Forces on spheres moving horizontally in a rotating stratified fluid

Publisher Website
Google Scholar
Abstract
Measurements have been made of the net horizontal force F acting on a sphere moving with horizontal velocity U (Reynolds numbers in the range 102-104) through a stratified fluid rotating about a vertical axis with uniform angular velocity Ω. In both homogeneous and stratified rotating fluids with small Rossby number R(R = U/Ωa ≲ 1 where a is the radius of the sphere) the force F is of magnitude 2ΩρUV (where ρ is the density of the fluid and V is the volume of the sphere). In a homogeneous fluid the relative directions of F and U were found to depend on the quantity F = 8Ωa 2/UD (where D is the depth of the fluid in which the object is placed (Mason, 1975)). In a rotating stratified fluid the relative directions of F and U are found to depend on the inverse Froude number k(k = Na/U where N 2 = (g/δ)∂ρ/∂z) provided D > 4aΩ/N. In a homogeneous fluid with F ≲ 1 the force F is mainly in the U direction (a drag force due to inertial wave radiation) and is ∼ −0.4 |MX 2ΩρUV For F ≲ 1 a “Taylor column” occurs and the force, in correspondence with theoretical expectations, is ∼ - 2Ω |MX UρV In a rotating stratified fluid with N ∼2Ω and k ≲ 1 the force F is mainly in the U direction but is roughly one half of that occurring in the homogeneous situation with F ≲ 1 (tentatively explained as due to the evanescence of inertia-gravity disturbances). In a rotating stratified fluid with k ≫ 1 the flow should have no vertical motion (as with F ≫ 1) and again in correspondence with theoretical expectations the drag is ∼ −2 Ω |MX UρV. In a non-rotating stratified fluid the drag coefficient C D(C D = F U/½∂ρU 2) was measured in the range k = 0.1 to 10 and had a maximum value ∼ 1.2 for k ∼ 3.

This publication has 13 references indexed in Scilit: