Turbulent wakes of linearly stratified flow past a sphere

Experimental observations and associated scaling analyses are presented for the flow of a linearly stratified fluid past a sphere for conditions under which the wake is fully turbulent. It is shown that for internal Froude numbers Fi≲2, the turbulent wake is suppressed by stratification in the immediate lee of the sphere. For Fi≳2, the normalized thickness δT/D grows as t1/3 before the wake height reaches its maximum (which takes place at Nt≊2.0), much the same as for wakes of spheres in homogeneous flow; here D is the sphere diameter, N is the buoyancy frequency, and t is the time. The normalized horizontal wake dimension γT/D, on the other hand, grows in the near wake as t1/3 for all Fi but, for Nt≳2.0, grows somewhat more rapidly as t1/2. The Strouhal number for the far-wake vortex street is measured and shown to be roughly a constant St≊0.18, independent of the Reynolds and Froude numbers. It is suggested that the frequency of the far-wake, quasi-two-dimensional vortices is established by the eddy shedding frequency of the near wake and thus is independent of stratification effects.