An Experimental Study of the Inverse Cascade of Energy in Two-Dimensional Turbulence
A quasi two dimensional turbulence is studied, which is created in a horizontal layer of mercury submitted to a vertical, homogeneous and permanent magnetic field B (of which effect is to stabilize the flow to a bidimensional state ). A well controlled injection of electrical currents from a periodic network of electrodes allows us to drive the flow. In Fourier space, this corresponds to injection of enstrophy and energy on the discrete two dimensional set of wavenumbers corresponding to the spacial periodic repartition of exciting electrodes . The flow is studied by streak photography or using measuring electrodes (Fig. 1) which have been arranged at the bottom of the box. In theses types of flows the measured potential, when removed the part generated by injection currents, is directly proportional to the stream function. A good model of the evolution of this flow is given by the two dimensional Navier Stokes equations with a steady forcing term and a linear friction one due to the Hartmann layer, of which effect is estimated by the parameter Rh. Two different shapes of boxes have been used in this study.
KeywordsNavier Stoke Equation Measuring Electrode Linear Friction Inverse Cascade Hexagonal Network
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