. 1986).

b. Calculating CTW modal amplitudes

As the second step, CTWs were introduced along the southern boundary of JBOM (Fig. 1), as we did for individual modes in section 3a, but here we calculate the amplitudes of modes 1, 2, and 3 using the method below. The CTW modal structures were given in Fig. 4.

Given that the local wind stress along the east coast of Australia makes only a minor contribution to the CTWs propagating along the east coast (Church et al. 1986; Liao and Wang 2018), we assume here that the amplitudes of the first three CTWs remain unchanged from Eden to Fort Denison and that the CTW signals consist of only these three modes. Therefore, the modal amplitudes can be calculated based on measurements from four coastal stations by using a least squares method. In this paper, sea level data at Eden, Point Perpendicular, Port Kembla, and Fort Denison, Australia, were used to calculate the amplitudes of modes 1, 2, and 3 according to Eqs. (3) and (4). It should be noted here that the relative time delay between SLAs at these stations was considered in the calculations of modal amplitudes.
eq2
eq3
eq4
e3
where t is time and the Pi are the observed sea levels at these locations. The variables F11, F12, and F13 are the structures of modes 1–3 evaluated at Eden; F21, F22, and F23 at Point Perpendicular; F31, F32, and F33 at Port Kembla; and F41, F42, and F43 at Fort Denison; ϕ1, ϕ2, and ϕ3 are the amplitudes of modes 1–3. The coefficients Fij were calculated from Brink and Chapman’s (1985) program.
In each sampling time t, the Fij and Pi(t) are all known variables in the Eqs. (3); and thus, the amplitudes ϕ1, ϕ2, and ϕ3 can be estimated based on least squares criteria. With the help of redundant observations, the least squares criteria can effectively suppress the noise and obtain the optimum solution in data fitting. When the fitting model is a linear function that can be expressed using linear equations like Eqs. (3), the optimum solution can be calculated using Eq. (4) based on the Gauss–Helmert model (Koch 2014),
e4
where
eq5
is the coefficient matrix, is the weight matrix (using an identity matrix), is the observation vector, is the estimated solution, n is the number of observations, and m is the number of estimated variables. The number of observations (n = 4 in this paper) must be larger than that of estimated variables m (m = 3 in this paper). By solving the linear Eq. (4), the amplitudes of modes ϕi(t) can be sequentially calculated at the corresponding sampling time t. For all sampling times, the averaged R-square coefficient is R2 = 0.71, which indicates the goodness of fit is acceptable.
Then, the alongshore current at the southern boundary was calculated from the following equation [Eq. (A7) in Church et al. (1986)]; the modal structures Gi(x, z) were calculated from Brink and Chapman’s (1985) program,
eq6

c. Analysis of wind at Jervis Bay in the summer of 1988/89

Figure 13 shows the components of the wind vector in the E/W and N/S directions and the corresponding PSDs from 20 November 1988 to 20 January 1989. The PSDs show that the wind component in the N/S direction had a clear period of around 7 days, whereas the wind component in the E/W direction was much weaker in the frequency domain around 7 days. Given that the observed period of temperature anomalies was around one week (Craig and Holloway 1993), the N/S wind component was clearly a candidate for generating the CTWs in Jervis Bay.

Fig. 13.
Fig. 13.

Wind in JB from 20 Nov 1998 to 20 Jan 1989. Wind component (a) in the E/W direction, (b) in the N/S direction, and (c) the PSDs of the wind component in the E/W (black line) and the N/S direction (blue line). The arrow in (c) shows the period of the local PSD peak of the oscillations in the wind.

Citation: Journal of Physical Oceanography 48, 11; 10.1175/JPO-D-18-0106.1

d. Identification of forcing for the subinertial oscillations in Jervis Bay

To identify the relative importance of the local wind stress and the external CTWs on the adjacent shelf in generating the observed subinertial oscillations in the 1988/89 observational program, three numerical experiments were conducted in this study. The first, case h, had the forcing by the local wind stress; the second, case i, had the forcing by external CTWs; the third, case j, had the forcing by both the local wind stress and the external CTWs. The initial temperature stratification was the same as the stratification in sections 3a and 3b. To obtain the external CTW forcing, the least squares method (section 4b) was used to calculate the modal amplitudes of the first three CTWs modes.

To determine which forcing was dominant in generating the subinertial oscillations in Jervis Bay, the temperatures at 18.5-m depth at station SC (from the model; cases h–j) were compared with the observed temperatures for the time period of 600 h starting from 7 December 1988, as shown in Fig. 14.

Fig. 14.
Fig. 14.

Comparisons of (top) temperature anomalies and (bottom) the corresponding spectral analyses from both observations and model results for (from left to right) cases h–j at depth 18.5 m at station SC. The top row indicates the confidence interval (CI) of the correlation coefficient.

Citation: Journal of Physical Oceanography 48, 11; 10.1175/JPO-D-18-0106.1

In case h, in which the only forcing was the wind stress in the whole model domain (Table 1), the model temperatures agreed well with the observed temperatures, with a correlation of 0.77. In addition, the spectral analysis in Fig. 14h(2) indicates that the model amplitudes were similar to the observations.

In case i, in which the only forcing was the CTWs along the southern boundary of JBOM (Table 1), the agreement between the model results and the observations was poor. The spectral analysis also shows that the external CTWs alone cannot generate the observed strong oscillations in the bay.

In case j, in which both the wind stress in the whole model domain and external CTWs were applied in JBOM (Table 1), the correlation between the model-predicted temperature and the measured temperature was also high (0.61). This indicates that the local wind stress dominated the forcing generating the observed subinertial oscillations in Jervis Bay during the observational program, and that these oscillations were mainly a result of the wind-forced subinertial circulation over the shelf but not so much in the bay.

5. Summary

To investigate the CTWs in Jervis Bay, a numerical ocean model JBOM was developed and applied; the principal results are as follows:

  1. External CTWs can scatter into Jervis Bay under the typical summer temperature stratification.
  2. Local wind stress on the adjacent shelf can generate CTWs inside Jervis Bay by exciting temperature oscillations in the mouth of the bay. Local N/S wind stress inside the bay can also generate CTWs, beginning at the west coast of Jervis Bay. The actual subinertial circulation in Jervis Bay is the result of wave interference, that is, the combined effect of the CTWs generated by the wind stress inside the bay, those generated by the wind stress on the adjacent shelf, and those scatted from external CTWs through the mouth of the bay.
  3. CTWs were detected along the Australian east coast during the period of the observational program in the summer of 1988/89. Three numerical experiments here further indicated that the observed subinertial oscillations were mainly forced by the local wind stress over the shelf, with only a minor contribution from the scattering of external CTWs into Jervis Bay. This disagreed with the findings of Craig and Holloway (1993) and Wang and Wang (2003).

Jervis Bay represents a typical shallow embayment with horizontal scales on the order of 10 km, vertical depth on the order of 20 m, and a narrow opening of 3.5 km wide. The scale of such a bay is much smaller than the wavelength of CTWs and also smaller than most of the lakes and embayments where CTWs have been investigated. Here, we showed that external CTWs were scattered into Jervis Bay and that the local wind stress inside the bay and on the shelf can also generate CTWs. The results here should be applicable to embayments of a similar scale to Jervis Bay.

Acknowledgments

Fanglou Liao is supported by the China Scholarship Council and a UNSW Canberra top-up Scholarship. We are grateful to the Australian Bureau of Meteorology for kindly providing the tide gauge data; to the ERA-Interim of ECMWF for the wind, sea surface pressure, and surface heat flux data; and to the Royal Australian Navy and the ETOPO1 global relief model for the bathymetry data. Dr. Peter McIntyre was very helpful in improving the manuscript. Dr. Yue Ma was very helpful in the least squares fitting. The constructive comments from two anonymous reviewers have greatly improved the manuscript. This is publication number 53 of the Sino-Australian Research Centre for Coastal Management.

REFERENCES

  • Adams, J. K., and V. T. Buchwald, 1969: The generation of continental shelf waves. J. Fluid Mech., 35, 815826, https://doi.org/10.1017/S0022112069001455.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Brink, K. H., 1991: Coastal-trapped waves and wind-driven currents over the continental shelf. Annu. Rev. Fluid Mech., 23, 389412, https://doi.org/10.1146/annurev.fl.23.010191.002133.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Brink, K. H., and D. C. Chapman, 1985: Programs for computing properties of coastal-trapped waves and wind-driven motions over the continental shelf and slope. Woods Hole Oceanographic Institution Tech. Rep. WHOI-85-17, 99 pp., https://doi.org/10.1575/1912/5363.

    • Crossref
    • Export Citation
  • Church, J. A., H. J. Freeland, and R. L. Smith, 1986: Coastal-trapped waves on the east Australian continental shelf—Part I: Propagation of modes. J. Phys. Oceanogr., 16, 19291943, https://doi.org/10.1175/1520-0485(1986)016<1929:CTWOTE>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Clarke, A. J., 1977: Observational and numerical evidence for wind-forced coastal trapped long waves. J. Phys. Oceanogr., 7, 231247, https://doi.org/10.1175/1520-0485(1977)007<0231:OANEFW>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Craig, P. D., and P. E. Holloway, 1993: The influence of coastally trapped waves on the circulation in Jervis Bay, New South Wales. Dynamics and Exchanges in Estuaries and the Coastal Zone, D. Prandle, Ed., Coastal and Estuarine Studies, Vol. 40, Amer. Geophys. Union, 9–33, https://doi.org/10.1029/CE040p0009.

    • Crossref
    • Export Citation
  • Csanady, G. T., 1967: Large‐scale motion in the Great Lakes. J. Geophys. Res., 72, 41514162, https://doi.org/10.1029/JZ072i016p04151.

  • Dee, D. P., and et al. , 2011: The ERA-Interim reanalysis: Configuration and performance of the data assimilation system. Quart. J. Roy. Meteor. Soc., 137, 553597, https://doi.org/10.1002/qj.828.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Ding, Y., X. Bao, and M. Shi, 2012: Characteristics of coastal trapped waves along the northern coast of the South China Sea during year 1990. Ocean Dyn., 62, 12591285, https://doi.org/10.1007/s10236-012-0563-3.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Freeland, H. J., and et al. , 1986: The Australian Coastal Experiment: A search for coastal-trapped waves. J. Phys. Oceanogr., 16, 12301249, https://doi.org/10.1175/1520-0485(1986)016<1230:TACEAS>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gill, A. E., and A. J. Clarke, 1974: Wind-induced upwelling, coastal currents and sea-level changes. Deep-Sea Res. Oceanogr. Abstr., 21, 325345, https://doi.org/10.1016/0011-7471(74)90038-2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Huthnance, J. M., 1975: On trapped waves over a continental shelf. J. Fluid Mech., 69, 689704, https://doi.org/10.1017/S0022112075001632.

  • Huthnance, J. M., 1978: On coastal trapped waves: Analysis and numerical calculation by inverse iteration. J. Phys. Oceanogr., 8, 7492, https://doi.org/10.1175/1520-0485(1978)008<0074:OCTWAA>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Igeta, Y., T. Watanabe, H. Yamada, K. Takayama, and O. Katoh, 2011: Coastal currents caused by superposition of coastal-trapped waves and near-inertial oscillations observed near the Noto Peninsula, Japan. Cont. Shelf Res., 31, 17391749, https://doi.org/10.1016/j.csr.2011.07.014.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Koch, K. R., 2014: Robust estimations for the nonlinear Gauss Helmert model by the expectation maximization algorithm. J. Geod., 88, 263271, https://doi.org/10.1007/s00190-013-0681-9.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Liao, F., and X. H. Wang, 2018: A study of low-frequency, wind-driven, coastal-trapped waves along the southeast coast of Australia. J. Phys. Oceanogr., 48, 301316, https://doi.org/10.1175/JPO-D-17-0046.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Mellor, G. L., 2004: User’s guide for a three-dimensional, primitive equation, numerical ocean model. Princeton University Rep., 56 pp.

  • Middleton, J. F., 1994: The baroclinic response of straits and bays to coastal-trapped wave scattering. J. Phys. Oceanogr., 24, 521539, https://doi.org/10.1175/1520-0485(1994)024<0521:TBROSA>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Mortimer, C. H., 1963: Frontiers in physical limnology with particular reference to long waves in rotating basins. Proc. Sixth Conf. Great Lakes Research, Ann Arbor, Michigan, University of Michigan and American Society of Limnology and Oceanography, 9–42.

  • Mysak, L. A., 1980: Topographically trapped waves. Annu. Rev. Fluid Mech., 12, 4576, https://doi.org/10.1146/annurev.fl.12.010180.000401.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Oey, L. Y., and P. Chen, 1992: A model simulation of circulation in the northeast Atlantic shelves and seas. J. Geophys. Res., 97, 20 08720 115, https://doi.org/10.1029/92JC01990.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Schumann, E. H., and K. H. Brink, 1990: Coastal-trapped waves off the coast of South Africa: Generation, propagation and current structures. J. Phys. Oceanogr., 20, 12061218, https://doi.org/10.1175/1520-0485(1990)020<1206:CTWOTC>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Smith, R. L., 1978: Poleward propagating perturbations in currents and sea levels along the Peru coast. J. Geophys. Res., 83, 60836092, https://doi.org/10.1029/JC083iC12p06083.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sun, Y.-J., I. Jalón-Rojas, X. H. Wang, and D. Jiang, 2018: Coastal upwelling by wind-driven forcing in Jervis Bay, New South Wales: A numerical study for 2011. Estuarine Coastal Shelf Sci., 206, 101115, https://doi.org/10.1016/j.ecss.2017.11.022.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wang, D.-P., and C. N. K. Mooers, 1976: Coastal-trapped waves in a continuously stratified ocean. J. Phys. Oceanogr., 6, 853863, https://doi.org/10.1175/1520-0485(1976)006<0853:CTWIAC>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wang, X. H., and X. L. Wang, 2003: A numerical study of water circulation in a thermally stratified embayment. J. Ocean Univ. Qingdao (Engl. Ed.), 2, 2434, https://doi.org/10.1007/s11802-003-0022-3.

    • Crossref
    • Search Google Scholar
    • Export Citation
Save