Pierre Augier

A New Formulation of the Spectral Energy Budget of the Atmosphere, with Application to Two High-Resolution General Circulation Models

A new formulation of the spectral energy budget of kinetic and available potential energies of the atmosphere is derived, with spherical harmonics as base functions. Compared to previous formulations, there are three main improvements: (i) the topography is taken into account, (ii) the exact three-dimensional advection terms are considered, and (iii) the vertical flux is separated from the energy transfer between different spherical harmonics. Using this formulation, results from two different high-resolution GCMs are analyzed: the Atmospheric GCM for the Earth Simulator (AFES) T639L24 and the European Centre for Medium-Range Weather Forecasts (ECMWF) Integrated Forecast System (IFS) T1279L91. The spectral fluxes show that the AFES, which reproduces quite realistic horizontal spectra with a k−5/3 inertial range at the mesoscales, simulates a strong downscale energy cascade. In contrast, neither the k−5/3 vertically integrated spectra nor the downscale energy cascade are produced by the ECMWF IFS.

Experimental study of stratified turbulence forced with columnar dipoles

We present a novel experimental setup aimed at producing a forced strongly stratified turbulent flow. The flow is forced by an arena of 12 vortex pair generators in a large tank. The continuous interactions of the randomly produced vortex pairs give rise to a statistically stationary disordered flow in contrast to previous experiments where the stratified turbulence is decaying. The buoyancy frequency N is set to its highest value N = 1.7 rad/s using salt as stratifying agent so that the horizontal Froude number F h = Ω/N is low, while the buoyancy Reynolds number R=ReFh2 , where Re = Ωa 2/ν is the classical Reynolds number, is as high as possible given the experimental constraints (Ω is the maximum angular velocity of the vortices, a their radius and ν the viscosity). PIV measurements show that the flow is not homogeneous in the horizontal plane and is organised into horizontal layers along the vertical. When R is increased, we observe a progressive evolution from the viscosity dominated regime with smooth layers to a regime with small scales superimposed on the layers and for which the vertical Froude number is of order one. The latter regime resembles the strongly stratified turbulent regime with a downscale cascade that has been predicted for large R . However, horizontal second order structure functions do not exhibit a clear inertial range for the largest R achieved R=310 . In addition, the corresponding turbulent buoyancy Reynolds number Rt=P/(νN2) based on an estimation of the injection rate of energy P is only of order unity Rt≃0.4 indicating that only the edge of the strongly stratified turbulent regime has been reached. However, these results suggest that sufficiently large turbulent buoyancy Reynolds numbers, Rt≃10 , could be achieved experimentally by scaling up five times this novel set-up.

Experimental study of forced stratified turbulence

Recent results have shown that strongly stratified turbulence has a three dimensional dynamic instead of a quasi-two dimensional dynamic conjectured previously. The structures are strongly anisotropic with an aspect ratio scaling like the Froude number \( l_v /l_h F_h\) [1]. A direct cascade of energy from large scales to small scales associated with a kh -5/3 horizontal kinetic energy spectrum has been predicted and observed in DNS of forced stratified turbulence when the buoyancy Reynolds number Rt is sufficiently large [2]. In constrast, for small Rt, the flow is dominated by vertical viscous effects even if the Reynolds number is large [3, 4].