Resonant excitation of trapped waves by Poincaré waves in the coastal waveguides

2011 ◽  
Vol 673 ◽  
pp. 349-394
Author(s):  
G. M. REZNIK ◽  
V. ZEITLIN
Keyword(s):  
Resonant Interaction ◽  
Resonant Excitation ◽  
Spatial Modulation ◽  
Water Model ◽  
Energy Redistribution ◽  
Waveguide Modes ◽  
Linear Waves ◽  
Excitation Mechanisms ◽  
Poincare Waves ◽  
Rotating Shallow Water

After having revisited the theory of linear waves in the rotating shallow-water model with a straight coast and arbitrary shelf/beach bathymetry, we undertake a detailed study of resonant interaction of free Poincaré waves with modes trapped in the coastal waveguide. We describe and quantify the mechanisms of resonant excitation of waveguide modes and their subsequent nonlinear saturation. We obtain the modulation equations for the amplitudes of excited waveguide modes in the absence and in the presence of spatial modulation and analyse their solutions. Different saturation regimes are exhibited, depending on the nature of the modes involved. The excitation is proved to be efficient, i.e. the saturated amplitudes of the excited waves considerably exceed the amplitude of the generator waves. Back-influence of the excited waveguide modes onto the open ocean results in a phase shift of the reflected Poincaré waves and possible energy redistribution between them. A comparison of rotating and non-rotating cases displays substantial differences in excitation mechanisms in the two cases.

Explicit nonlinear waves of fluid models on extended domains and unbounded growth with backscatter

2020 ◽  
Author(s):  
Artur Prugger ◽  
Jens Rademacher
Keyword(s):  
Nonlinear Waves ◽  
Large Scale ◽  
Water Model ◽  
Explicit Solutions ◽  
Stationary Waves ◽  
Fluid Models ◽  
Fully Nonlinear ◽  
Geostrophic Balance ◽  
Linear Waves ◽  
Rotating Shallow Water

<p>Large scale motions in geophysical fluid models are often characterised by linear waves, which are obtained by linearising the equations. But there are also many explicit solutions of the fully nonlinear equations when posed the full space. The exact solutions we are investigating often characterise Rossby waves, since they are in geostrophic balance. They also can be compositions of waves, some are interacting with each other and some do not, showing wave interactions as explicit solutions in the fully nonlinear problem.</p><p>In this talk I will briefly introduce the idea behind these explicit nonlinear waves and show some of their properties, and their occurrence in different fluid models in extended domains.</p><p>As an application, we especially focus on a rotating shallow water model with simplified backscatter. In this case one finds not only geostrophic explicit solutions, but also ageostrophic ones. Moreover, here energy accumulates in selected scales due to the backscatter terms and causes exponentially and unboundedly growing ageostrophic nonlinear waves. This also relates to instability of coexisting stationary waves and is an instance of the role of nonlinear waves in energy transfer, and illustrates their role in preventing energy equidistribution for general data.</p>

scholarly journals Resonant excitation of coastal Kelvin waves in the two-layer rotating shallow water model

2013 ◽  
Vol 20 (6) ◽  
pp. 993-999 ◽  
Author(s):  
V. Zeitlin
Keyword(s):  
Shallow Water ◽  
Kelvin Waves ◽  
Resonant Excitation ◽  
Water Model ◽  
Coastal Current ◽  
Kelvin Wave ◽  
Baroclinic Model ◽  
Rotating Shallow Water ◽  
The One ◽  
Coastal Kelvin Waves

Abstract. Resonant excitation of coastal Kelvin waves by free inertia–gravity waves impinging on the coast is studied in the framework of the simplest baroclinic model: two-layer rotating shallow water with an idealized straight coast. It is shown that, with respect to the previous results obtained with the one-layer model, new resonances leading to a possible excitation of Kelvin waves appear. The most interesting ones, described in the paper, are resonances of a baroclinic inertia–gravity wave with either another wave of this kind, or with a coastal current, leading to generation of a barotropic Kelvin wave. A forced Hopf equation results in any case for the evolution of the Kelvin wave amplitude.

Instabilities of coupled density fronts and their nonlinear evolution in the two-layer rotating shallow-water model: influence of the lower layer and of the topography

2013 ◽  
Vol 716 ◽  
pp. 528-565 ◽  
Author(s):  
Bruno Ribstein ◽  
Vladimir Zeitlin
Keyword(s):  
Shallow Water ◽  
Nonlinear Evolution ◽  
Lower Layer ◽  
Phase Locking ◽  
Water Model ◽  
Shallow Water Model ◽  
Wave Instability ◽  
Rotating Shallow Water ◽  
New Generation ◽  
Rotating Shallow Water Equations

AbstractWe undertake a detailed analysis of linear stability of geostrophically balanced double density fronts in the framework of the two-layer rotating shallow-water model on the $f$-plane with topography, the latter being represented by an escarpment beneath the fronts. We use the pseudospectral collocation method to identify and quantify different kinds of instabilities resulting from phase locking and resonances of frontal, Rossby, Poincaré and topographic waves. A swap in the leading long-wave instability from the classical barotropic form, resulting from the resonance of two frontal waves, to a baroclinic form, resulting from the resonance of Rossby and frontal waves, takes place with decreasing depth of the lower layer. Nonlinear development and saturation of these instabilities, and of an instability of topographic origin, resulting from the resonance of frontal and topographic waves, are studied and compared with the help of a new-generation well-balanced finite-volume code for multilayer rotating shallow-water equations. The results of the saturation for different instabilities are shown to produce very different secondary coherent structures. The influence of the topography on these processes is highlighted.

scholarly journals Improved moist-convective rotating shallow water model and its application to instabilities of hurricane-like vortices

2018 ◽  
Author(s):  
LMD
Keyword(s):  
Tropical Cyclone ◽  
Shallow Water ◽  
Water Vapour ◽  
Large Scale ◽  
Precipitable Water ◽  
Water Model ◽  
Moist Convection ◽  
Shallow Water Model ◽  
Atmospheric Motions ◽  
Rotating Shallow Water

We show how the two-layer moist-convective rotating shallow water model (mcRSW), which proved to be a simple and robust tool for studying effects of moist convection on large-scale atmospheric motions, can be improved by including, in addition to the water vapour, precipitable water, and the effects of vaporisation, entrainment, and precipitation. Thus improved mcRSW becomes cloud-resolving. It is applied, as an illustration, to model the development of instabilities of tropical cyclone-like vortices.

scholarly journals Symmetries and exact solutions of the rotating shallow-water equations

2009 ◽  
Vol 20 (5) ◽  
pp. 461-477 ◽  
Author(s):  
A. A. CHESNOKOV
Keyword(s):  
Exact Solutions ◽  
Shallow Water ◽  
Shallow Water Equations ◽  
Water Model ◽  
New Class ◽  
New Exact Solutions ◽  
Time Periodic Solutions ◽  
Rotating Shallow Water ◽  
Rotating Shallow Water Equations ◽  
Time Periodic

Lie symmetry analysis is applied to study the non-linear rotating shallow-water equations. The 9-dimensional Lie algebra of point symmetries admitted by the model is found. It is shown that the rotating shallow-water equations can be transformed to the classical shallow-water model. The derived symmetries are used to generate new exact solutions of the rotating shallow-water equations. In particular, a new class of time-periodic solutions with quasi-closed particle trajectories is constructed and studied. The symmetry reduction method is also used to obtain some invariant solutions of the model. Examples of these solutions are presented with a brief physical interpretation.

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