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.

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.

scholarly journals Numerical and the MU radar estimations of gravity wave enhancement and turbulent ozone fluxes near the tropopause

2004 ◽  
Vol 22 (11) ◽  
pp. 3889-3898 ◽  
Author(s):  
N. M. Gavrilov ◽  
S. Fukao
Keyword(s):  
Gravity Waves ◽  
Wave Breaking ◽  
Internal Gravity Waves ◽  
Vertical Temperature ◽  
Turbulent Diffusion Coefficient ◽  
Middle Latitudes ◽  
Mu Radar ◽  
Different Seasons ◽  
Ozone Fluxes ◽  
Vertical Ozone

Abstract. It is shown with a numerical simulation that a sharp increase in the vertical temperature gradient and Brunt-Väisälä frequency near the tropopause may produce an increase in the amplitudes of internal gravity waves (IGWs) propagating upward from the troposphere, wave breaking and generation of stronger turbulence. This may enhance the transport of admixtures between the troposphere and stratosphere in the middle latitudes. Turbulent diffusion coefficient calculated numerically and measured with the MU radar are of 1-10m2/s in different seasons in Shigaraki, Japan (35° N, 136° E). These values lead to the estimation of vertical ozone flux from the stratosphere to the troposphere of (1-10)x1014, which may substantially add to the usually supposed ozone downward transport with the general atmospheric circulation. Therefore, local enhancements of IGW intensity and turbulence at tropospheric altitudes over mountains due to their orographic excitation and due to other wave sources may lead to the changes in tropospheric and total ozone over different regions.

scholarly journals Internal wave breaking and the fate of planets around solar-type stars

2010 ◽  
Vol 6 (S271) ◽  
pp. 363-364
Author(s):  
Adrian J. Barker ◽  
Gordon I. Ogilvie
Keyword(s):  
Gravity Waves ◽  
Wave Breaking ◽  
Internal Gravity Waves ◽  
Amplitude Dependence ◽  
Tidal Dissipation ◽  
Short Period ◽  
Central Regions ◽  
Solar Type ◽  
The Waves ◽  
Solar Type Star

AbstractInternal gravity waves are excited at the interface of convection and radiation zones of a solar-type star, by the tidal forcing of a short-period planet. The fate of these waves as they approach the centre of the star depends on their amplitude. We discuss the results of numerical simulations of these waves approaching the centre of a star, and the resulting evolution of the spin of the central regions of the star and the orbit of the planet. If the waves break, we find efficient tidal dissipation, which is not present if the waves perfectly reflect from the centre. This highlights an important amplitude dependence of the (stellar) tidal quality factor Q′, which has implications for the survival of planets on short-period orbits around solar-type stars, with radiative cores.

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 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.

A note on breaking waves

1988 ◽  
Vol 419 (1857) ◽  
pp. 323-335 ◽  
Keyword(s):  
Phase Velocity ◽  
Gravity Waves ◽  
Turbulent Mixing ◽  
Wave Breaking ◽  
Richardson Number ◽  
Breaking Waves ◽  
Internal Gravity Waves ◽  
Time Interval ◽  
Wave Groups ◽  
Surface Gravity Waves

Some simple general properties of wave breaking are deduced from the known behaviour of surface gravity waves in deep water, on the assumption that breaking occurs in association with wave groups. In particular we derive equations for the time interval, ז, between the onset of breaking of successive waves: ז ═ T / |1 – ( c ⋅ c g )/ c 2 |, and for the propagation vector c b (referred to as the ‘wave-breaking vector’) of the position at which breaking, once initiated, will proceed: c b ═ c (1 – c ⋅ c g / c 2 )+ c g . Here c is the phase velocity, and c g the group velocity, of waves of period T . Interfacial waves, internal gravity waves, inertial waves and planetary waves are considered as particular examples. The results apply not only to wave breaking, but to the movement of any property (e. g. fluid acceleration, gradient Richardson number) that is carried through a medium in association with waves. One application is to describe the distribution, in space and time, of regions of turbulent mixing, or transitional phenomena, in the oceans or atmosphere.

Simulation and stability of two-dimensional internal gravity waves in a stratified shear flow

1993 ◽  
Vol 19 (1-4) ◽  
pp. 325-366 ◽  
Author(s):  
C.-L. Lin ◽  
J.H. Ferziger ◽  
J.R. Koseff ◽  
S.G. Monismith
Keyword(s):  
Shear Flow ◽  
Gravity Waves ◽  
Internal Gravity Waves ◽  
Two Dimensional ◽  
Stratified Shear Flow

A general method for solving steady-state internal gravity wave problems

1972 ◽  
Vol 56 (4) ◽  
pp. 721-740 ◽  
Author(s):  
D. G. Hurley
Keyword(s):  
Steady State ◽  
Circular Cylinder ◽  
Gravity Waves ◽  
Internal Gravity Wave ◽  
Internal Gravity Waves ◽  
Two Dimensional ◽  
Wave Problem ◽  
Wave Problems ◽  
General Method ◽  
Stratified Liquid

The paper describes a simple but general method for solving 'steady-state’ problems involving internal gravity waves in a stably stratified liquid. Under the assumption that the motion is two-dimensional and that the Brunt-Väisälä frequency is constant, the method is used to re-derive in a very simple way the solutions to problems where the boundary of the liquid is either a wedge or a circular cylinder. The method is then used to investigate the effect that a model of the continental shelf has on an incident train of internal gravity waves. The method involves analytic continuation in the frequency of the disturbance, and may well prove to be effective for other types of wave problem.

Excitation and breaking of internal gravity waves by parametric instability

1998 ◽  
Vol 374 ◽  
pp. 117-144 ◽  
Author(s):  
DOMINIQUE BENIELLI ◽  
JOËL SOMMERIA
Keyword(s):  
Gravity Waves ◽  
Wave Breaking ◽  
Parametric Instability ◽  
Excitation Frequency ◽  
Vertical Plane ◽  
Excitation Amplitude ◽  
Internal Gravity Waves ◽  
Stratified Medium ◽  
Primary Wave ◽  
Maximum Slope

We study the dynamics of internal gravity waves excited by parametric instability in a stably stratified medium, either at the interface between a water and a kerosene layer, or in brine with a uniform gradient of salinity. The tank has a rectangular section, and is narrow to favour standing waves with motion in the vertical plane. The fluid container undergoes vertical oscillations, and the resulting modulation of the apparent gravity excites the internal waves by parametric instability.Each internal wave mode is amplified for an excitation frequency close to twice its natural frequency, when the excitation amplitude is sufficient to overcome viscous damping (these conditions define an ‘instability tongue’ in the parameter space frequency-amplitude). In the interfacial case, each mode is well separated from the others in frequency, and behaves like a simple pendulum. The case of a continuous stratification is more complex as different modes have overlapping instability tongues. In both cases, the growth rates and saturation amplitudes behave as predicted by the theory of parametric instability for an oscillator. However, complex friction effects are observed, probably owing to the development of boundary-layer instabilities.In the uniformly stratified case, the excited standing wave is unstable via a secondary parametric instability: a wave packet with small wavelength and half the primary wave frequency develops in the vertical plane. This energy transfer toward a smaller scale increases the maximum slope of the iso-density surfaces, leading to local turning and rapid growth of three-dimensional instabilities and wave breaking. These results illustrate earlier stability analyses and numerical studies. The combined effect of the primary excitation mechanism and wave breaking leads to a remarkable intermittent behaviour, with successive phases of growth and decay for the primary wave over long timescales.

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