Modelling Internal Solitary Waves in the Coastal Ocean (original) (raw)
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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,
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.
Ocean Science, 2017
Numerical solutions of the Kortewegde Vries (KdV) and extended Korteweg-de Vries (eKdV) equations are used to model the transformation of a sinusoidal internal tide as it propagates across the continental shelf. The ocean is idealized as being a two-layer fluid, justified by the fact that most of the oceanic internal wave signal is contained in the gravest mode. The model accounts for nonlinear and dispersive effects but neglects friction, rotation and mean shear. The KdV model is run for a number of idealized stratifications and unique realistic topographies to study the role of the nonlinear and dispersive effects. In all model solutions the internal tide steepens forming a sharp front from which a packet of nonlinear solitary-like waves evolve. Comparisons between KdV and eKdV solutions are made. The model results for realistic topography and stratification are compared with observations made at moorings off Massachusetts in the Middle Atlantic Bight. Some features of the observations compare well with the model. The leading face of the internal tide steepens to form a shock-like front, while nonlinear high-frequency waves evolve shortly after the appearance of the jump. Although not rank ordered, the wave of maximum amplitude is always close to the jump. Some features of the observations are not found in the model. Nonlinear waves can be very widely spaced and persist over a tidal period.
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.
Combined Effect of Rotation and Topography on Shoaling Oceanic Internal Solitary Waves
Journal of Physical Oceanography, 2014
Internal solitary waves commonly observed in the coastal ocean are often modeled by a nonlinear evolution equation of the Korteweg–de Vries type. Because these waves often propagate for long distances over several inertial periods, the effect of Earth’s background rotation is potentially significant. The relevant extension of the Kortweg–de Vries is then the Ostrovsky equation, which for internal waves does not support a steady solitary wave solution. Recent studies using a combination of asymptotic theory, numerical simulations, and laboratory experiments have shown that the long time effect of rotation is the destruction of the initial internal solitary wave by the radiation of small-amplitude inertia–gravity waves, and the eventual emergence of a coherent, steadily propagating, nonlinear wave packet. However, in the ocean, internal solitary waves are often propagating over variable topography, and this alone can cause quite dramatic deformation and transformation of an internal s...
Modeling internal solitary waves on the Australian North West Shelf
2005
The transformation of nonlinear internal waves and the development of internal solitary waves on the Australian North West Shelf is studied numerically in the framework of the generalized 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 computed results demonstrate that a wide variety of nonlinear wave shapes can be explained by the synergetic action of cubic nonlinearity and the variability of the hydrology along the wave path.
Modelling internal solitary waves on the Australian North West Shelf
Marine and Freshwater Research, 2006
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.
Structure of Large-Amplitude Internal Solitary Waves
Journal of Physical Oceanography, 2000
The horizontal and vertical structure of large-amplitude internal solitary waves propagating in stratified waters on a continental shelf is investigated by analyzing the results of numerical simulations and in situ measurements. Numerical simulations aimed at obtaining stationary, solitary wave solutions of different amplitudes were carried out using a nonstationary model based on the incompressible two-dimensional Euler equations in the frame of the Boussinesq approximation. The numerical solutions, which refer to different density stratifications typical for midlatitude continental shelves, were obtained by letting an initial disturbance evolve according to the numerical model. Several intriguing characteristics of the structure of the simulated large-amplitude internal solitary waves like, for example, wavelength-amplitude and phase speed-amplitude relationship as well as form of the locus of zero horizontal velocity emerge, consistent with those obtained previously using stationary Euler models. The authors' approach, which tends to exclude unstable oceanic internal solitary waves as they are filtered out during the evolution process, was also employed to perform a detailed comparison between model results and characteristics of large-amplitude internal solitary waves found in high-resolution in situ data acquired north and south of the Strait of Messina, in the Mediterranean Sea. From this comparison the importance of using higher-order theoretical models for a detailed description of large-amplitude internal solitary waves observed in the real ocean emerge. Implications of the results showing the complexity related to a possible inversion of sea surface manifestations of oceanic internal solitary waves into characteristics of the interior ocean dynamics are finally discussed.
Large Internal Solitary Waves in Shallow Waters
2018
The propagation of finite amplitude internal waves over an uneven bottom is considered. One of the specific features of the large amplitude internal waves is the ability of the waves to carry fluid in the “trapped core” for a long distance. The velocity of particles in the “trapped core” is very close and, even, exceeds the wave speed. Such waves are detected in different parts of seas and oceans as internal waves of depression and elevation as well as short intrusions at interfaces. Laboratory experiments on the generation, interaction and decay of solitary waves in a two-layer fluid are discussed. Analytical and numerical solutions describing the evolution of internal waves in a shelf zone are constructed by the three-layer shallow water model. Laboratory investigations of the different types of internal waves (bottom, subsurface and interlayer waves) are demonstrating, that the model can be effectively applied to the numerical solution of unsteady wave motions, and the traveling ...
Breaking Location of Internal Solitary Waves Over a Sloping Seabed
Journal of Geophysical Research: Oceans, 2020
We present a semi‐analytical model for predicting the breaking location of internal solitary waves (ISWs) over a sloping seabed. Our conceptual model is based on laboratory experiments, performed in a wave tank, that reproduce the ISW breaking mechanisms and show how the steepening of the trailing edge leads to verticalization of the wave profile during the shoaling phase. We derive the location of ISWs breaking, that is, the wave verticalization point, through two‐layer, interfacial theoretical models and conservation of wave mass. We apply our model to the case of tidally forced ISWs that are generated in the Strait of Messina (Central Mediterranean Sea), where northward traveling ISWs are expected to refract and break over the frontal slope of Capo Vaticano. Our application is then assessed through numerical investigations, which allow to consider realistic field conditions in terms of water column stratification and geometrical setting. Our results, and the expected ISW‐induced ...