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Forces on spheres moving horizontally in a rotating stratified fluid

 

作者: P.J. Mason,  

 

期刊: Geophysical & Astrophysical Fluid Dynamics  (Taylor Available online 1977)
卷期: Volume 8, issue 1  

页码: 137-154

 

ISSN:0309-1929

 

年代: 1977

 

DOI:10.1080/03091927708240374

 

出版商: Taylor & Francis Group

 

数据来源: Taylor

 

摘要:

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 numberR(R=U/Ωa≲ 1 whereais the radius of the sphere) the force F is of magnitude 2ΩρUV(where ρ is the density of the fluid andVis the volume of the sphere). In a homogeneous fluid the relative directions of F and U were found to depend on the quantity F = 8Ωa2/UD(whereDis 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 numberk(k=Na/UwhereN2= (g/δ)∂ρ/∂z) providedD> 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 2ΩρUVFor F ≲ 1 a “Taylor column” occurs and the force, in correspondence with theoretical expectations, is ∼ - 2Ω |MX UρVIn a rotating stratified fluid withN∼2Ω andk≲ 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 withk≫ 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 coefficientCD(CD= F U/½∂ρU2) was measured in the rangek= 0.1 to 10 and had a maximum value ∼ 1.2 fork∼ 3.

 

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