A loss of memory in stratified momentum wakes

Abstract

In this paper we compare the wakes of various bluff bodies in a stratified fluid at moderately high Froude numbers (Fϵ2U B /NDϾ8) and Reynolds numbers ͑ReϷ5000͒. The size and amplitude of the long-lasting wakes clearly depend on the shape of the bluff body, the wake width being small for a streamlined object and large for an object with sharp edges. However, the wake width can be collapsed when it is normalized by an effective diameter based on the drag force, often called the momentum thickness. General laws for the wake width, the velocity defect, and the Strouhal number are thus deduced and fit the data well. Finally, the cross-fluctuations of the velocity and the turbulent kinetic energy are analyzed. Their amplitudes and widths are proportional to those of the mean profile. Thus, the wake remembers only the momentum flux given by the bluff body to the fluid and not any other aspects of its geometry.

Self-preservation in stratified momentum wakes

“…In late wakes of towed bluff bodies in stratified fluids R 2 was found to be close to 15, regardless of initial conditions (within 30%) [13], so this numerical value is retained in the following. By neglecting the vertical Reynolds stress while retaining the horizontal Reynolds stress in (5), we reach again a standard diffusion equation for the buoyancy-controlled flow,…”

“…The experimental results were obtained for the particular case of the wake of a sphere, but were successfully extended to the general case of other bluff bodies [13], by considering the momentum thickness as the proper lengthscale rather than the body diameter. For an axisymmetric bluff body, the momentum thickness is defined as…”

“…The empirical scaling laws describing the velocity defect and wake width as developed in [3,4,13,14] apply to any bluff body wake or jet in a uniform, stable density gradient. However, they remain empirical findings, linked by incomplete arguments and a coherent theoretical framework has not been proposed.…”

Empirical scaling of antisymmetric stratified wakes

“…A mean value of the turbulent Reynolds number for α ≤ 5 0 lies around Rt = 25 ± 20. For non-propelled body experiments, Meunier and Spedding (2004) found a similar value of Rt 15, and concurred that it may not be considered constant until after N t = 100.…”

“…Chomaz et al (1993b), Spedding et al (1996) , Spedding (1997)). The effect of the shape of the bluff body was investigated by Meunier and Spedding (2004), who showed that all bluff body wakes, regardless of body geometry, could be rescaled with parameters that depended only on the initial momentum flux in the wake. Meunier and Spedding (2005) described the wakes of propelled bodies, finding similarly general scaling behaviour at all but a small class of wakes that were almost exactly momentumless.…”