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Turbulence, similarity scaling and vortex geometry in the wake of a towed sphere in a stably stratified fluid

Published online by Cambridge University Press:  26 April 2006

G. R. Spedding ,
F. K. Browand  and
A. M. Fincham
G. R. Spedding
Affiliation:
Department of Aerospace Engineering, University of Southern California, Los Angeles, CA 90089-1191, USA
F. K. Browand
Affiliation:
Department of Aerospace Engineering, University of Southern California, Los Angeles, CA 90089-1191, USA
A. M. Fincham
Affiliation:
Department of Aerospace Engineering, University of Southern California, Los Angeles, CA 90089-1191, USA
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Abstract

Late wakes (Nt > 20) of towed spheres in a stably stratified fluid were analysed in a plane using a reliable, customized DPIV technique that provides sufficient spatial and temporal resolution to cover all important scales of motion in this freely decaying geophysical flow. Systematic experiments were conducted with independent variation of Re ∈ [103, 104] and F ∈ [1, 10] (F ≡ 2U/ND is an internal Froude number based on the buoyancy frequency, N, and the sphere radius, D/2), and for selected {Re, F} pairs above this range.

The normalized wake width grows at approximately the same rate as in a three-dimensional unstratified wake, but it becomes narrower, not wider, with decreasing F (i.e. as stratification effects become more important). The centreline defect velocity, on the other hand, reaches values an order of magnitude above those measured for three-dimensional unstratified wakes at equivalent downstream locations. Both observations are argued to be consequences of the very high degree of order and coherence that emerge in the late-wake vortex structures.

Streamwise-averaged turbulence quantities, such as the velocity fluctuation magnitude, and mean-square enstrophy, show similar power law behaviour for all Re ≤ 5 × 103, with exponents equal to those expected in three-dimensional axisym-metric turbulent wakes. There is no obvious physical reason why three-dimensional arguments are so successful in such a flow, and at such long evolution times. The scaling collapses none of the cases for Re below 4 – 5 × 103, appearing to establish a minimum Re for a class of self-similar stratified wake flows that evolve from fully turbulent initial conditions.

Individual vortex cross-sections appear to be well approximated by Gaussian distributions at all Re, F and Nt studied here. The scaling behaviour of individual vortices mimics that of the statistical, wake-averaged quantities, and differs measurably from a simple two-dimensional viscous diffusion model. The importance of formulating a realistic three-dimensional model is discussed, and some limited steps in this direction point to future useful experiments and modelling efforts.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 314 , 10 May 1996 , pp. 53 - 103
Copyright
© 1996 Cambridge University Press

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