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Two-dimensional turbulence is investigated experimentally in thin liquid films. This study shows the spontaneous formation of couples of opposite-sign vortices in von Kármán 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.

In this paper we study the statistical laws of relative dispersion in two-dimensional turbulence by deriving an exact equation governing its evolution in time, then evaluating the magnitude of its various terms in numerical experiments, which allows us to check the validity of the classical dispersion laws: the equivalent to the Richardson-Obukhov t3 law in the energy cascade range, and the Kraichnan-Lin exponential law in the enstrophy cascade range. We examine theoretically and experimentally the conditions of validity of both laws. It is found that the t3 law is obtained in the energy inertial range provided the separation scale of the particles is smaller by an order of magnitude than the injection scale. When the t3 law is reached, the relative acceleration correlations are observed to have reached a statistical quasistationary stage: this would tend to justify in the energy inertial range of two-dimensional turbulence a working hypothesis formulated by Lin & Reid (1963); also, the necessity of starting from very small initial separations to get the t3 law may be explained by the time necessary for relative acceleration correlations to reach the statistical quasi-stationary regime. On the other hand, the Kraichnan-Lin exponential law is, strictly speaking, never observed; it is in fact reduced to a very short transient stage when the relative dispersion characteristic time reaches its minimum value, as predicted by Batchelor.

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A field experiment in the southwesternIndian Ocean provides new insights into ocean-atmosphere interactions in a key climatic region. W hile easterly trade winds blow year-round over the southern Indian Ocean, surface winds experience a striking reversal north of 10°S. During boreal summer, the low-level easterly flow penetrates northward, is deflected when crossing the equator, and forms the strong Indian monsoon jet. During boreal winter, northeasterly winds also bend while crossing the equator southward and form a weak low-level westerly jet between the equator and 10°S (Fig. la)

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.

The dynamics of vorticity in two-dimensional turbulence is studied by means of semi-direct numerical simulations, in parallel with passive-scalar dynamics. It is shown that a passive scalar forced and dissipated in the same conditions as vorticity, has a quite different behaviour. The passive scalar obeys the similarity theory à la Kolmogorov, while the enstrophy spectrum is much steeper, owing to a hierarchy of strong coherent vortices. The condensation of vorticity into such vortices depends critically both on the existence of an energy invariant (intimately related to the feedback of vorticity transport on velocity, absent in passive-scalar dynamics, and neglected in the Kolmogorov theory of the enstrophy inertial range); and on the localness of flow dynamics in physical space (again not considered by the Kolmogorov theory, and not accessible to closure model simulations). When space localness is artificially destroyed, the enstrophy spectrum again obeys a k−1 law like a passive scalar. In the wavenumber range accessible to our experiments, two-dimensional turbulence can be described as a hierarchy of strong coherent vortices superimposed on a weak vorticity continuum which behaves like a passive scalar.