Large-scale characteristics of stratified wake turbulence at varying Reynolds number
Date
2019-08-09
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Abstract
We analyze a large-eddy simulation data set of wakes of a towed sphere of diameter D at speed U in a uniformly stratified Boussinesq fluid with buoyancy frequency N and kinematic viscosity ν. These temporally evolving wakes are simulated using a spectral multidomain penalty-method-based incompressible Navier-Stokes solver for Fr≡2U/ND∈{4,16,64} and Re≡UD/ν∈{5×103,105,4×105, enabling a systematic examination of stratified wakes at three different values of Re sufficiently separated in magnitude. As such, particular attention is paid to the effects of varying Re on the evolution of large-scale characteristics of stratified wake turbulence. We examine the evolution of horizontal and vertical integral length scales (ℓh and ℓv), horizontal and vertical fluctuation velocities (U and W), local vertical shear, as well as the resulting dimensionless parameters based on the above quantities. In particular, the vertical turbulent Froude number Fr★v≡2πU/Nℓv is found to be of order unity, a signature of the dynamics in the strongly stratified regime where shear instabilities develop between anisotropic flow layers. The horizontal turbulent Reynolds number Reh≡Uℓh/ν stays approximately constant in time and the horizontal turbulent Froude number Frh≡U/Nℓh decays in time as (Nt)−1, consistent with scaling analysis of freely decaying turbulence. We characterize the transitions between distinct stratified flow regimes and examine the effects of body-based parameters Re and Fr on these transitions. The transition from the weakly to the strongly stratified regime, which is marked by Fr★v decaying to unity, occurs when Frh≃O(0.01). We further show that the initial value of Reh at which the flow completes the above transition scales as ReFr−2/3, which provides a way to predict the possibility of accessing the strongly stratified regime for a wake of given Re and Fr. The analysis reported here constitutes an attempt to obtain the predictive capability of stratified wake turbulence in terms of Reynolds number Re, applying select elements of strongly stratified turbulence theory, so far typically utilized for homogeneous turbulence, to a canonical inhomogeneous turbulent free-shear flow.