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Center for Nonlinear Studies |
THIS SEMINAR IS PART OF THE CNLS WORKSHOP: NEW DIRECTIONS IN TWO-DIMENSIONAL TURBULENCE BEING HELD AUGUST 28 - SEPTEMBER 1, 2006 AT CNLS.
As predicted by Kraichnan, two different inertial ranges are observed when a two-dimensional fluid system is forced at intermediate scales, smaller than the domain size and larger than the viscous dissipative length-scales. In particular, the energy flows toward the large scales giving rise to an inverse energy cascade characterized by the k–5/3 Kolmogorov spectrum while small-scale statistics is governed by a direct enstrophy cascade which is expected to develop a smooth flow with a k –3 energy spectrum. In this context, I will present experimental results both on a decaying and on a forced system in which the flow is produced by applying a combination of electric and magnetic fields on a thin layer of an electrolyte solution (i.e. EM cell). Flow measurements are performed through image analysis. In particular I will focus on Feature Tracking (FT), a tracking technique based on correlation windows which has allowed to obtain at the same time a large amount of Lagrangian data (i.e. the seeding density can be very high and trajectories can be followed for large time intervals) and high-resolution Eulerian velocity fields. A discussion on the influence of the bottom friction in the flow dynamics will be carried out. As a matter of fact, the presence of a linear friction term strongly affects the direct cascade: the enstrophy flux across scales is no longer constant and the scaling exponent of the spectrum differs from the Kraichnan prediction k-3 by a correction proportional to the friction intensity. The origin of this correction can be understood by exploiting the analogy between two-dimensional vorticity field and a scalar field passively advected by a smooth velocity field. In the case of a passive scalar with a finite lifetime, it is possible to obtain explicit expressions for the scaling exponents of the power spectrum which depend on the intensity of the linear damping and on the statistics of finite-time Lyapunov exponents. Finally, the influence of strong rotation on the 2D dynamics will be introduced. Preliminary results showing the effect on the flow field of the change of the Coriolis force with latitude will be shown. The flow is generated considering the same EM cell in a rotating reference frame (i.e. a rotating table). In agreement with theoretical prediction and previous experiments, results corresponding to high values of rotation show a preferential transfer of energy towards zonal modes and the consequent organization of a weak anticyclonic circulation in correspondence of the ‘polar’ zone. Moreover, the analysis of the one-dimensional energy spectra shows a scaling low steeper than Kolmogorov law and a peak in correspondence of Rhines scale indicating a soft barrier of the energy transfer towards slow wave-numbers.
Host: Misha Chertkov