Combined Effect of Rotation and Topography on Shoaling Oceanic Internal Solitary Waves (original) (raw)
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Studies in Applied Mathematics, 2019
This paper presents specific features of solitary wave dynamics within the framework of the Ostrovsky equation with variable coefficients in relation to surface and internal waves in a rotating ocean with a variable bottom topography. For solitary waves moving toward the beach, the terminal decay caused by the rotation effect can be suppressed by the shoaling effect. Two basic examples of a bottom profile are analyzed in detail and supported by direct numerical modelling. One of them is a constant-slope bottom and the other is a specific bottom profile providing a constant amplitude solitary wave. Estimates with real oceanic parameters show that the predicted effects of stable soliton dynamics in a coastal zone can occur, in particular, for internal waves.
The effects of interplay between rotation and shoaling for a solitary wave on variable
arXiv (Cornell University), 2018
This paper presents specific features of solitary wave dynamics within the framework of the Ostrovsky equation with variable coefficients in relation to surface and internal waves in a rotating ocean with a variable bottom topography. For solitary waves moving toward the beach, the terminal decay caused by the rotation effect can be suppressed by the shoaling effect. Two basic examples of a bottom profile are analyzed in detail and supported by direct numerical modelling. One of them is a constant-slope bottom and the other is a specific bottom profile providing a constant amplitude solitary wave. Estimates with real oceanic parameters show that the predicted effects of stable soliton dynamics in a coastal zone can occur, in particular, for internal waves.
Modelling Internal Solitary Waves in the Coastal Ocean
Surveys in Geophysics, 2007
In the coastal oceans, the interaction of currents (such as the barotropic tide) with topography can generate large-amplitude, horizontally propagating internal solitary waves. These waves often occur in regions where the waveguide properties vary in the direction of propagation. We consider the modeling of these waves by nonlinear evolution equations of the Korteweg-de Vries type with variable coefficients, and we describe how these models to describe the shoaling of internal solitary waves over the continental shelf and slope. The theories are compared with various numerical simulations.
Internal solitary waves: propagation, deformation and disintegration
Nonlinear Processes in Geophysics, 2010
In coastal seas and straits, the interaction of barotropic tidal currents with the continental shelf, seamounts or sills is often observed to generate largeamplitude, horizontally propagating internal solitary waves. Typically these waves occur in regions of variable bottom topography, with the consequence that they are often modeled by nonlinear evolution equations of the Kortewegde Vries type with variable coefficients. We shall review how these models are used to describe the propagation, deformation and disintegration of internal solitary waves as they propagate over the continental shelf and slope.
Simulation of the Transformation of Internal Solitary Waves on Oceanic Shelves
Journal of Physical Oceanography, 2004
Due to the horizontal variability of oceanic hydrology (density and current stratification) and the variable depth over the continental shelf, internal solitary waves transform as they propagate shorewards into the coastal zone. If the background variability is smooth enough, a solitary 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 a slowly-varying solitary wave. Direct numerical simulation of the variablecoefficient extended Korteweg-de Vries equation is performed for several oceanic shelves (North-west Shelf of Australia, Malin Shelf Edge, 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 confirms why internal solitons are observed widely in the world's oceans. In some cases the background stratification contains critical points (when the coefficients of the nonlinear terms in the extended Korteweg-de Vries equation change sign), or does not vary sufficiently smoothly; in such cases the solitary wave deforms a group of secondary waves. This stage is studied numerically.
Long Nonlinear Surface and Internal Gravity Waves in a Rotating Ocean
Surveys in Geophysics, 1998
Nonlinear dynamics of surface and internal waves in a stratified ocean under the influence of the Earth's rotation is discussed. Attention is focussed upon guided waves long compared to the ocean depth. The effect of rotation on linear processes is reviewed in detail as well as the existing nonlinear models describing weakly and strongly nonlinear dynamics of long waves. The
Long-term evolution of strongly nonlinear internal solitary waves in a rotating channel
Nonlinear Processes in Geophysics, 2009
The evolution of internal solitary waves (ISWs) propagating in a rotating channel is studied numerically in the framework of a fully-nonlinear, nonhydrostatic numerical model. The aim of modelling efforts was the investigation of strongly-nonlinear effects, which are beyond the applicability of weakly nonlinear theories. Results reveal that small-amplitude waves and sufficiently strong ISWs evolve differently under the action of rotation. At the first stage of evolution an initially two-dimensional ISW transforms according to the scenario described by the rotation modified Kadomtsev-Petviashvili equation, namely, it starts to evolve into a Kelvin wave (with exponential decay of the wave amplitude across the channel) with front curved backwards. This transition is accompanied by a permanent radiation of secondary Poincaré waves attached to the leading wave. However, in a strongly-nonlinear limit not all the energy is transmitted to secondary radiated waves. Part of it returns to the leading wave as a result of nonlinear interactions with secondary Kelvin waves generated in the course of time. This leads to the formation of a slowly attenuating quasi-stationary system of leading Kelvin waves, capable of propagating for several hundreds hours as a localized wave packet. 1 Introduction Oceanic internal solitary waves (ISWs) are typically the most energetic vertical motions of the World Ocean. In some places, their amplitude reach 100 m or even more (Wesson and Gregg, 1988; Yang et al., 2004). These waves produce shear currents and turbulence (Garrett, 2003
Experimental study of the effect of rotation on nonlinear internal waves
Physics of Fluids, 2013
Nonlinear internal waves are commonly observed in the coastal ocean. In the weakly nonlinear long wave régime, they are often modeled by the Korteweg-de Vries equation, which predicts that the long-time outcome of generic localised initial conditions is a train of internal solitary waves. However, when the effect of background rotation is taken into account, it is known from several theoretical and numerical studies that the formation of solitary waves is inhibited, and instead nonlinear wave packets form. In this paper, we report the results from a laboratory experiment at the LEGI-Coriolis Laboratory which describes this process.
Modeling Internal Solitary Waves in the Coastal Ocean
2000
In the coastal oceans, the interaction of currents (such as the barotropic tide) with topography can generate large-amplitude, hori- zontally propagating internal solitary waves. These waves often occur in regions where the waveguide properties vary in the direction of propagation. We consider the modeling of these waves by nonlinear evolution equations of the Korteweg-de Vries type with variable co- ecients,
Izvestiya, Atmospheric and Oceanic Physics, 2020
This review presents theoretical, numerical, and experimental results of a study of the structure and dynamics of weakly nonlinear internal waves in a rotating ocean accumulated over the past 40 years since the time when the approximate equation, called the Ostrovsky equation, was derived in 1978. The relationship of this equation with other well-known wave equations, the integrability of the Ostrovsky equation, and the condition for the existence of stationary solitary waves and envelope solitary waves are discussed. The adiabatic dynamics of Korteweg-de Vries solitons in the presence of fluid rotation is described. The mutual influence of the ocean inhomogeneity and rotation effect on the dynamics of solitary waves is considered. The universality of the Ostrovsky equation as applied to waves in other media (solids, plasma, quark-gluon plasma, and optics) is noted.