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 less than or similar to 2, the turbulent wake is suppressed by stratification in the immediate lee of the sphere. For Fi greater than or similar to 2, the normalized thickness delta(T)/D grows as t1/3 before the wake height reaches its maximum (which takes place at Nt almost-equal-to 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 gamma(T)/D, on the other hand, grows in the near wake as t1/3 for all Fi but, for Nt greater than or similar to 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 almost-equal-to 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.