Numerical Simulations of the Nonhydrostatic Transformation of Basin-Scale Internal Gravity Waves and Wave-Enhanced Meromixis in Lakes

2011 ◽  
pp. 193-276 ◽  
Author(s):  
V. Maderich ◽  
I. Brovchenko ◽  
K. Terletska ◽  
K. Hutter
Keyword(s):  
Numerical Simulations ◽  
Gravity Waves ◽  
Internal Gravity Waves ◽  
Basin Scale

An experimental study of the free evolution of rotating, nonlinear internal gravity waves in a two-layer stratified fluid

2014 ◽  
Vol 742 ◽  
pp. 308-339 ◽  
Author(s):  
Hugo N. Ulloa ◽  
Alberto de la Fuente ◽  
Yarko Niño
Keyword(s):  
Gravity Waves ◽  
Large Scale ◽  
Laboratory Experiments ◽  
Internal Gravity Waves ◽  
Kelvin Wave ◽  
Nonlinear Processes ◽  
Transfer Energy ◽  
Type Wave ◽  
Basin Scale ◽  
Layer Flow

AbstractThe temporal evolution of nonlinear large-scale internal gravity waves, in a two-layer flow affected by background rotation, is studied via laboratory experiments conducted in a cylindrical tank, mounted on a rotating turntable. The internal wave field is excited by the relaxation of an initial forced tilt of the density interface ($\eta _{i}$), which generates internal waves, such as Kelvin and Poincaré waves, in response to rotation effects. The behaviour of $\eta _{i}$, in the shore region, is analysed in terms of the background rotation and the nonlinear steepening of the basin-scale waves. The results show that the degeneration of the fundamental Kelvin wave into a solitary-type wave packet is caused by nonlinear steepening and it is influenced by the background rotation. In addition, the physical scales of the leading solitary-type wave are closer to Korteweg–de Vries theory as the rotation increases. Moreover, the nonlinear interaction between the Kelvin wave and the Poincaré wave can transfer energy to higher or lower frequencies than the frequency of the fundamental Kelvin wave, as a function of the background rotation. In particular, a specific normal mode in the off-shore region could be energized by this interaction. Finally, the bulk decay rate of the fundamental Kelvin wave, $\tau _{dk}$, was investigated. The results exhibit that $\tau _{dk}$ is concordant with the Ekman damping time scale when there is no evidence of steepening in the basin-scale waves. However, as nonlinear processes increase, $\tau _{dk}$ shows a strong decrease. In this context, the nonlinear processes play an important role in the decay of the fundamental Kelvin wave, via the energy radiation to other modes. The results reported demonstrate that the background rotation and nonlinear processes are essential aspects in understanding the degeneration and the decay of large-scale internal gravity waves on enclosed basins.

scholarly journals Direct numerical simulations of an inertial wave attractor in linear and nonlinear regimes

2014 ◽  
Vol 745 ◽  
pp. 223-250 ◽  
Author(s):  
Laurène Jouve ◽  
Gordon I. Ogilvie
Keyword(s):  
Numerical Simulations ◽  
Gravity Waves ◽  
Dissipation Rate ◽  
Laboratory Experiments ◽  
Rotation Axis ◽  
Internal Gravity Waves ◽  
Direct Numerical Simulations ◽  
Inertial Wave ◽  
Linear And Nonlinear ◽  
Nonlinear Regimes

AbstractIn a uniformly rotating fluid, inertial waves propagate along rays that are inclined to the rotation axis by an angle that depends on the wave frequency. In closed domains, multiple reflections from the boundaries may cause inertial waves to focus onto particular structures known as wave attractors. These attractors are likely to appear in fluid containers with at least one boundary that is neither parallel nor normal to the rotation axis. A closely related process also applies to internal gravity waves in a stably stratified fluid. Such structures have previously been studied from a theoretical point of view, in laboratory experiments, in linear numerical calculations and in some recent numerical simulations. In the present paper, two-dimensional direct numerical simulations of an inertial wave attractor are presented. By varying the amplitude at which the system is forced periodically, we are able to describe the transition between the linear and nonlinear regimes as well as the characteristic properties of the two situations. In the linear regime, we first recover the results of the linear calculations and asymptotic theory of Ogilvie (J. Fluid Mech., vol. 543, 2005, pp. 19–44) who considered a prototypical problem involving the focusing of linear internal waves into a narrow beam centred on a wave attractor in a steady state. The velocity profile of the beam and its scalings with the Ekman number, as well as the asymptotic value of the dissipation rate, are found to be in agreement with the linear theory. We also find that, as the beam builds up around the wave attractor, the power input by the applied force reaches its limiting value more rapidly than the dissipation rate, which saturates only when the beam has reached its final thickness. In the nonlinear regime, the beam is strongly affected and becomes unstable to a subharmonic instability. This instability transfers energy to secondary waves possessing shorter wavelengths and lower frequencies. The onset of the instability of a narrow inertial wave beam is investigated by means of a separate linear analysis and the results, such as the onset of the instability, are found to be consistent with the global simulations of the wave attractor. The excitation of such secondary waves described theoretically in this work has also been seen in recent laboratory experiments on internal gravity waves.

scholarly journals Photometric detection of internal gravity waves in upper main-sequence stars

2019 ◽  
Vol 621 ◽  
pp. A135 ◽  
Author(s):  
D. M. Bowman ◽  
C. Aerts ◽  
C. Johnston ◽  
M. G. Pedersen ◽  
T. M. Rogers ◽  
...  
Keyword(s):  
Numerical Simulations ◽  
Gravity Waves ◽  
Main Sequence ◽  
Low Frequency ◽  
Internal Gravity Waves ◽  
Main Sequence Stars ◽  
Photometric Detection ◽  
F Stars ◽  
Low Frequency Power ◽  
Frequency Power

Context. Main sequence stars with a convective core are predicted to stochastically excite internal gravity waves (IGWs), which effectively transport angular momentum throughout the stellar interior and explain the observed near-uniform interior rotation rates of intermediate-mass stars. However, there are few detections of IGWs, and fewer still made using photometry, with more detections needed to constrain numerical simulations. Aims. We aim to formalise the detection and characterisation of IGWs in photometric observations of stars born with convective cores (M ≳ 1.5 M⊙) and parameterise the low-frequency power excess caused by IGWs. Methods. Using the most recent CoRoT light curves for a sample of O, B, A and F stars, we parameterised the morphology of the flux contribution of IGWs in Fourier space using an MCMC numerical scheme within a Bayesian framework. We compared this to predictions from IGW numerical simulations and investigated how the observed morphology changes as a function of stellar parameters. Results. We demonstrate that a common morphology for the low-frequency power excess is observed in early-type stars observed by CoRoT. Our study shows that a background frequency-dependent source of astrophysical signal is common, which we interpret as IGWs. We provide constraints on the amplitudes of IGWs and the shape of their detected frequency spectrum across a range of mass, which is the first ensemble study of stochastic variability in such a diverse sample of stars. Conclusions. The evidence of a low-frequency power excess across a wide mass range supports the interpretation of IGWs in photometry of O, B, A and F stars. We also discuss the prospects of observing hundreds of massive stars with the Transiting Exoplanet Survey Satellite (TESS) in the near future.

scholarly journals 3D simulations of internal gravity waves in solar-like stars

2013 ◽  
Vol 9 (S301) ◽  
pp. 375-376
Author(s):  
Lucie Alvan ◽  
Allan Sacha Brun ◽  
Stéphane Mathis
Keyword(s):  
Numerical Simulations ◽  
Gravity Waves ◽  
Rotation Rate ◽  
Spherical Harmonic ◽  
Internal Gravity Waves ◽  
3D Simulations ◽  
Frequency Splitting ◽  
Theoretical Predictions ◽  
First Time ◽  
Good Agreement

AbstractWe perform numerical simulations of the whole Sun using the 3D anelastic spherical harmonic (ASH) code. In such models, the radiative and convective zones are non-linearly coupled and in the radiative interior a wave-like pattern is observed. For the first time, we are thus able to model in 3D the excitation and propagation of internal gravity waves (IGWs) in a solar-like star's radiative zone. We compare the properties of our waves to theoretical predictions and results of oscillation calculations. The obtained good agreement allows us to validate the consistency of our approach and to study the characteristics of IGWs. We find that a wave's spectrum is excited up to radial order n=58. This spectrum evolves with depth and time; we show that the lifetime of the highest-frequency modes must be greater than 550 days. We also test the sensitivity of waves to rotation and are able to retrieve the rotation rate to within 5% error by measuring the frequency splitting.

Model of the internal gravity waves excited by lithospheric greenhouse effect gases

2001 ◽  
Vol 7 (2s) ◽  
pp. 26-33 ◽  
Author(s):  
O.E. Gotynyan ◽  
◽  
V.N. Ivchenko ◽  
Yu.G. Rapoport ◽  
◽  
...  
Keyword(s):  
Gravity Waves ◽  
Greenhouse Effect ◽  
Internal Gravity Waves

scholarly journals Internal gravity waves generated by an impulsive plume

2019 ◽  
Vol 4 (1) ◽  
Author(s):  
Alan Brandt ◽  
Kara R. Shipley
Keyword(s):  
Gravity Waves ◽  
Internal Gravity Waves

scholarly journals Shear-induced breaking of internal gravity waves

2021 ◽  
Vol 921 ◽  
Author(s):  
Christopher J. Howland ◽  
John R. Taylor ◽  
C.P. Caulfield
Keyword(s):  
Gravity Waves ◽  
Internal Gravity Waves

Abstract

scholarly journals Rolls of the internal gravity waves in the Earth's atmosphere

2014 ◽  
Vol 32 (2) ◽  
pp. 181-186 ◽  
Author(s):  
O. Onishchenko ◽  
O. Pokhotelov ◽  
W. Horton ◽  
A. Smolyakov ◽  
T. Kaladze ◽  
...  
Keyword(s):  
Nonlinear Dynamics ◽  
Gravity Waves ◽  
Closed System ◽  
Wind Shear ◽  
Internal Gravity Waves ◽  
Temperature Gradients ◽  
System Of Equations ◽  
Vertical Temperature ◽  
Earth’S Atmosphere ◽  
Earth's Atmosphere

Abstract. The effect of the wind shear on the roll structures of nonlinear internal gravity waves (IGWs) in the Earth's atmosphere with the finite vertical temperature gradients is investigated. A closed system of equations is derived for the nonlinear dynamics of the IGWs in the presence of temperature gradients and sheared wind. The solution in the form of rolls has been obtained. The new condition for the existence of such structures was found by taking into account the roll spatial scale, the horizontal speed and wind shear parameters. We have shown that the roll structures can exist in a dynamically unstable atmosphere.

scholarly journals Five-Wave Resonances in Deep Water Gravity Waves: Integrability, Numerical Simulations and Experiments

Fluids ◽  
2021 ◽  
Vol 6 (6) ◽  
pp. 205
Author(s):  
Dan Lucas ◽  
Marc Perlin ◽  
Dian-Yong Liu ◽  
Shane Walsh ◽  
Rossen Ivanov ◽  
...  
Keyword(s):  
Normal Form ◽  
Numerical Simulations ◽  
Gravity Waves ◽  
Deep Water ◽  
Plane Waves ◽  
Surface Elevation ◽  
Wave Interactions ◽  
Frequency Space ◽  
Target Mode ◽  
The Hilbert Transform

In this work we consider the problem of finding the simplest arrangement of resonant deep-water gravity waves in one-dimensional propagation, from three perspectives: Theoretical, numerical and experimental. Theoretically this requires using a normal-form Hamiltonian that focuses on 5-wave resonances. The simplest arrangement is based on a triad of wavevectors K1+K2=K3 (satisfying specific ratios) along with their negatives, corresponding to a scenario of encountering wavepackets, amenable to experiments and numerical simulations. The normal-form equations for these encountering waves in resonance are shown to be non-integrable, but they admit an integrable reduction in a symmetric configuration. Numerical simulations of the governing equations in natural variables using pseudospectral methods require the inclusion of up to 6-wave interactions, which imposes a strong dealiasing cut-off in order to properly resolve the evolving waves. We study the resonance numerically by looking at a target mode in the base triad and showing that the energy transfer to this mode is more efficient when the system is close to satisfying the resonant conditions. We first look at encountering plane waves with base frequencies in the range 1.32–2.35 Hz and steepnesses below 0.1, and show that the time evolution of the target mode’s energy is dramatically changed at the resonance. We then look at a scenario that is closer to experiments: Encountering wavepackets in a 400-m long numerical tank, where the interaction time is reduced with respect to the plane-wave case but the resonance is still observed; by mimicking a probe measurement of surface elevation we obtain efficiencies of up to 10% in frequency space after including near-resonant contributions. Finally, we perform preliminary experiments of encountering wavepackets in a 35-m long tank, which seem to show that the resonance exists physically. The measured efficiencies via probe measurements of surface elevation are relatively small, indicating that a finer search is needed along with longer wave flumes with much larger amplitudes and lower frequency waves. A further analysis of phases generated from probe data via the analytic signal approach (using the Hilbert transform) shows a strong triad phase synchronisation at the resonance, thus providing independent experimental evidence of the resonance.

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