Abstracts - KTH Mechanics

94
A general theory for stratified wakes
P. Meunier ∗ , G. R. Spedding † and P. Diamessis †
The stratification of the ocean and the atmosphere plays a major role in geophysical
flows (wakes of mountains, islands or sea-mounts) and in nautical applications
(wakes of submarines) since it largely modifies the late stages of the wake. Although
several experiments 1,2 and numerical simulations 3,4,5 described in detail the evolution
of the wake and found empirical scalings for the decaying laws, there has been
no theory predicting the characteristics of a stratified wake.
Here, we extend the model of a self-preserved non-stratified wake to the case of a
stratified fluid, by assuming that the wake expands in the horizontal direction due to
an eddy diffusivity (which was derived from experimental results) and in the vertical
direction due to viscous diffusion. The mean characteristics of the wake (wake height
and width, velocity defect) are derived analytically, and show a good agreement with
the previous empirical results (see figure1). The three regimes from the literature are
recovered and two new regimes are discovered. These results are valid for any bluff
body once its momentum thickness is known, and can thus be directly applied to
geophysical and nautical applications.
The support of ONR Grant no. N00014-04-1-0034 administered by Dr. R. Joslin
is most gratefully acknowledged.
∗ IRPHE, CNRS, Univ. Aix-Marseille I&II, BP 46,F-13384 Marseille Cedex 13, France.
† AME Dept., Univ. Southern California, Los Angeles, California, USA.
1 Spedding, J. Fluid Mech. 337, 283 (1997).
2 Bonnier and Eiff, Phys. Fluids 14, 791 (2002)
3 Gourlay et al., Phys. Fluids 13, 3783 (2001).
4 Dommermuth et al., J. Fluid Mech. 473, 83 (2002).
5 Diamessis et al., J. Comp. Phys. 202, 298 (2005).
L y / D m
10 1
10 0
10 0
3D NEQ (+ 2D) Q2D
10 1
10 2
x / D
m
10 3
10 4
U 0 / U B
10 0
10 -1
10 -2
10 0
3D NEQ (+ 2D) Q2D
Figure 1: (a) Wake width and (b) velocity defect of a stratified momentum wake.
The theoretical predictions (solid line) are compared with previous experimental results
(dashed line 1 and crosses 2 ) and numerical simulations (diamonds 3 ,squares 4 and
circles 5 ).
10 1
10 2
x / D
m
10 3
10 4