Untitled

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, bodyinclusive, large-eddy simulation of [1] by a temporal-model, direct numerical simulation. Simulation of stratified sphere wake at Re = U ∞ D/ν = 10 4 and F r = U ∞ /N D = 3 is performed; U ∞ , D, and N are sphere velocity, sphere diameter, and buoyancy frequency. Four findings are as follows. 1) Toward the end of the mid wake, centerline mean streamwise velocity deficit continues to decay with the power-law exponent t −0.4 ; with t = x/U ∞ is proportional to the distance (x) from the sphere. The progression of horizontal wake span is at t 1/3 but the vertical wake extent remains stagnant. 2) The beginning of transition into the late wake is found to be where the mean wake is geometrically most anisotropic. The transitioning is a gradual process that lasts 50 ≤ N t ≤ 250. 3) In the late wake, vertical profile of the defect velocity 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 t −3/4 . Horizontal extension growth rate is reduced to t 1/4 , disagreeing with many previous studies. The exponential growth rate of wake height is found to be t 1/2 , an indication of the dominating viscous diffusion process. 4) Throughout the wake lifetime, deviation of density from the background state exists in the vertical center plane but small in magnitude. The deviation causes an enchancement in wake-core stratification that manifests itself until the transition into the late wake.