Claude Basdevant

EXPERIMENTAL AND NUMERICAL STUDY OF VORTEX COUPLES IN TWO-DIMENSIONAL FLOWS

Two-dimensional turbulence is investigated experimentally in thin liquid films. This study shows the spontaneous formation of couples of opposite-sign vortices in von Karman wakes. The structure of these couples, their behaviour and their role in turbulent flows is then studied using both a numerical simulation and laboratory results.

A Study of Barotropic Model Flows: Intermittency, Waves and Predictability

Abstract The regime flows corresponding to the barotropic nondivergent equation with forcing, drag and subgrid-scale dissipation are studied using spectral model on the plane and on the sphere. The flow regimes obtained exhibit clear evidence of the existence of an enstrophy-cascading inertial range, together with a reverse energy cascade toward small wavenumbers. It is shown, however, that the enstrophy cascade is not associated with the k−3 spectral slope expected from the Kolmogorov-Kraichnan theory of two-dimensional turbulence; the slopes obtained are significantly steeper. This apparent paradox is tentatively resolved by a phenomenological theory of space-time intermittency in two dimensions; it is further shown that such intermittency associated with steeper spectra also restores locality of the nonlinear transfers in wavenumber space. In contrast to the well-known nonlocality typical of two-dimensional non-intermittent turbulent flows. The effect of differential rotation in connection with Rossby ...

Wavelet spectra compared to Fourier spectra

The relation between Fourier spectra and spectra obtained from wavelet analysis is established. Small scale asymptotic analysis shows that the wavelet spectrum is meaningful only when the analyzing wavelet has enough vanishing moments. These results are related to regularity theorems in Besov spaces. For the analysis of infinitely regular signals, a new wavelet, with an infinite number of cancellations is proposed.

Spectral and finite difference solutions of the Burgers equation

Abstract Spectral methods (Fourier Galerkin, Fourier pseudospectral, Chebyshev Tau, Chebyshev collocation, spectral element) and standard finite differences are applied to solve the Burgers equation with small viscosity ( v = 1 100 π ). This equation admits a (nonsingular) thin internal layer that must be resolved if accurate numerical solutions are to be obtained. From the reported computations, it appears that spectral schemes offer the best accuracy, especially if coordinate transformation or elemental subdivision is used to resolve the regions of large variation of the dependent variable.

Cirene: Air—Sea Interactions in the Seychelles—Chagos Thermocline Ridge Region

The Vasco-Cirene program explores how strong air-sea interactions promoted by the shallow thermocline and high sea surface temperature in the Seychelles-Chagos thermocline ridge results in marked variability at synoptic, intraseasonal, and interannual time scales. The Cirene oceanographic cruise collected oceanic, atmospheric, and air-sea flux observations in this region in January–February 2007. The contemporaneous Vasco field experiment complemented these measurements with balloon deployments from the Seychelles. Cirene also contributed to the development of the Indian Ocean observing system via deployment of a mooring and 12 Argo profilers. Unusual conditions prevailed in the Indian Ocean during January and February 2007, following the Indian Ocean dipole climate anomaly of late 2006. Cirene measurements show that the Seychelles-Chagos thermocline ridge had higher-than-usual heat content with subsurface anomalies up to 7°C. The ocean surface was warmer and fresher than average, and unusual eastward cur...

On the validity of the “Weiss criterion” in two-dimensional turbulence

Abstract The “Weiss criterion” for two-dimensional incompressible turbulent flows separates flow regions where the motion is hyperbolic in character from regions where it is elliptic. This criterion is based on the hypothesis that the velocity gradient varies slowly with respect to the vorticity gradient. We inspected this hypothesis and derived a criterion linking its validity to the curvature of the pressure field. It turns out from numerical experiments that the hypothesis on which relies the “Weiss criterion” is nearly only valid in vortex cores, that is in strongly elliptic regions and near stagnation points (high pressures).

Structure Functions and Dispersion Laws in Two-Dimensional Turbulence

Abstract The classical phenomenological relations between dispersion laws, second-order structure functions and energy spectra are reexamined from a more quantitative standpoint. It is shown that when a nonlocal energy spectrum (steeper than k−3) is substituted into the relation giving structure functions or dispersion laws, an infrared divergence occurs so that the structure functions or dispersion laws at inertial-range separation are not dominated by contributions from the inertial range spectrum; they saturate and become independent of spectral steepness. It follows that the spectral steepness of real flows in the enstrophy inertial range must be extremely difficult to estimate from correlation or dispersion measurements alone. This might explain why the existence of steep spectra, speculated on the basis of numerical modeling, has not been confirmed by real flow measurements.

Parameterization of subgrid scale barotropic and baroclinic eddies in quasi-geostrophic models: anticipated potential vorticity method

Abstract A lateral diffusion scheme designed to efficiently parameterize the subgrid scale lures associated with barotropic and baroclinic transients is presented and tested on a quasi-geostrophic, two layer model, with law-scale thermal forcing. The scheme is based on formal energy conservation and potential enstrophy dissipation. At very coarse resolutions, where the cutoff scale is of the order of the internal radius of deformation, the diffusion scheme is shown to produce a realistic amount of potential-to-kinetic energy conversions, and realistic amplitudes of the large-scale barotropic modes.

Relative dispersion in two-dimensional turbulence

The statistical laws of relative dispersion in two-dimensional turbulence are studied by deriving an exact equation governing its evolution in time and then evaluating the magnitude of its various terms in numerical experiments.

Intermodal energy transfers in a proper orthogonal decomposition-Galerkin representation of a turbulent separated flow

Energy transfers between modes obtained from the proper orthogonal decomposition (POD) of a turbulent flow past a backward-facing step are analysed with the aim of providing guidelines for modelling unresolved modes in truncated POD–Galerkin models. It is observed that energy transfers are local in the POD basis, and that the Fourier-decomposition-based concepts of forward and backward energy cascades are also valid in the POD basis, the net effect being a forward energy cascade. General features of the eddy-viscosity representation of kinetic energy transfers are investigated through a priori tests. It is observed that the ideal eddy-viscosity model should exhibit a cusp behaviour near the cutoff mode.