The Downstream of a Density-Stratified Sphere Wake

Abstract

The objective of the present work is to access moderately-stratified wake statistics into the far downstream. This is accomplished via a continuation of the solution from the stratified-wake, body-inclusive, large-eddy simulation of Chongsiripinyo & Sarkar (TSFP10) by a temporal-model, direct numerical simulation. Simulation of stratified wake at Re = U∞D/ν = 10^4 and Fr = U∞/ND = 3 is performed; U∞, D, and N are sphere velocity, sphere diameter, and buoyancy frequency. Three findings are as follows. 1) In the late-NEQ regime, centerline mean streamwise velocity deficit continues to decay with the power-law exponent U0 ∝ t^{−0.4} and while the progression of horizontal wake span is at LH ∝ t^{1/3}, vertical wake extent remains stagnant (LV ∝ t^0). 2) The beginning of NEQ-Q2D transitioning is found to be where the mean wake is geometrically most anisotropic, that is the ratio LV /LH is at a minimum. The transitioning is a gradual process that lasts 50 ≤ N t ≤ 250. 3) In the Q2D regime, vertical profile of the mean streamwise defect velocity (Ud) exhibits self-similarity. This self-similar state is not of Gaussian-type but better fitted with individual plane-wake self-similarity solution. The centerline defect velocity rapidly decays at a rate U0 ∝ t^{−3/4}. Horizontal extension growth rate is reduced to be LH ∝ t^{1/4} and the exponential growth rate of wake height is found to be LV ∝ t^{1/2}, an indication of the dominating viscous diffusion process.