Numerical Modeling of Internal Waves Generated by Turbulent Wakes Behind Self-Propelled and Towed Bodies in Stratified M
A flow that arises in a turbulent wake behind a body that moves in a stratified fluid is rather peculiar. With a relatively weak stratification a turbulent wake first develops essentially in the same way as in a homogeneous fluid and extends symmetrically
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Institute of Computational Technologies, Siberian Division of Russian Academy of Sciences, 6 Lavrentjev Ave., Novosibirsk, 630090, Russia. Suranaree University of Technology, School of Mathematics, Institute of Science, Nakhon Ratchasima, 30000, Thailand.
Introduction
A flow that arises in a turbulent wake behind a body that moves in a stratified fluid is rather peculiar. With a relatively weak stratification a turbulent wake first develops essentially in the same way as in a homogeneous fluid and extends symmetrically. However, buoyancy forces oppose vertical turbulent diffusion. Therefore a wake has a flattened form at large distances from the body and, finally, ceases to extend in a vertical direction. Because of turbulent mixing the fluid density within the wake is distributed more uniformly than outside it. unperturbed state of a stable stratification. As a result, convective flows, which give rise to internal waves in an ambient fluid, arise in the plane perpendicular to the wake axis. Turbulent wakes behind bodies of revolution in stratified fluids have been considered in many publications [1-7]. Analyzing these works we note that the results of the numerical modeling of internal waves generated by turbulent wakes are incomplete. There are, in particular, no data on the numerical analysis of the characteristics of the internal waves generated by drag wake in stratified media, and there are no data on comparison of characteristics of the internal waves generated by the wakes behind the self-propelled and towed bodies. In the present work an attempt is made at filling the gaps available in the numerical modeling.
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Pro blem formulation
To describe the flow in a far turbulent wake of a body of revolution in a stratified medium the following parabolized system of the averaged equations for the motion, continuity and incompressibility in the Oberbeck-Boussinesq approach
* This research was partially supported by Russian Foundation of Basic Research (9801-00736) and the Siberian Division of the Russian Academy of Science (Integration grant No. 2000-1). N. Satofuka (ed.), Computational Fluid Dynamics 2000 © Springer-Verlag Berlin Heidelberg 2001
456
G. G. Chernykh, N. P. Moshkin et al.
is used: TT
UO
Uo oV oX UooW ox
OUd oX
+
VOUd oy
+
WOUd _ ~( I ') ~(I ') OZ - oy U v + OZ U w ,
(1)
+ V oV + W oV = _~ O(Pi) _ ~(vl2) _ ~(V'W'), oy
OZ
Po oy
oy
(2)
oz
+ VoW + WoW = _~ O(Pi) _ ~(V'W/) _ ~(W'2) _ 9 (Pi), (3) oy
UoO(Pi) ox
OZ
po oz
oy
+ VO(Pi) + W O(Pl) + W dps OZ
oy
oV
dz
oW
OZ
= _~(V' oy
po
') - ~(W' '), P OZ P
OUd
+OZ - =oxoy
(4)
(5)
In equations (1)-(5), Uo is the free stream velocity; Ud = Uo - U is the defect of the mean streamwise velocity component; U, V, Ware velocity components of the mean flow in the direction of the axes x, y, Z; Pi is the deviation of the pressure from the hydrostatic one conditioned by the stratification Ps; 9 is the gravity acceleration; (Pi) is the mean density defect: Pi = P- ps; Ps = Ps(z) is the undisturbed fluid density: dp./dz :::; 0
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