Wave Transience in a Compressible Atmosphere. Part I: Transient Internal Wave, Mean-Flow Interaction

1981 ◽  
Vol 38 (2) ◽  
pp. 281-297 ◽  
Author(s):  
Timothy J. Dunkerton
Keyword(s):  
Internal Wave ◽  
Mean Flow ◽  
Flow Interaction ◽  
Compressible Atmosphere

scholarly journals A Closure for Internal Wave–Mean Flow Interaction. Part II: Wave Drag

2017 ◽  
Vol 47 (6) ◽  
pp. 1403-1412 ◽  
Author(s):  
Carsten Eden ◽  
Dirk Olbers
Keyword(s):  
Wave Propagation ◽  
Internal Wave ◽  
Ocean Circulation ◽  
Wave Drag ◽  
Ocean Model ◽  
Vertical Shear ◽  
Mean Flow ◽  
Flow Interaction ◽  
Two Dimensional Flow ◽  
Novel Concept

AbstractA novel concept for parameterizing internal wave–mean flow interaction in ocean circulation models is extended to an arbitrary two-dimensional flow with vertical shear. The concept is based on the description of the entire wave field by the wave-energy density in physical and wavenumber space and its prognostic computation by the radiative transfer equation integrated in wavenumber space. Energy compartments result for the horizontal direction of wave propagation as additional prognostic model variables, of which only four are taken here for simplicity. The mean flow is interpreted as residual velocities with respect to the wave activity. The effect of wave drag and energy exchange due to the vertical shear of the residual mean flow is then given simply by a vertical flux of momentum. This flux is related to the asymmetries in upward, downward, alongflow, and counterflow wave propagation described by the energy compartments. A numerical implementation in a realistic eddying ocean model shows that the wave drag effect is a significant sink of kinetic energy in the interior ocean.

scholarly journals A Closure for Internal Wave–Mean Flow Interaction. Part I: Energy Conversion

2017 ◽  
Vol 47 (6) ◽  
pp. 1389-1401 ◽  
Author(s):  
Dirk Olbers ◽  
Carsten Eden
Keyword(s):  
Radiative Transfer ◽  
Internal Wave ◽  
Ocean Circulation ◽  
Transfer Equation ◽  
Radiative Transfer Equation ◽  
Exchange Energy ◽  
Mean Flow ◽  
Flow Interaction ◽  
The Mean ◽  
Internal Inertia

AbstractWhen internal (inertia-)gravity waves propagate in a vertically sheared geostrophic (eddying or mean) flow, they exchange energy with the flow. A novel concept parameterizing internal wave–mean flow interaction in ocean circulation models is demonstrated, based on the description of the entire wave field by the wave-energy density in physical and wavenumber space and its prognostic computation by the radiative transfer equation. The concept enables a simplification of the radiative transfer equation with a small number of reasonable assumptions and a derivation of simple but consistent parameterizations in terms of spectrally integrated energy compartments that are used as prognostic model variables. The effect of the waves on the mean flow in this paradigm is in accordance with the nonacceleration theorem: only in the presence of dissipation do waves globally exchange energy with the mean flow in the time mean. The exchange can have either direction. These basic features of wave–mean flow interaction are theoretically derived in a Wentzel–Kramers–Brillouin (WKB) approximation of the wave dynamics and confirmed in a suite of numerical experiments with unidirectional shear flow.

Numerical study on the eddy–mean flow interaction between a cyclonic eddy and Kuroshio

2016 ◽  
Vol 72 (5) ◽  
pp. 727-745 ◽  
Author(s):  
Wu Geng ◽  
Qiang Xie ◽  
Gengxin Chen ◽  
Tingting Zu ◽  
Dongxiao Wang
Keyword(s):  
Numerical Study ◽  
Cyclonic Eddy ◽  
Mean Flow ◽  
Flow Interaction

On the irreversibility of internal-wave dynamics due to wave trapping by mean flow inhomogeneities. Part 1. Local analysis

1993 ◽  
Vol 251 ◽  
pp. 21-53 ◽  
Author(s):  
Sergei I. Badulin ◽  
Victor I. Shrira
Keyword(s):  
Shear Flow ◽  
Internal Wave ◽  
Wave Field ◽  
Large Scale ◽  
Spatial Scales ◽  
Energy Concentration ◽  
Local Analysis ◽  
Mean Flow ◽  
Wave Trapping ◽  
Wave Dynamics

The propagation of guided internal waves on non-uniform large-scale flows of arbitrary geometry is studied within the framework of linear inviscid theory in the WKB-approximation. Our study is based on a set of Hamiltonian ray equations, with the Hamiltonian being determined from the Taylor-Goldstein boundary-value problem for a stratified shear flow. Attention is focused on the fundamental fact that the generic smooth non-uniformities of the large-scale flow result in specific singularities of the Hamiltonian. Interpreting wave packets as particles with momenta equal to their wave vectors moving in a certain force field, one can consider these singularities as infinitely deep potential holes acting quite similarly to the ‘black holes’ of astrophysics. It is shown that the particles fall for infinitely long time, each into its own ‘black hole‘. In terms of a particular wave packet this falling implies infinite growth with time of the wavenumber and the amplitude, as well as wave motion focusing at a certain depth. For internal-wave-field dynamics this provides a robust mechanism of a very specific conservative and moreover Hamiltonian irreversibility.This phenomenon was previously studied for the simplest model of the flow non-uniformity, parallel shear flow (Badulin, Shrira & Tsimring 1985), where the term ‘trapping’ for it was introduced and the basic features were established. In the present paper we study the case of arbitrary flow geometry. Our main conclusion is that although the wave dynamics in the general case is incomparably more complicated, the phenomenon persists and retains its most fundamental features. Qualitatively new features appear as well, namely, the possibility of three-dimensional wave focusing and of ‘non-dispersive’ focusing. In terms of the particle analogy, the latter means that a certain group of particles fall into the same hole.These results indicate a robust tendency of the wave field towards an irreversible transformation into small spatial scales, due to the presence of large-scale flows and towards considerable wave energy concentration in narrow spatial zones.

scholarly journals Interaction of linear modulated waves and unsteady dispersive hydrodynamic states with application to shallow water waves

2019 ◽  
Vol 875 ◽  
pp. 1145-1174 ◽  
Author(s):  
T. Congy ◽  
G. A. El ◽  
M. A. Hoefer
Keyword(s):  
Water Waves ◽  
Large Scale ◽  
Kdv Equation ◽  
Linear Wave ◽  
Mean Flow ◽  
Undular Bore ◽  
Expansion Waves ◽  
Flow Interaction ◽  
The Kdv Equation ◽  
New Type

A new type of wave–mean flow interaction is identified and studied in which a small-amplitude, linear, dispersive modulated wave propagates through an evolving, nonlinear, large-scale fluid state such as an expansion (rarefaction) wave or a dispersive shock wave (undular bore). The Korteweg–de Vries (KdV) equation is considered as a prototypical example of dynamic wavepacket–mean flow interaction. Modulation equations are derived for the coupling between linear wave modulations and a nonlinear mean flow. These equations admit a particular class of solutions that describe the transmission or trapping of a linear wavepacket by an unsteady hydrodynamic state. Two adiabatic invariants of motion are identified that determine the transmission, trapping conditions and show that wavepackets incident upon smooth expansion waves or compressive, rapidly oscillating dispersive shock waves exhibit so-called hydrodynamic reciprocity recently described in Maiden et al. (Phys. Rev. Lett., vol. 120, 2018, 144101) in the context of hydrodynamic soliton tunnelling. The modulation theory results are in excellent agreement with direct numerical simulations of full KdV dynamics. The integrability of the KdV equation is not invoked so these results can be extended to other nonlinear dispersive fluid mechanic models.

Effect of background mean flow on PSI of internal wave beams

2019 ◽  
Vol 869 ◽  
Author(s):  
Boyu Fan ◽  
T. R. Akylas
Keyword(s):  
Internal Wave ◽  
Evolution Equations ◽  
Internal Gravity Wave ◽  
Necessary Condition ◽  
Finite Width ◽  
Asymptotic Model ◽  
Mean Flow ◽  
Short Scale ◽  
The Mean ◽  
Parametric Subharmonic Instability

An asymptotic model is developed for the parametric subharmonic instability (PSI) of finite-width nearly monochromatic internal gravity wave beams in the presence of a background constant horizontal mean flow. The subharmonic perturbations are taken to be short-scale wavepackets that may extract energy via resonant triad interactions while in contact with the underlying beam, and the mean flow is assumed to be small so that its advection effect on the perturbations is as important as dispersion, triad nonlinearity and viscous dissipation. In this ‘distinguished limit’, the perturbation dynamics are governed by the same evolution equations as those derived in Karimi & Akylas (J. Fluid Mech., vol. 757, 2014, pp. 381–402), except for a mean flow term that affects the group velocity of the perturbations and imposes an additional necessary condition for PSI, which stabilizes very short-scale perturbations. As a result, it is possible for a small amount of mean flow to weaken PSI dramatically.

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