The accessibility of strongly stratified turbulence in towed-sphere wakes*

The strongly stratified turbulence (SST) flow regime (Brethouwer et al. 2007) is characterized by small turbulent horizontal Froude number, i.e. Fr_h « 1, and large buoyancy Reynolds number, i.e. Re_hFr_h² » 1, two quantities that could vary significantly with time in temporally evolving free-shear turbulent flows, such as a towed-sphere wake. We investigate a large-eddy simulation dataset of stratified towed-sphere wakes of varying Reynolds number, Re ≡ UD/ν = [5×10³, 10⁵, 4×10⁵], and Froude number, Fr ≡ 2U/(ND) = [4,16,64], where U is tow speed, D is sphere diameter and N is buoyancy frequency. By examining relevant stratified turbulence parameters in appropriately defined phase diagrams, we show that these wakes can indeed access the SST regime if ReFr^-2/3 > O(10³). The length of time during which the wake turbulence would operate within this regime also depends strongly on Re and Fr. This analysis constitutes a first attempt to obtain a predictive capability of stratified wake turbulence in terms of Re, while extending the investigations of SST from space-filling homogeneous turbulence to a canonical inhomogeneous free-shear flow.