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.

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.

A conservation law for internal gravity waves

1976 ◽  
Vol 78 (2) ◽  
pp. 209-216 ◽  
Author(s):  
Michael Milder
Keyword(s):  
Internal Wave ◽  
Group Velocity ◽  
Internal Waves ◽  
Gravity Waves ◽  
Conservation Law ◽  
Short Wavelength ◽  
Internal Gravity Waves ◽  
Volume Integral ◽  
Weak Density ◽  
Progressive Waves

The scaled vorticity Ω/N and strain ∇ ζ associated with internal waves in a weak density gradient of arbitrary depth dependence together comprise a quantity that is conserved in the usual linearized approximation. This quantity I is the volume integral of the dimensionless density DI = ½[Ω2/N2 + (∇ ζ)2]. For progressive waves the ‘kinetic’ and ‘potential’ parts are equal, and in the short-wavelength limit the density DI and flux FI are related by the ordinary group velocity: FI = DIcg. The properties of DI suggest that it may be a useful measure of local internal-wave saturation.

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.

On the shape and breaking of finite amplitude internal gravity waves in a shear flow

1978 ◽  
Vol 85 (1) ◽  
pp. 7-31 ◽  
Author(s):  
S. A. Thorpe
Keyword(s):  
Shear Flow ◽  
Internal Waves ◽  
Gravity Waves ◽  
Second Harmonic ◽  
Mixing Layer ◽  
Phase Speed ◽  
Internal Gravity Waves ◽  
Finite Amplitude ◽  
Depth Interval ◽  
Plane Shear

This paper is concerned with two important aspects of nonlinear internal gravity waves in a stably stratified inviscid plane shear flow, their shape and their breaking, particularly in conditions which are frequently encountered in geophysical applications when the vertical gradients of the horizontal current and the density are concentrated in a fairly narrow depth interval (e.g. the thermocline in the ocean). The present theoretical and experimental study of the wave shape extends earlier work on waves in the absence of shear and shows that the shape may be significantly altered by shear, the second-harmonic terms which describe the wave profile changing sign when the shear is increased sufficiently in an appropriate sense.In the second part of the paper we show that the slope of internal waves at which breaking occurs (the particle speeds exceeding the phase speed of the waves) may be considerably reduced by the presence of shear. Internal waves on a thermocline which encounter an increasing shear, perhaps because of wind action accelerating the upper mixing layer of the ocean, may be prone to such breaking.This work may alternatively be regarded as a study of the stability of a parallel stratified shear flow in the presence of a particular finite disturbance which corresponds to internal gravity waves propagating horizontally in the plane of the flow.

COMPARISON OF TWO AND THREE SPATIAL DIMENSIONAL SOLUTIONS OF A PARABOLIC APPROXIMATION OF THE WAVE EQUATION AT OCEAN-BASIN SCALES IN THE PRESENCE OF INTERNAL WAVES: 100–150Hz

2010 ◽  
Vol 18 (02) ◽  
pp. 117-129 ◽  
Author(s):  
JOHN L. SPIESBERGER
Keyword(s):  
Wave Equation ◽  
Acoustic Wave ◽  
Internal Waves ◽  
Gravity Waves ◽  
Numerical Solutions ◽  
Internal Gravity Waves ◽  
Ocean Basin ◽  
Acoustic Wave Equation ◽  
Parabolic Approximation ◽  
Spatial Dimensions

Numerical solutions are given for a parabolic approximation to the acoustic wave equation at 100 and 150 Hz in two and three spatial dimensions to determine if azimuthal coupling in the horizontal coordinate significantly affects horizontal correlation in the presence of internal gravity waves in the sea. Coupling is a small effect at 4000 km. This implies that accurate solutions are possible using computations from uncoupled vertical slices. Shape of horizontal correlation is inconsistent with shapes given by two theories. Estimates of horizontal correlation at 4000 km and 100 and 150 Hz are about 1 km and 0.5 km respectively.

COMPARISON OF TWO AND THREE SPATIAL DIMENSIONAL SOLUTIONS OF THE WAVE EQUATION AT OCEAN-BASIN SCALES IN THE PRESENCE OF INTERNAL WAVES

2007 ◽  
Vol 15 (03) ◽  
pp. 319-332 ◽  
Author(s):  
JOHN L. SPIESBERGER
Keyword(s):  
Wave Equation ◽  
Acoustic Wave ◽  
Internal Waves ◽  
Gravity Waves ◽  
Numerical Solutions ◽  
Internal Gravity Waves ◽  
Ocean Basin ◽  
Acoustic Wave Equation ◽  
Parabolic Approximation ◽  
Spatial Dimensions

Numerical solutions are given for a parabolic approximation to the acoustic wave equation at 75 Hz in two and three spatial dimensions to determine if azimuthal coupling of the field significantly affects horizontal coherence. Coupling is a small effect at 4000 km in the presence of internal gravity waves. This implies that accurate solutions are possible using computations from uncoupled vertical slices through the field. The shape of horizontal coherence is inconsistent with shapes given by two theories. Estimates of horizontal coherence at 4000 km and 25, 50, and 75 Hz are 10, 2, and 1 km respectively.

scholarly journals Rossby Waves with Continuous Stratification and Bottom Friction

2018 ◽  
Vol 48 (9) ◽  
pp. 2209-2219 ◽  
Author(s):  
K. H. Brink ◽  
J. Pedlosky
Keyword(s):  
Vertical Structure ◽  
Rossby Waves ◽  
Short Wave ◽  
Bottom Friction ◽  
Ocean Current ◽  
Nonlinear Phenomenon ◽  
Flat Bottom ◽  
Stratified Ocean ◽  
Parameter Values ◽  
Strongly Damped

AbstractPublished observations of subinertial ocean current variability show that the vertical structure is often well described by a vertical mode that has a node of horizontal velocity at the bottom rather than the traditional node of vertical velocity. The theory of forced and free linear Rossby waves in a continuously stratified ocean with a sloping bottom and bottom friction is treated here to see if frictional effects can plausibly contribute to this phenomenon. For parameter values representative of the mesoscale, bottom dissipation by itself appears to be too weak to be an explanation, although caution is required because the present approach uses a linear model to address a nonlinear phenomenon. One novel outcome is the emergence of a short-wave, bottom-trapped, strongly damped mode that is present even with a flat bottom.

scholarly journals Internal gravity waves in a stratified layer atop a convecting liquid core in a non-rotating spherical shell

2021 ◽  
Author(s):  
M Bouffard ◽  
B Favier ◽  
D Lecoanet ◽  
M Le Bars
Keyword(s):  
Spherical Shell ◽  
Internal Waves ◽  
Gravity Waves ◽  
Large Scale ◽  
Liquid Core ◽  
Internal Gravity Waves ◽  
Earth’S Core ◽  
Earth's Core ◽  
Convective Region ◽  
Wide Range

Summary Seismic and magnetic observations have suggested the presence of a stably stratified layer atop Earth’s core. Such a layer could affect the morphology of the geomagnetic field and the evolution of the core, but the precise impact of this layer depends largely on its internal dynamics. Among other physical phenomena, stratified layers host internal gravity waves, which can be excited by adjacent convective motions. Internal waves are known to play an important role on the large scale dynamics of the Earth’s climate and on the long-term evolution of stars. Yet, they have received relatively little attention in the Earth’s outer core so far and deserve detailed investigations in this context. Here, we make a first step in that direction by running numerical simulations of internal gravity waves in a non-rotating spherical shell in which a stratified layer lies on top of a convective region. We use a non-linear equation of state to produce self-consistently such a two-layer system. Both propagating waves and global modes coexist in the stratified layer. We characterise the spectral properties of these waves and find that energy is distributed across a wide range of frequencies and length scales, that depends on the Prandtl number. For the control parameters considered and in the absence of rotational and magnetic effects, the mean kinetic energy in the layer is about 0.1 per cent that of the convective region. Gravity waves produce perturbations in the gravity field that may fall within the sensitivity limit of present-day instruments and could potentially be detected in available data. We finally provide a road map for future, more geophysically realistic, studies towards a more thorough understanding of the dynamics and impact of internal waves in a stratified layer atop Earth’s core.

Sign in / Sign up

Export Citation Format

Share Document