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 COMPARISON OF WAVE ACTIVITY IN THE MESOPAUSE REGION AT MAIMAGA STATION WITH EOS MLS (AURA) TEMPERATURE DATA AND ACTIVITY OF PLANETARY WAVES AT TIKSI STATION

2019 ◽  
pp. 182-189
Author(s):  
В.И. Сивцева ◽  
П.П. Аммосов ◽  
Г.А. Гаврильева ◽  
И.И. Колтовской ◽  
А.М. Аммосова
Keyword(s):  
Gravity Waves ◽  
Internal Gravity Waves ◽  
Temperature Data ◽  
Planetary Waves ◽  
Winter Period ◽  
Temperature Profiles ◽  
Night Temperature ◽  
Mesopause Region ◽  
The Difference ◽  
The Waves

Исследованы данные температуры области мезопаузы, полученные за период 2013-2018 гг. на станции Маймага (63.04N, 129.51E) и за период 2015-2018 гг. на станции Тикси (71.58 N, 128.77 E). В зимний период сезона наблюдений 2014-2015 характеристика активности внутренних гравитационных волн (ВГВ) gwимеет более низкие значения, чем в другие сезоны, а средненочная температура, наоборот, превышает аналогичные значения в другие сезоны. Для сопоставления рассматривались спутниковые данные температурных профилей полученные EOS MLS (Aura). После выделения и вычитания вклада гравитационной составляющей из температурных профилей EOS MLS для области над станцией Маймага заметно отличие в зимней стратопаузе сезона 2014-2015. В этот сезон в зимний период, с учетом вычета вклада флуктуаций температуры обусловленных ВГВ, наблюдается отсутствие резких потеплений в районе стратопаузы в отличие от остальных сезонов. Измерение параметров планетарных волн в течение периода 2015-2018 гг. совместных наблюдений на станциях Маймага и Тикси показали, что фазы наблюдаемых на обеих станциях волн совпадают, а амплитуды на станции Тикси несколько (12 К) превышают амплитуды на станции Маймага. The temperature data of the mesopause region obtained for the period 2013-2018 at the station Maimaga (63.04 N, 129.51 E) and for the period 2015-2018 at the station Tiksi (71.58 N, 128.77 E) was investigated. During the winter period of the 20142015 observation season, the characteristic of the internal gravity waves (IGW) activity sgw has lower values than in other seasons, and the average night temperature of the mesopause region, on the contrary, exceeds corresponding values in other seasons. For comparison, satellite data of temperature profiles obtained by EOS MLS (Aura) are given. After isolating and subtracting the contribution of the gravitaty waves from the EOS MLS temperature profiles for the region above the st. Maimaga, the difference in the winter stratopause of the 2014-2015 season is noticeable. In this season in winter there is a lack of sharp warming in the stratopause region, in contrast to other seasons, taking into account the deduction of the contribution of temperature fluctuations due to IGW. Measurement of the parameters of planetary waves during the period 2015-2018 of joint observations at Maimaga and Tiksi stations showed that the phases of the waves observed at both stations coincide, and the amplitudes at Tiksi station are several (1-2 K) higher than the amplitudes at Maimaga station.

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.

Wave Kinematics Computed With the Nonlinear Schro¨dinger Method for Deep Water

1999 ◽  
Vol 121 (2) ◽  
pp. 126-130 ◽  
Author(s):  
K. Trulsen
Keyword(s):  
Time Series ◽  
Gravity Waves ◽  
Deep Water ◽  
Water Wave ◽  
Surface Displacement ◽  
Horizontal Position ◽  
Two Dimensional ◽  
Limited Bandwidth ◽  
Wave Kinematics ◽  
The Waves

The nonlinear Schro¨dinger method for water wave kinematics under two-dimensional irregular deepwater gravity waves is developed. Its application is illustrated for computation of the velocity and acceleration fields from the time-series of the surface displacement measured at a fixed horizontal position. The method is based on the assumption that the waves have small steepness and limited bandwidth.

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.

The effect of viscosity and heat conduction on internal gravity waves at a critical level

1967 ◽  
Vol 30 (4) ◽  
pp. 775-783 ◽  
Author(s):  
Philip Hazel
Keyword(s):  
Differential Equation ◽  
Heat Conduction ◽  
Gravity Waves ◽  
Order Differential Equation ◽  
Fluid Velocity ◽  
Attenuation Factor ◽  
Internal Gravity Waves ◽  
Constant Factor ◽  
The Mean ◽  
The Waves

The differential equation for the vertical velocity of a gravity wave in an inviscid shear flow is singular at a level where the mean fluid velocity is equal to the horizontal phase velocity of the waves. It has been shown that a wave travelling through such a layer has its amplitude attenuated by a constant factor dependent on the local Richardson number. In this paper the results obtained by solving numerically the full sixth order differential equation, which is derived by including viscosity and heat conduction in the problem, (and is not singular) are discussed, and the same attenuation factor is found. Some experiments which confirm certain aspects of the theory are described in an appendix.

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.

Gravity waves as a mechanism of coupling oceanic and atmospheric acoustic waveguides to seismic sources

2020 ◽  
Author(s):  
Oleg Godin
Keyword(s):  
Gravity Waves ◽  
Acoustic Waves ◽  
Seismic Waves ◽  
Wind Waves ◽  
Normal Modes ◽  
Internal Gravity Waves ◽  
Body Waves ◽  
Surface Scattering ◽  
Seismic Sources ◽  
T Waves

<p>Direct excitation of acoustic normal modes in horizontally stratified oceanic waveguides is negligible even for shallow earthquakes because of the disparity between velocities of seismic waves and the sound speed in the water column. T-phases, which propagate at the speed of sound in water, are often reported to originate in the open ocean in the vicinity of the epicenter of an underwater earthquake, even in the absence of prominent bathymetric features or significant seafloor roughness. This paper aims to evaluate the contribution of scattering by hydrodynamic waves into generation of abyssal T-waves. Ocean is modeled as a range-independent waveguide with superimposed volume inhomogeneities due to internal gravity waves and surface roughness due to wind waves and sea swell. Guided acoustic waves are excited by volume and surface scattering of ballistic body waves. The surface scattering mechanism is shown to explain key observational features of abyssal T-waves, including their ubiquity, low-frequency cutoff, presence on seafloor sensors, and weak dependence on the earthquake focus depth. On the other hand, volume scattering due to internal gravity waves proves to be ineffective in coupling the seismic sources to T-waves. The theory is extended to explore a possible role that scattering by gravity waves may play in excitation of infrasonic normal modes of tropospheric and stratospheric waveguides by underwater earthquakes. Model predictions are compared to observations [L. G. Evers, D. Brown, K. D. Heaney, J. D. Assink, P. S. M. Smets, and M. Snellen (2014), Geophys. Res. Lett., <strong>41</strong>, 1644–1650] of infrasonic signals generated by the 2004 Macquarie Ridge earthquake.</p>

On the dispersion relation of random gravity waves. Part 2. An experiment

1979 ◽  
Vol 92 (4) ◽  
pp. 731-749 ◽  
Author(s):  
Hisashi Mitsuyasu ◽  
Yi-Yu Kuo ◽  
Akira Masuda
Keyword(s):  
Gravity Waves ◽  
Wind Wave ◽  
Linear Array ◽  
Two Dimensional ◽  
Random Waves ◽  
Angular Dispersion ◽  
Wave Flume ◽  
Phase Velocities ◽  
Spectral Components ◽  
The Waves

Random waves are generated by wind in the first half of a wind-wave flume. The latter half of the flume is kept free from wind to measure the waves unaffected by the wind and wind-generated current. The random waves in the latter area are measured with a linear array of wave gauges, and their phase velocities and coherences are determined by a usual technique of the cross-spectral analysis. The measured results are compared with the nonlinear theory of two-dimensional random waves, which has been presented in part 1 of this paper (Masuda, Kuo & Mitsuyasu 1979). Agreement between the theory and the experiment is satisfactory, and observed characteristics of the phase velocity and coherence of the spectral components can be attributed to the effects of the nonlinearity and angular dispersion of the random waves.

On the interaction between internal gravity waves and a shear flow

1968 ◽  
Vol 34 (4) ◽  
pp. 711-720 ◽  
Author(s):  
C. J. R. Garrett
Keyword(s):  
Wave Propagation ◽  
Stress Tensor ◽  
Gravity Waves ◽  
Internal Gravity Wave ◽  
Internal Gravity Waves ◽  
Basic Flow ◽  
Radiation Stress ◽  
Interaction Stress ◽  
The Waves ◽  
Uniform Plane

The theory of wave action conservation is summarized, and its interpretation in terms of the working, against the rate of strain of the basic flow, of an interaction stress associated with the waves is discussed. Usually this interaction stress is identical with the radiation stress of a uniform plane wave. The problem of internal gravity wave propagation in an incompressible, stratified Boussinesq liquid is considered in detail for a more general basic flow than has hitherto been treated, and the interaction stress is derived. One component of the interaction stress tensor is only equal to the corresponding component of the radiation stress tensor if we include in the latter, in addition to the Reynolds stress, a term associated with the redistribution of matter, on the average, by the wave. Two other components of the radiation stress tensor are modified in a similar manner, but the corresponding components of the interaction stress tensor are undefined, and so no comparison is possible.

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