scholarly journals Modelling internal solitary waves on the Australian North West Shelf

2006 ◽  
Vol 57 (3) ◽  
pp. 265 ◽  
Author(s):  
Roger Grimshaw ◽  
Efim Pelinovsky ◽  
Yury Stepanyants ◽  
Tatiana Talipova
Keyword(s):  
Solitary Waves ◽  
Vries Equation ◽  
Internal Tide ◽  
Internal Solitary Waves ◽  
Linear Wave ◽  
North West ◽  
Non Linear ◽  
Wave Path ◽  
Simulation Results ◽  
Synergetic Action

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

Simulation of the Transformation of Internal Solitary Waves on Oceanic Shelves

2004 ◽  
Vol 34 (12) ◽  
pp. 2774-2791 ◽  
Author(s):  
Roger Grimshaw ◽  
Efim Pelinovsky ◽  
Tatiana Talipova ◽  
Audrey Kurkin
Keyword(s):  
Solitary Wave ◽  
Solitary Waves ◽  
Variable Coefficient ◽  
Asymptotic Theory ◽  
Vries Equation ◽  
Internal Solitary Waves ◽  
Variable Depth ◽  
North West ◽  
Wave Parameters ◽  
De Vries

Abstract Internal solitary waves transform as they propagate shoreward over the continental shelf into the coastal zone, from a combination of the horizontal variability of the oceanic hydrology (density and current stratification) and the variable depth. If this background environment varies sufficiently slowly in comparison with an individual solitary wave, then that wave possesses a soliton-like form with varying amplitude and phase. This stage is studied in detail in the framework of the variable-coefficient extended Korteweg–de Vries equation where the variation of the solitary wave parameters can be described analytically through an asymptotic description as a slowly varying solitary wave. Direct numerical simulation of the variable-coefficient extended Korteweg–de Vries equation is performed for several oceanic shelves (North West shelf of Australia, Malin shelf edge, and Arctic shelf) to demonstrate the applicability of the asymptotic theory. It is shown that the solitary wave may maintain its soliton-like form for large distances (up to 100 km), and this fact helps to explain why internal solitons are widely observed in the world's oceans. In some cases the background stratification contains critical points (where the coefficients of the nonlinear terms in the extended Korteweg–de Vries equation change sign), or does not vary sufficiently slowly; in such cases the solitary wave deforms into a group of secondary waves. This stage is studied numerically.

Internal wave energetics modulated by Indonesian Throughflow at Lombok Strait

2020 ◽  
Author(s):  
Zhenhua Xu
Keyword(s):  
Solitary Waves ◽  
Southern Oscillation ◽  
Internal Tide ◽  
Internal Tides ◽  
Internal Solitary Waves ◽  
Indonesian Throughflow ◽  
Indonesian Seas ◽  
The North ◽  
Tide Propagation ◽  
Seasonal And Interannual Variations

<p>The interaction between the energetic internal waves in the Indonesian Seas and the Indonesian Throughflow (ITF) is not well known. Here we conduct a series of high-resolution numerical simulations surrounding the Lombok Strait, Indonesia, which is an important exit channel for the ITF, to explore the influences of the ITF on the spatiotemporal variations of M2 internal tides and associated internal solitary waves from the Strait. The ITF enhances the north-south asymmetry of internal tide propagation from the Lombok Strait, thus resulting in the spatial variability of northward and southward internal solitary waves. Interannual variability of internal tide generation and dissipation are due to ITF and air-sea freshwaterflux induced stratification variations associated with El Niño-Southern Oscillation. The local dissipation efficiency q exhibits substantial seasonal and interannual variations, which may provide effective feedback to the climate processes in the low-latitude equatorial oceans.</p>

scholarly journals Higher-order Korteweg-de Vries models for internal solitary waves in a stratified shear flow with a free surface

2002 ◽  
Vol 9 (3/4) ◽  
pp. 221-235 ◽  
Author(s):  
R. Grimshaw ◽  
E. Pelinovsky ◽  
O. Poloukhina
Keyword(s):  
Free Surface ◽  
Shear Flow ◽  
Solitary Waves ◽  
Vries Equation ◽  
Wave Theory ◽  
Higher Order ◽  
Internal Solitary Waves ◽  
Long Wave ◽  
De Vries ◽  
Stratified Shear Flow

Abstract. A higher-order extension of the familiar Korteweg-de Vries equation is derived for internal solitary waves in a density- and current-stratified shear flow with a free surface. All coefficients of this extended Korteweg-de Vries equation are expressed in terms of integrals of the modal function for the linear long-wave theory. An illustrative example of a two-layer shear flow is considered, for which we discuss the parameter dependence of the coefficients in the extended Korteweg-de Vries equation.

scholarly journals Internal Solitary Waves in the Andaman Sea Revealed by Long-term Mooring Observations

2021 ◽  
Author(s):  
Yunchao Yang ◽  
Xiaodong Huang ◽  
Wei Zhao ◽  
Chun Zhou ◽  
Siwei Huang ◽  
...  
Keyword(s):  
Solitary Waves ◽  
Internal Tide ◽  
Equatorial Indian Ocean ◽  
Temporal Variations ◽  
Andaman Sea ◽  
Internal Solitary Waves ◽  
Release Mechanism ◽  
Annual Variations ◽  
Northern Portion

AbstractThe complex behaviors of internal solitary waves (ISWs) in the Andaman Sea were revealed using data collected over nearly 22-month-long observation period completed by two moorings. Emanating from the submarine ridges northwest of Sumatra Island and south of Car Nicobar, two types of ISWs, referred to as S- and C-ISWs, respectively, were identified in the measurements, and S-ISWs were generally found to be stronger than C-ISWs. The observed S- and C-ISWs frequently appeared as multi-wave packets, accounting for 87% and 43% of their observed episodes, respectively. The simultaneous measurements collected by the two moorings featured evident variability along the S-ISW crests, with the average wave amplitude in the northern portion being 36% larger than that in the southern portion. The analyses of the arrival times revealed that the S-ISWs in the northern portion occurred more frequently and arrived more irregularly than those in the southern portion. Moreover, the temporal variability of ISWs drastically differed on monthly and seasonal time scales, characterized by relatively stronger S-ISWs in spring and autumn. Over interannual time scale, the temporal variations in ISWs were generally subtle. The monthly-to-annual variations of ISWs could be mostly explained by the variability in stratification, which could be modulated by the monsoons, the winds in equatorial Indian Ocean and the mesoscale eddies in Andaman Sea. From careful analyses preformed based on the long-term measurements, we argued that the observed ISWs were likely generated via internal tide release mechanism and their generation processes were obviously modulated by background circulations.

Interaction of Fully-Nonlinear Internal Solitary Waves of Opposite Polarity

2021 ◽  
Author(s):  
Kevin Lamb
Keyword(s):  
Wave Field ◽  
Solitary Waves ◽  
Kdv Equation ◽  
Nonlinear Coefficient ◽  
Opposite Polarity ◽  
Internal Solitary Waves ◽  
Linear Wave ◽  
Gardner Equation ◽  
Fully Nonlinear ◽  
The Kdv Equation

<p>Previous studies have suggested that fully nonlinear internal solitary waves (ISWs) are very soliton-like as the interaction of two ISWs results in only very small changes in amplitude of the interacting ISWs and in the production of a very small amplitude wave train. Previous studies have, however, considered ISWs with the polarity predicted by the sign of the quadratic nonlinear coefficient of the KdV equation. The Gardner equation, which is an extension of the KdV equation that includes a cubic nonlinear term, has ISWs of two polarities (i.e., waves of depression and elevation) when the cubic coefficient of the Gardner equation is positive. These waves are soliton solutions of the Gardner equations.  In this talk I will discuss the interaction of ISWs of opposite polarity in continuous asymmetric three layer stratifications. Regions in parameter space where ISWs of opposite polarity exist will be discussed and I will demonstrate via fully nonlinear numerical simulations that the interaction of ISWs of opposite polarity waves are far from soliton-like: their interaction can result in very large changes in wave amplitude and may produce a very complicated wave field with multiple large ISWs, a large linear wave field and breather-like waves.<span> </span></p>

scholarly journals Internal solitary wave generation by tidal flow over topography

2018 ◽  
Vol 839 ◽  
pp. 387-407 ◽  
Author(s):  
R. Grimshaw ◽  
K. R. Helfrich
Keyword(s):  
Froude Number ◽  
Solitary Waves ◽  
Vries Equation ◽  
Tidal Flow ◽  
Phase Speed ◽  
Wave Generation ◽  
Equation Model ◽  
Internal Solitary Waves ◽  
Generation Process ◽  
De Vries

Oceanic internal solitary waves are typically generated by barotropic tidal flow over localised topography. Wave generation can be characterised by the Froude number $F=U/c_{0}$, where $U$ is the tidal flow amplitude and $c_{0}$ is the intrinsic linear long wave phase speed, that is the speed in the absence of the tidal current. For steady tidal flow in the resonant regime, $\unicode[STIX]{x1D6E5}_{m}<F-1<\unicode[STIX]{x1D6E5}_{M}$, a theory based on the forced Korteweg–de Vries equation shows that upstream and downstream propagating undular bores are produced. The bandwidth limits $\unicode[STIX]{x1D6E5}_{m,M}$ depend on the height (or depth) of the topographic forcing term, which can be either positive or negative depending on whether the topography is equivalent to a hole or a sill. Here the wave generation process is studied numerically using a forced Korteweg–de Vries equation model with time-dependent Froude number, $F(t)$, representative of realistic tidal flow. The response depends on $\unicode[STIX]{x1D6E5}_{max}=F_{max}-1$, where $F_{max}$ is the maximum of $F(t)$ over half of a tidal cycle. When $\unicode[STIX]{x1D6E5}_{max}<\unicode[STIX]{x1D6E5}_{m}$ the flow is always subcritical and internal solitary waves appear after release of the downstream disturbance. When $\unicode[STIX]{x1D6E5}_{m}<\unicode[STIX]{x1D6E5}_{max}<\unicode[STIX]{x1D6E5}_{M}$ the flow reaches criticality at its peak, producing upstream and downstream undular bores that are released as the tide slackens. When $\unicode[STIX]{x1D6E5}_{max}>\unicode[STIX]{x1D6E5}_{M}$ the tidal flow goes through the resonant regime twice, producing undular bores with each passage. The numerical simulations are for both symmetrical topography, and for asymmetric topography representative of Stellwagen Bank and Knight Inlet.

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