Laminar-turbulent patterning in wall-bounded shear flows: a Galerkin model

On its way to turbulence, plane Couette flow - the flow between counter-translating parallel plates - displays a puzzling steady oblique laminar-turbulent pattern. We approach this problem via Galerkin modelling of the Navier-Stokes equations. The wall-normal dependence of the hydrodynamic field is treated by means of expansions on functional bases fitting the boundary conditions exactly. This yields a set of partial differential equations for the spatiotemporal dynamics in the plane of the flow. Truncating this set beyond lowest nontrivial order is numerically shown to produce the expected pattern, therefore improving over what was obtained at cruder effective wall-normal resolution. Perspectives opened by the approach are discussed.Comment: to appear in Fluid Dynamics Research; 14 pages, 5 figure

An Evolved Wavelet Library Based on Genetic Algorithm

As the size of the images being captured increases, there is a need for a robust algorithm for image compression which satiates the bandwidth limitation of the transmitted channels and preserves the image resolution without considerable loss in the image quality. Many conventional image compression algorithms use wavelet transform which can significantly reduce the number of bits needed to represent a pixel and the process of quantization and thresholding further increases the compression. In this paper the authors evolve two sets of wavelet filter coefficients using genetic algorithm (GA), one for the whole image portion except the edge areas and the other for the portions near the edges in the image (i.e., global and local filters). Images are initially separated into several groups based on their frequency content, edges, and textures and the wavelet filter coefficients are evolved separately for each group. As there is a possibility of the GA settling in local maximum, we introduce a new shuffling operator to prevent the GA from this effect. The GA used to evolve filter coefficients primarily focuses on maximizing the peak signal to noise ratio (PSNR). The evolved filter coefficients by the proposed method outperform the existing methods by a 0.31 dB improvement in the average PSNR and a 0.39 dB improvement in the maximum PSNR

The onset of turbulent rotating dynamos at the low magnetic Prandtl number limit

We demonstrate that the critical magnetic Reynolds number Rm c for a turbulent nonhelical dynamo in the limit of low magnetic Prandtl number Pm (i.e. Pm=Rm/Re ≪ 1) can be significantly reduced if the flow is subjected to global rotation. Even for moderate rotation rates the required energy injection rate can be reduced by a factor of more than 10 3 . This strong decrease in the onset is attributed to the transfer of energy to the large scales, forming a large-scale condensate, and the reduction in the turbulent fluctuations that cause the flow to have a much larger cutoff length scale than in a non-rotating flow of the same Reynolds number. The dynamo thus behaves as if it is driven just by the large scales that act as a laminar flow (i.e. it behaves as a high Pm dynamo) even though the actual Reynolds number is much higher than the magnetic Reynolds number (i.e. low Pm). Our finding thus points to a new paradigm for the design of new experiments on liquid metal dynamos

The onset of turbulent rotating dynamos at the low magnetic Prandtl number limit

We demonstrate that the critical magnetic Reynolds number Rm c for a turbulent nonhelical dynamo in the limit of low magnetic Prandtl number Pm (i.e. Pm=Rm/Re ≪ 1) can be significantly reduced if the flow is subjected to global rotation. Even for moderate rotation rates the required energy injection rate can be reduced by a factor of more than 10 3 . This strong decrease in the onset is attributed to the transfer of energy to the large scales, forming a large-scale condensate, and the reduction in the turbulent fluctuations that cause the flow to have a much larger cutoff length scale than in a non-rotating flow of the same Reynolds number. The dynamo thus behaves as if it is driven just by the large scales that act as a laminar flow (i.e. it behaves as a high Pm dynamo) even though the actual Reynolds number is much higher than the magnetic Reynolds number (i.e. low Pm). Our finding thus points to a new paradigm for the design of new experiments on liquid metal dynamos