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.

Onset of energy equipartition among surface and body waves

2021 ◽  
Vol 477 (2246) ◽  
pp. 20200775
Author(s):  
L. Borcea ◽  
J. Garnier ◽  
K. Sølna
Keyword(s):  
Radiative Transfer ◽  
Thin Layer ◽  
Surface Waves ◽  
Transfer Equation ◽  
Radiative Transfer Equation ◽  
Body Waves ◽  
Homogeneous Layer ◽  
Power Exchange ◽  
Energy Equipartition ◽  
The Mean

We derive a radiative transfer equation that accounts for coupling from surface waves to body waves and the other way around. The model is the acoustic wave equation in a two-dimensional waveguide with reflecting boundary. The waveguide has a thin, weakly randomly heterogeneous layer near the top surface, and a thick homogeneous layer beneath it. There are two types of modes that propagate along the axis of the waveguide: those that are almost trapped in the thin layer, and thus model surface waves, and those that penetrate deep in the waveguide, and thus model body waves. The remaining modes are evanescent waves. We introduce a mathematical theory of mode coupling induced by scattering in the thin layer, and derive a radiative transfer equation which quantifies the mean mode power exchange. We study the solution of this equation in the asymptotic limit of infinite width of the waveguide. The main result is a quantification of the rate of convergence of the mean mode powers toward equipartition.

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.

A new parameterization of gravity waves for atmospheric circulation models based on the radiative transfer equation

2020 ◽  
Author(s):  
Matthäus Mai ◽  
Erich Becker
Keyword(s):  
Radiative Transfer ◽  
Wave Field ◽  
Gravity Wave ◽  
Gravity Waves ◽  
Transfer Equation ◽  
Middle Atmosphere ◽  
Radiative Transfer Equation ◽  
Dynamical Instability ◽  
Mean Flow ◽  
Wave Dissipation

<p>Gravity waves play an important role in the momentum and heat budgets of the middle atmosphere. Global circulation models used for long-term simulations need to parameterize the transport of wave momentum and energy from the lower to the middle atmosphere and the associated wave-mean flow interaction. This gravity wave-mean flow interaction is usually due to dynamical instability triggered by wave refraction and amplitude growth, giving rise to wave dissipation. In addition, gravity waves can interact with the mean flow through the passage of finite wave packets without dissipation. Conventional gravity wave parameterizations cannot describe this effect; nor can they account for wave sources being continuous in space and time, for the finite duration of vertical propagation, or wave acceleration induced by a temporally varying mean flow.<br>All these effects are accommodated when the wave field is described by the wave-energy density in wave number and physical space, and its evolution is computed by the radiative transfer equation for the wave field. A corresponding parameterization called IDEMIX has successfully been applied in ocean models. Here we present a corresponding parameterization for atmosphere models in single-column approximation. The new scheme is validated in off-line simulations. Results show that the evolution of wave packets forced in the troposphere and propagating upward into stratospheric and mesospheric jets is simulated consistently with theoretical expectations. This includes wave reflection and critical layers. Furthermore, an explicit diffusion scheme was added to account for wave dissipation due to dynamical instability.</p>

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