Energy Transfers Between Balanced and Unbalanced Motions in Geophysical Flows

2020 ◽  
Author(s):  
Manita Chouksey
Keyword(s):  
Gravity Waves ◽  
Internal Gravity Waves ◽  
Geophysical Flows ◽  
Rossby Number ◽  
Energy Transfers ◽  
Model Setup ◽  
Energy And Momentum ◽  
Second Procedure ◽  
Vorticity Balance ◽  
Model Affect

<p>Geophysical flows such as the atmosphere and the ocean are characterized by rotation and stratification, which together give rise to two dominant motions: the slow balanced and the fast unbalanced motions. The interaction between the balanced and unbalanced motions and the energy transfers between them impact the energy and momentum cycle of the flow, and is therefore crucial to understand the underlying energetics of the atmosphere and the ocean. Balanced motions, for instance mesoscale eddies, can transfer their energy to unbalanced motions, such as internal gravity waves, by spontaneous loss of balance amongst other processes. The exact mechanism of wave generation, however, remain less understood and is hindered to an extent by the challenge of separating the flow field into balanced and unbalanced motions.</p><p>This separation is achieved using two different balancing procedures in an identical model setup and assess the differences in the obtained balanced state and the resultant energy transfer to unbalanced motions. The first procedure we implement is a non-linear initialisation procedure based on Machenhauer (1977) but extended to higher orders in Rossby number. The second procedure implemented is the optimal potential vorticity balance to achieve the balanced state. The results show that the numerics of the model affect the obtained balanced state from the two procedures, and thus the residual signal which we interpret as the unbalanced motions, i.e. internal gravity waves.  A further complication is the presence of slaved modes, which appear along the unbalanced motions but are tied to the balanced motions, for which we need to extend the separation to higher orders in Rossby number. Further, we assess the energy transfers between balanced and unbalanced motions in experiments with different Rossby numbers and for different orders in Rossby number. We find that it is crucial to consider the effect of the numerics in models and make a suitable choice of the balancing procedure, as well as diagnose the unbalanced motions at higher orders to precisely detect the unbalanced wave signal.</p>

A non-linear investigation of critical levels for internal atmospheric gravity waves

1971 ◽  
Vol 50 (3) ◽  
pp. 545-563 ◽  
Author(s):  
R. J. Breeding
Keyword(s):  
Steady State ◽  
Linear Theory ◽  
Gravity Waves ◽  
Incident Wave ◽  
Critical Level ◽  
Internal Gravity Waves ◽  
Mean Flow ◽  
Non Linear ◽  
Energy And Momentum ◽  
Almost All

The behaviour of internal gravity waves near a critical level is investigated by means of a transient two dimensional finite difference model. All the important non-linear, viscosity and thermal conduction terms are included, but the rotational terms are omitted and the perturbations are assumed to be incompressible. For Richardson numbers greater than 2·0 the interaction of the incident wave and the mean flow is largely as predicted by the linear theory–very little of the incident wave penetrates through the critical level and almost all of the wave's energy and momentum are absorbed by changes in the original wind. However, these changes in the wind are centred above the critical level, so that the change in the wind has only a small effect on the height of the critical level. For Richardson numbers less than 2·0 and greater than 0·25 a significant fraction of the incident wave is reflected, part of which could have been predicted by the linear theory. For these stable Richardson numbers a steady state is apparently reached where the maximum wind change continues to grow slowly, but the minimum Richardson number and wave magnitudes remain constant. This condition represents a balance between the diffusion outward of the added momentum and the rate at which it is absorbed. For Richardson numbers less than 0·25, over-reflexion, predicted from the linear theory, is observed, but because the system is dynamically unstable no over-reflecting steady state is ever reached.

The evolution of a stratified turbulent cloud

2013 ◽  
Vol 739 ◽  
pp. 229-253 ◽  
Author(s):  
Andrea Maffioli ◽  
P. A. Davidson ◽  
S. B. Dalziel ◽  
N. Swaminathan
Keyword(s):  
Gravity Waves ◽  
Large Scale ◽  
Wave Packets ◽  
Three Dimensional ◽  
Internal Gravity Wave ◽  
Internal Gravity Waves ◽  
Group Speed ◽  
Propagating Waves ◽  
The Subject ◽  
Energy And Momentum

AbstractLocalized regions of turbulence, or turbulent clouds, in a stratified fluid are the subject of this study, which focuses on the edge dynamics occurring between the turbulence and the surrounding quiescent region. Through laboratory experiments and numerical simulations of stratified turbulent clouds, we confirm that the edge dynamics can be subdivided into materially driven intrusions and horizontally travelling internal wave-packets. Three-dimensional visualizations show that the internal gravity wave-packets are in fact large-scale pancake structures that grow out of the turbulent cloud into the adjacent quiescent region. The wave-packets were tracked in time, and it is found that their speed obeys the group speed relation for linear internal gravity waves. The energetics of the propagating waves, which include waveforms that are inclined with respect to the horizontal, are also considered and it is found that, after a period of two eddy turnover times, the internal gravity waves carry up to 16 % of the cloud kinetic energy into the initially quiescent region. Turbulent events in nature are often in the form of decaying turbulent clouds, and it is therefore suggested that internal gravity waves radiated from an initial cloud could play a significant role in the reorganization of energy and momentum in the atmosphere and oceans.

Towards a Global Spectral Energy Budget for Internal Gravity Waves in the Ocean

2020 ◽  
Vol 50 (4) ◽  
pp. 935-944 ◽  
Author(s):  
Carsten Eden ◽  
Friederike Pollmann ◽  
Dirk Olbers
Keyword(s):  
Kinetic Equation ◽  
Gravity Waves ◽  
Energy Budget ◽  
Wave Energy ◽  
Internal Gravity Waves ◽  
Rate Of Change ◽  
Spectral Energy ◽  
Spectral Space ◽  
Wave Interactions ◽  
Energy Transfers

AbstractEnergy transfers by internal gravity wave–wave interactions in spectral space are diagnosed from numerical model simulations initialized with realizations of the Garrett–Munk spectrum in physical space and compared with the predictions of the so-called scattering integral or kinetic equation. Averaging the random phase of the initialization, the energy transfers by wave–wave interactions in the model agree well with the predictions of the kinetic equation for certain ranges of frequency and wavenumbers. This validation allows now, in principle, the use of the energy transfers predicted by the kinetic equation to design a global spectral energy budget for internal gravity waves in the ocean where divergences of energy transports in physical and spectral space balance forcing, dissipation, the energy transfers by the wave–wave interactions, or the rate of change of the spectral wave energy. First global estimates show indeed accumulation of the wave energy in a range of latitude ϕ consistent with tidal waves at frequency ωT propagating toward the latitudinal window where 2 < ωT/f(ϕ) < 3, as predicted by the kinetic equation.

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 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.

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