A Nonlinear Model of Internal Tide Transformation on the Australian North West Shelf

Holloway, Peter J.; Pelinovsky, Efim; Talipova, Tatiana; Barnes, Belinda

doi:10.1175/1520-0485(1997)027<0871:anmoit>2.0.co;2

Cited by 230 publications

(155 citation statements)

References 27 publications

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“…A useful derivation of the equation is given in Pelinovsky et al (1977). The research prior to 1989 is reviewed in OS, while more recent progress has been made by Pierini (1989), Holloway et al (1997), Gerkema (1996), Lamb and Yan (1996), and Brandt et al (1996) amongst many others.…”

Section: Non-linear Internal Tide Theory: Solitons and Boresmentioning

confidence: 99%

“…Bay of Biscay: Pingree et al, 1983; Australian North-West shelf: Holloway et al, 1997) indicate these internal tide period waves are usually accompanied by higher frequency internal waves, typically in the 10 min±1 h period range. These features are commonly seen in remotely sensed data such as high-resolution imaging radar images from Synthetic Aperture Radar (SAR, Alpers 1985;Gasparovic et al, 1988), in packets separated by the wavelength of the internal tide, and they have been observed to obtain large amplitudes (e.g.…”

Section: Introductionmentioning

confidence: 99%

“…Holloway et al, 1997, Lamb 1994). The classic explanation was detailed by Zabusky and Kruskal (1965), in terms of the theory of non-linear waves formulated by Korteweg and de-Vries (KdV: 1895): initially non-linear e ects steepen the wave to form an internal hydraulic bore, then non-hydrostatic dispersive e ects act to form wave-like instabilities behind the bore which grow, separate, and eventually form a sequence of solitary waves.…”

Section: Introductionmentioning

confidence: 99%

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The evolution of an internal bore at the Malin shelf break

Small¹,

Sawyer²,

Scott³

1999

Ann Geophysicae

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Abstract. Observations of internal waves were made at the Malin shelf edge during SESAME (Shelf Edge Studies Acoustic Measurement Experiment), a part of the NERC LOIS-SES experiment, in August-September 1996. These measurements provide a high resolution dataset demonstrating internal wave generation and propagation. This note presents observations of the evolution of an internal bore. The process is shown clearly in a sequence of thermistor chain tows across the shelf break covering a complete tidal cycle, as the double-sided bore transforms into a group of undulations and eventually into more distinct solitary waveforms. Current structures associated with the bore and waves were also observed by ship-mounted ADCP. Analysis of the waveforms in terms of the linear modes and empirical orthogonal functions (EOFs) indicate the dominance of the ®rst mode, which is typical of a shallow water seasonal thermocline environment. Determination of the phase speed of the waves from the consecutive ship surveys enabled the Doppler shift in the towed data to be removed, allowing analysis of the real length scales of the waves. The bore evolution has been modelled using a ®rst order non-linear KdV model for the ®rst mode, initialised with the waveform in the ®rst survey. Comparison of the model and the observations show close agreement in the amplitudes, length scales, phase speeds and separations of the leading internal waves as they evolve. Finally, analysis of the observed internal wave shapes indicates that, within the uncertainties of measurement, the wave-lengths lie between those predicted by ®rst and second order soliton theory.

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Section: Non-linear Internal Tide Theory: Solitons and Boresmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

The evolution of an internal bore at the Malin shelf break

Small¹,

Sawyer²,

Scott³

1999

Ann Geophysicae

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“…For instance, the Princeton Ocean Model, based on the nonlinear primitive equations, shows a high degree of spatial variability in the amplitude and phase of internal wave currents and vertical displacements [Craig, 1988;Holloway, 1996;Holloway and Barnes, 1998]. On the other hand, weakly nonlinear and weakly dispersive models based on generalizations of the Korteweg-de Vries (KdV) equation also demonstrate the appearance of intense short-scale solitons from the internal tide on the NWS [Smyth & Holloway, 1988;Holloway et al, 1997Holloway et al, , 1999Holloway et al, , 2001Grimshaw et al, 2004]. Together these numerical and theoretical modeling studies demonstrate the important role of each of nonlinearity, dispersion, the Earth's rotation, the bottom slope and the horizontal variability of density stratification and the background current.…”

mentioning

confidence: 99%

“…The basic generalized KdV equation is briefly described in section 2. The coefficients of the model are calculated using the hydrological data on the NWS obtained by Holloway et al (1997Holloway et al ( , 1999; they are presented in section 3. Our results of numerical simulation of the solitary wave dynamics on the NWS are presented in section 4.…”

mentioning

confidence: 99%

Modelling internal solitary waves on the Australian North West Shelf

Grimshaw

Pelinovsky

Stepanyants

et al. 2006

Mar. Freshwater Res.

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Abstract:The transformation of the nonlinear internal tide and the consequent development of internal solitary waves on the Australian North West Shelf is studied numerically in the framework of the generalized rotation-modified Korteweg-de Vries equation. This model contains both nonlinearity (quadratic and cubic), the Coriolis effect, depth variation and horizontal variability of the density stratification. The simulation results demonstrate that a wide variety of nonlinear wave shapes can be explained by the synergetic action of nonlinearity and the variability of the hydrology along the wave path.2

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Observation of internal wave polarity conversion generated by a rising tide

Wang

Grimshaw

2015

Geophysical Research Letters

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The observations reported here are based on time series of in situ observation data in Laoshan Bay off the Qingdao coast. A chain of thermistors (T‐chain) at a fixed location recorded a sequence of elevation internal waves followed by depression internal waves passing by over an elapsed time of about 1 h. This observed polarity conversion at a fixed location is caused by the vertical stratification variation mainly induced by the rising tide, which is believed to be the first reported observation of this kind. The process of an elevation internal wave train converting to a depression wave train is simulated using the variable‐coefficient extended Korteweg‐de Vries (veKdV) equation, which also provides a further comparison between theory and the reported observations.

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A Nonlinear Model of Internal Tide Transformation on the Australian North West Shelf

Cited by 230 publications

References 27 publications

The evolution of an internal bore at the Malin shelf break

The evolution of an internal bore at the Malin shelf break

Modelling internal solitary waves on the Australian North West Shelf

Observation of internal wave polarity conversion generated by a rising tide

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