Abstract
The two-dimensional (2D) freely decaying turbulence is investigated experimentally in an electron plasma confined in a Malmberg–Penning trap and studied using a wavelet-based multiresolution analysis. The coherent and incoherent parts of the flow are extracted using a recursive denoising algorithm with an adaptive self-consistent threshold. Only a small number of wavelet coefficients (but corresponding to the greatest part of the enstrophy or energy contents) turns out to be necessary to represent the coherent component. The remaining small amplitude coefficients represent the incoherent component, which is characterized by a near Gaussian vorticity PDF. Scale contributions to the measured enstrophy and energy distributions are inferred, and the results are compared with recent experiments and theoretical pictures of the 2D turbulence. The results suggest that the computational complexity of 2D turbulent flows may be reduced in simulations by considering only coherent structures interacting with a statistically modeled background.
Highlights
The laboratory investigation of two-dimensional (2D) Eulerian flows is a challenging task
The light emitted by the screen is collected by a 12 bit charge-coupled device (CCD) camera
The method described in [25] is applied here in order to separate the coherent structures from the incoherent vorticity distribution with the minimum degree of arbitrariness and perform a separated spectral analysis on the coherent and incoherent parts of the flow
Summary
The laboratory investigation of two-dimensional (2D) Eulerian flows is a challenging task. The analysis of the turbulence, performed on the basis of the experimental data, should be able to discriminate the coherent and the incoherent parts of the flow. For this reason, in the present paper wavelet transforms [13] are used, which, contrary to Fourier transforms, have welllocalized basis functions both in physical and ‘wave-number’ space In the present case of 2D turbulence in an electron plasma, the presence of localized coherent structures introduces non-negligible contributions at all scales (wavenumbers) in the Fourier space, determining a piling-up effect at small spatial scales, so that the Fourier analysis is no longer a proper inspection tool.
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