Scattering of internal tides by irregular bathymetry of large extent

2014 ◽  
Vol 747 ◽  
pp. 481-505 ◽  
Author(s):  
Yile Li ◽  
Chiang C. Mei
Keyword(s):  
Gravity Waves ◽  
Method Of Characteristics ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Internal Gravity Waves ◽  
Internal Tides ◽  
Two Dimensional ◽  
One Dimensional ◽  
Stratified Ocean ◽  
Stationary Random Function

AbstractWe present an analytical theory of scattering of tide-generated internal gravity waves in a continuously stratified ocean with a randomly rough seabed. Based on a linearized approximation, the idealized case of constant mean sea depth and Brunt–Väisälä frequency is considered. The depth fluctuation is assumed to be a stationary random function of space, characterized by small amplitude and a correlation length comparable to the typical wavelength. For both one- and two-dimensional topographies the effects of scattering on the wave phase over long distances are derived explicitly by the method of multiple scales. For one-dimensional topography, numerical results are compared with Bühler & Holmes-Cerfon (J. Fluid Mech., vol. 678, 2011, pp. 271–293), computed by the method of characteristics. For two-dimensional topography, new results are presented for both statistically isotropic and anisotropic cases.

On the damping of internal gravity waves in a continuously stratified ocean

1966 ◽  
Vol 25 (1) ◽  
pp. 121-142 ◽  
Author(s):  
Paul H. LeBlond
Keyword(s):  
Internal Waves ◽  
Gravity Waves ◽  
Internal Gravity Waves ◽  
Bottom Friction ◽  
Internal Tides ◽  
Attenuation Rate ◽  
Mixing Coefficients ◽  
Stratified Ocean ◽  
Shallow Seas ◽  
Strongly Damped

The problem studied here is that of the attenuation of internal waves through turbulent mixing in a weakly and exponentially stratified fluid. The equations are linearized and it is assumed that the action of turbulence can be parametrically represented by eddy mixing coefficients and that the influence of bottom friction is restricted to a thin bottom boundary layer. The simple case where there is no rotation and only one component to the stratification is first examined in detail, and the modifications caused by introducing rotation and a second component are subsequently investigated. Subject quantitatively to the choice made for the eddy coefficients, but qualitatively not strongly dependent on that choice, the following conclusions are drawn: (i) very short internal waves (length < 100 m) are strongly damped in basins of all depths; (ii) long internal waves or seiches in shallow seas (depth ≃ 100 m) will not last more than a few cycles as free oscillations; (iii) the attenuation rate for long internal tides is small enough that these should be observable very far from the coasts, but large enough to exclude the possibility of oceanic standing wave systems; (iv) for very long internal waves the damping is predominantly due to the effect of bottom friction, and the attenuation rate becomes almost independent of the actual form of the stratification present in the fluid.

scholarly journals Interaction Features of Internal Wave Breathers in a Stratified Ocean

Fluids ◽  
2020 ◽  
Vol 5 (4) ◽  
pp. 205
Author(s):  
Ekaterina Didenkulova ◽  
Efim Pelinovsky
Keyword(s):  
Internal Wave ◽  
Internal Waves ◽  
Gravity Waves ◽  
Fourth Order ◽  
Numerical Experiments ◽  
Vries Equation ◽  
Internal Gravity Waves ◽  
Wave Fields ◽  
Tidal Waves ◽  
Stratified Ocean

Oscillating wave packets (breathers) are a significant part of the dynamics of internal gravity waves in a stratified ocean. The formation of these waves can be provoked, in particular, by the decay of long internal tidal waves. Breather interactions can significantly change the dynamics of the wave fields. In the present study, a series of numerical experiments on the interaction of breathers in the frameworks of the etalon equation of internal waves—the modified Korteweg–de Vries equation (mKdV)—were conducted. Wave field extrema, spectra, and statistical moments up to the fourth order were calculated.

scholarly journals On the appearance of internal wave attractors due to an initial or parametrically excited disturbance

2013 ◽  
Vol 714 ◽  
pp. 283-311 ◽  
Author(s):  
Janis Bajars ◽  
Jason Frank ◽  
Leo R. M. Maas
Keyword(s):  
Gravity Waves ◽  
Normal Modes ◽  
Internal Gravity Waves ◽  
Harmonic Oscillators ◽  
Two Dimensional ◽  
Boussinesq Model ◽  
Resonant Modes ◽  
The Waves ◽  
Shaped Domain ◽  
Parametric Forcing

AbstractIn this paper we solve two initial value problems for two-dimensional internal gravity waves. The waves are contained in a uniformly stratified, square-shaped domain whose sidewalls are tilted with respect to the direction of gravity. We consider several disturbances of the initial stream function field and solve both for its free evolution and for its evolution under parametric excitation. We do this by developing a structure-preserving numerical method for internal gravity waves in a two-dimensional stratified fluid domain. We recall the linearized, inviscid Euler–Boussinesq model, identify its Hamiltonian structure, and derive a staggered finite difference scheme that preserves this structure. For the discretized model, the initial condition can be projected onto normal modes whose dynamics is described by independent harmonic oscillators. This fact is used to explain the persistence of various classes of wave attractors in a freely evolving (i.e. unforced) flow. Under parametric forcing, the discrete dynamics can likewise be decoupled into Mathieu equations. The most unstable resonant modes dominate the solution, forming wave attractors.

scholarly journals An Energy Compartment Model for Propagation, Nonlinear Interaction, and Dissipation of Internal Gravity Waves

2014 ◽  
Vol 44 (8) ◽  
pp. 2093-2106 ◽  
Author(s):  
Carsten Eden ◽  
Dirk Olbers
Keyword(s):  
Gravity Waves ◽  
Bottom Topography ◽  
Compartment Model ◽  
Tidal Energy ◽  
Internal Gravity Waves ◽  
Internal Tides ◽  
Continental Margins ◽  
Wave Interactions ◽  
Dissipation Energy ◽  
Parametric Subharmonic Instability

Abstract The recently proposed Internal Wave Dissipation, Energy and Mixing (IDEMIX) model, describing the propagation and dissipation of internal gravity waves in the ocean, is extended. Compartments describing the energy contained in the internal tides and the near-inertial waves at low, vertical wavenumber are added to a compartment of the wave continuum at higher wavenumbers. Conservation equations for each compartment are derived based on integrated versions of the radiative transfer equation of weakly interacting waves. The compartments interact with each other by the scattering of tidal energy to the wave continuum by triad wave–wave interactions, which are strongly enhanced equatorward of 28° due to parametric subharmonic instability of the tide and by scattering to the continuum of both tidal and near-inertial wave energy over rough topography and at continental margins. Global numerical simulations of the resulting model using observed stratification, forcing functions, and bottom topography yield good agreement with available observations.

scholarly journals Momentum Flux Spectrum of Convectively Forced Internal Gravity Waves and Its Application to Gravity Wave Drag Parameterization. Part I: Theory

2005 ◽  
Vol 62 (1) ◽  
pp. 107-124 ◽  
Author(s):  
In-Sun Song ◽  
Hye-Yeong Chun
Keyword(s):  
Gravity Waves ◽  
Momentum Flux ◽  
Three Dimensional ◽  
Internal Gravity Waves ◽  
Buoyancy Frequency ◽  
Spectral Structure ◽  
Two Dimensional ◽  
Resonance Factor ◽  
Flux Spectrum ◽  
Wave Momentum

Abstract The phase-speed spectrum of momentum flux by convectively forced internal gravity waves is analytically formulated in two- and three-dimensional frameworks. For this, a three-layer atmosphere that has a constant vertical wind shear in the lowest layer, a uniform wind above, and piecewise constant buoyancy frequency in a forcing region and above is considered. The wave momentum flux at cloud top is determined by the spectral combination of a wave-filtering and resonance factor and diabatic forcing. The wave-filtering and resonance factor that is determined by the basic-state wind and stability and the vertical configuration of forcing restricts the effectiveness of the forcing, and thus only a part of the forcing spectrum can be used for generating gravity waves that propagate above cumulus clouds. The spectral distribution of the wave momentum flux is largely determined by the wave-filtering and resonance factor, but the magnitude of the momentum flux varies significantly according to spatial and time scales and moving speed of the forcing. The wave momentum flux formulation in the two-dimensional framework is extended to the three-dimensional framework. The three-dimensional momentum flux formulation is similar to the two-dimensional one except that the wave propagation in various horizontal directions and the three-dimensionality of forcing are allowed. The wave momentum flux spectrum formulated in this study is validated using mesoscale numerical model results and can reproduce the overall spectral structure and magnitude of the wave momentum flux spectra induced by numerically simulated mesoscale convective systems reasonably well.

Transport by breaking internal gravity waves on slopes

2016 ◽  
Vol 789 ◽  
pp. 93-126 ◽  
Author(s):  
Robert S. Arthur ◽  
Oliver B. Fringer
Keyword(s):  
Gravity Waves ◽  
Wave Breaking ◽  
Internal Gravity Waves ◽  
Length Scale ◽  
Two Dimensional ◽  
Turbulent Diffusivity ◽  
Nepheloid Layer ◽  
Molecular Diffusivity ◽  
Tracking Model ◽  
Offshore Transport

We use the results of a direct numerical simulation (DNS) with a particle-tracking model to investigate three-dimensional transport by breaking internal gravity waves on slopes. Onshore transport occurs within an upslope surge of dense fluid after breaking. Offshore transport occurs due to an intrusion of mixed fluid that propagates offshore and resembles an intermediate nepheloid layer (INL). Entrainment of particles into the INL is related to irreversible mixing of the density field during wave breaking. Maximum onshore and offshore transport are calculated as a function of initial particle position, and can be of the order of the initial wave length scale for particles initialized within the breaking region. An effective cross-shore dispersion coefficient is also calculated, and is roughly three orders of magnitude larger than the molecular diffusivity within the breaking region. Particles are transported laterally due to turbulence that develops during wave breaking, and this lateral spreading is quantified with a lateral turbulent diffusivity. Lateral turbulent diffusivity values calculated using particles are elevated by more than one order of magnitude above the molecular diffusivity, and are shown to agree well with turbulent diffusivities estimated using a generic length scale turbulence closure model. Based on a favourable comparison of DNS results with those of a similar two-dimensional case, we use two-dimensional simulations to extend our cross-shore transport results to additional wave amplitude and bathymetric slope conditions.

scholarly journals (2+1)-Dimensional Davey-Stewartson II Equation for a Two-Dimensional Nonlinear Monatomic Lattice

2006 ◽  
Vol 61 (1-2) ◽  
pp. 45-52 ◽  
Author(s):  
Zhi-Fang Li ◽  
Hang-Yu Ruan
Keyword(s):  
Rational Function ◽  
Nearest Neighbor ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Soliton Solutions ◽  
Explicit Solutions ◽  
Two Dimensional ◽  
Difference System ◽  
Leading Order ◽  
Neighbor Interaction

A two-dimensional monatomic lattice with nearest-neighbor interaction is investigated by the method of multiple scales combined with a quasidiscreteness approximation. The Davey-Stewartson II equation (DS-II) is obtained from the original two-dimensional (2D) differential-difference system. By solving the DS-II, explicit periodic solutions, soliton solutions and rational function solutions are obtained, and the leading order approximated solutions of the 2D monatomic lattice are constructed by explicit solutions of the DS-II.

On Nonlinear Modes of Continuous Systems

1994 ◽  
Vol 116 (1) ◽  
pp. 129-136 ◽  
Author(s):  
A. H. Nayfeh ◽  
S. A. Nayfeh
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Boundary Conditions ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Continuous Systems ◽  
Partial Differential ◽  
Nonlinear Beam ◽  
Nonlinear Modes ◽  
One Dimensional

We use several methods to study the nonlinear modes of one-dimensional continuous systems with cubic inertia and geometric nonlinearities. Invariant manifold and perturbation methods applied to the discretized system and the method of multiple scales applied to the partial-differential equation and boundary conditions are discussed and their equivalence is demonstrated. The method of multiple scales is then applied directly to the partial-differential equation and boundary conditions governing several nonlinear beam problems.

Sign in / Sign up

Export Citation Format

Share Document