Vortex structures and kinetic energy budget in two-dimensional flow past a square cylinder

Abstract

Direct Numerical Simulation of unsteady, two-dimensional flow past a square cylinder placed centrally in a channel has been carried out using a higher order finite difference scheme. A Reynolds number of 100 has been considered in the computation. The flow in the wake is found to be unsteady with a strong periodic component. The instantaneous vorticity field at this Reynolds number is seen to be spatially coherent. Maps of stress components formed from the oscillatory components of the velocity field u^~ and v^~ show double peaks in u^~u^~ and u^~v^~ but a single peak in v^~v^~. The maps are seen to be symmetric about the centreline of the flowspace. The results obtained in the present work are qualitatively similar to the phase-averaged plots from the experiments reported at high Reynolds numbers. Hence, the primary conclusion of the present study is that the unsteady flows with one or a few dominating frequencies (periodic or quasi-periodic) are statistically similar to a fully turbulent flow. To assess the similarity further, the energy transfer mechanism between the mean motion and the fluctuations has been studied through different terms associated with kinetic energy budget of the fluctuating velocities. The total pressure, the advection of the time-mean flow and production terms are found to be primarily responsible for the energy cascade. In contrast, diffusion and dissipation do not appear to have a significant influence on the energy transfer mechanism.