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HILBERT-BASED VORTICITY STATISTICS IN TWO-DIMENSIONAL TURBULENCE

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In this paper, we report for a measurement of the high-order scaling exponents ζωF (q) (forward) and ζωI (q) (inverse) for the vorticity in two-dimensional (2D) turbulence. This is accomplished by applying a Hilbert-based technique to the vorticity fields obtained from a 2D high-resolution direct numerical simulation with an Ekman friction. It confirms that the inverse enstrophy cascade is nonintermittent with a scaling exponent linear with the statistical order q, i.e., q/3. While the measured scaling exponents ζωF (q) is found to be nonlinear with q and can be described by a log-Poisson like formula, i.e., ζωF (q) = q/3 + 2/5(1 − (2/5)q ). This confirms experimentally that the forward enstrophy cascade in the 2D turbulence is intermittent.

Author(s):

Huanshu Tan    
Shanghai Institute of Applied Mathematics and Mechanics, Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai University
China

Yongxiang Huang    
Shanghai Institute of Applied Mathematics and Mechanics, Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai University
China

Jianping Meng    
Department of Mechanical Engineering & Aerospace University of Strathclyde Glasgow,
United Kingdom