Drag on a sphere moving horizontally through a stratified liquid

Abstract

The drag on a sphere moving horizontally through stably stratified salt water is measured in laboratory experiments. The increment ΔCD in drag coefficient due to the stratification is obtained as a function of a stratification parameter κ and, in principle, the usual Reynolds number R. In these experiments, where R ranges from 150 to 5000, ΔCD is insensitive to R. But, as a function of κ, ΔCD has both positive and negative values attributable respectively to lee-wave drag and to suppression of turbulence in the wake. An observed delay in flow separation also apparently results from the lee-wave drag.

Surface characters of internal waves generated by Rankine ovoid

“…In the general case for a smooth function (z), the solution of Eqs. (12) and (13) can be represented in the form…”

“…Chomaz et al [12] studied the wake structures in the near field of a sphere and obtained the Schlieren shadowgraphies of the Mach front, the internal Mach wake and the turbulent wake etc. Lofquist et al [13] and Xu et al [14] carried out the experiments of the drag of the sphere and Rankine ovoid, respectively. The previous investigations described above enriched the knowledge on this kind of internal waves.…”

High-Reynolds-number weakly stratified flow past an obstacle

“…This is consistent with the visual observations made during the towing tank experiments, which typically had H = 20. Our computations (and those of Natarajan et al 1993) suggest that for a fully laminar case Re = 33 would yield L = 20 for H = 20 so, assuming that the variation of eddy viscosity in the turbulent wake is such as to make the effective Reynolds number about 30, we deduce an effective value of about 0.9 for H / k i R e . This is, of course, far from rigorous, but the experimental data on figure 11 are, on that basis, quite consistent with the numerical results ~ showing a somewhat lower fall with Ri than occurs for, say, H / k i Re = 0.172, as expected on the basis of the theory.…”

“…There is experimental evidence that for high-Reynolds-number flow over bodies which generate a separated wake region, stratification first acts (in the supercritical regime) to reduce both the size of this region and the obstacle drag (e.g. Davis 1969;Lofquist & Purtell 1984;Castro, Snyder & Baines, 1990). Castro et al (and Hanazaki 1988) demonstrated via numerical computation that these effects also occur in low-Reynolds-number (laminar) flows although, again, interest was concentrated on the subcritical parameter regime in which wave motions interact with the near wake and may also propagate upstream.…”

Drag increment of internal waves generated by horizontally moving spheroid in supercritical regime

“…The elemental special solution is a so called retarded Green's function. In terms of a simplest source distribution, the drag of a sphere moving horizontally and uniformly in uniformly stratified fluids with a constant Brunt-Väisälä frequency was studied theoretically and experimentally [6][7][8], whereas the experimental study of the Rankine ovoid moving horizontally and uniformly in a pycnocline was carried out by authors [9].…”