scholarly journals Damping effects in boundary layers for rotating fluids with small viscosity

2020 ◽  
Vol 71 (2) ◽  
Author(s):  
Van-Sang Ngo
Keyword(s):  
Boundary Layers ◽  
Rotating Fluids ◽  
Small Viscosity ◽  
Damping Effects

Vortex decay above a stationary boundary

1967 ◽  
Vol 27 (1) ◽  
pp. 155-175 ◽  
Author(s):  
Albert I. Barcilon
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Plate Boundary ◽  
Swirling Flows ◽  
Rigid Boundary ◽  
Free Vortex ◽  
Stationary Boundary ◽  
Small Viscosity

An attempt is made to understand the decay of a free vortex normal to a stationary, infinite boundary. For rapidly swirling flows in fluids of small viscosity, thin boundary layers develop along the rigid boundary and along the axis, the axial boundary layer being strongly influenced by the behaviour of the plate boundary. An over-all picture of the flow is sought, with only moderate success in the region far from the origin. Near the origin, the eruption of the plate boundary layer into the axial boundary layer is studied.

scholarly journals The rise of a body through a rotating fluid in a container of finite length

1968 ◽  
Vol 31 (4) ◽  
pp. 635-642 ◽  
Author(s):  
D. W Moore ◽  
P. G. Saffman
Keyword(s):  
Boundary Layers ◽  
Finite Length ◽  
Vertical Axis ◽  
Axisymmetric Body ◽  
The Body ◽  
Rotating Fluid ◽  
Compatibility Conditions ◽  
Inertia Effects ◽  
Small Viscosity ◽  
Taylor Column

The drag on an axisymmetric body rising through a rotating fluid of small viscosity rotating about a vertical axis is calculated on the assumption that there is a Taylor column ahead of and behind the body, in which the geostrophic flow is determined by compatibility conditions on the Ekman boundary-layers on the body and the end surfaces. It is assumed that inertia effects may be neglected. Estimates are given of the conditions for which the theory should be valid.

Linear theory of rotating stratified fluid motions

1967 ◽  
Vol 29 (1) ◽  
pp. 1-16 ◽  
Author(s):  
V. Barcilon ◽  
J. Pedlosky
Keyword(s):  
Boundary Layer ◽  
Boundary Layers ◽  
Linear Theory ◽  
Stable Stratification ◽  
Ekman Layer ◽  
Stratified Fluid ◽  
Rotating Fluids ◽  
Ekman Layers ◽  
Steady Motions ◽  
Rotating Stratified Fluid

A linear theory for steady motions in a rotating stratified fluid is presented, valid under the assumption that ε < E, where ε and E are respectively the Rossby and Ekman numbers. The fact that the stable stratification inhibits vertical motions has important consequences and many features of the dynamics of homogeneous rotating fluids are no longer present. For instance, in addition to the absence of the Taylor-Proudman constraint, it is found that Ekman layer suction no longer controls the interior dynamics. In fact, the Ekman layers themselves are frequently absent. Furthermore, the vertical Stewartson boundary layers are replaced by a new kind of boundary layer whose structure is characteristic of rotating stratified fluids. The interior dynamics are found to be controlled by dissipative processes.

SINGULAR PERTURBATION ANALYSIS ON A HOMOGENEOUS OCEAN CIRCULATION MODEL

2011 ◽  
Vol 09 (03) ◽  
pp. 275-313 ◽  
Author(s):  
CHANG-YEOL JUNG ◽  
MADALINA PETCU ◽  
ROGER TEMAM
Keyword(s):  
Singular Perturbation ◽  
Boundary Layers ◽  
Ocean Circulation ◽  
Perturbation Analysis ◽  
Circulation Model ◽  
Auxiliary Result ◽  
Nonlinear Case ◽  
Ocean Circulation Model ◽  
Singular Perturbation Analysis ◽  
Small Viscosity

In this article, we consider the barotropic quasigeostrophic equation of the ocean in the context of the β-plane approximation and small viscosity (see, e.g., [21, 22]). The aim is to study the behavior of the solutions when the viscosity goes to zero. To avoid the substantial complications due to the corners (see, e.g., [25]) which will be addressed elsewhere, we assume periodicity in one direction (0y). The behavior of the solution in the boundary layers at x = 0, 1 necessitate the introduction of several correctors, solving various analogues of the Prandtl equation. Convergence is obtained at all orders even in the nonlinear case. We also establish as an auxiliary result, the [Formula: see text] regularity of the solutions of the viscous and inviscid quasigeotrophic equations.

scholarly journals Ekman Boundary Layers for Rotating Fluids

2006 ◽  
Author(s):  
Jean-Yves Chemin ◽  
Benoit Desjardins ◽  
Isabelle Gallagher ◽  
Emmanuel Grenier
Keyword(s):  
Vector Field ◽  
Boundary Conditions ◽  
Boundary Layers ◽  
Dirichlet Boundary ◽  
Turbulent Viscosity ◽  
Viscous Fluids ◽  
Dirichlet Boundary Conditions ◽  
Rotating Fluids ◽  
Free Condition ◽  
Divergence Free

In this chapter, we investigate the problem of rapidly rotating viscous fluids between two horizontal plates with Dirichlet boundary conditions. We present the model with so-called “turbulent” viscosity. More precisely, we shall study the limit when ε tends to 0 of the system where Ω = Ωh×]0, 1[: here Ωh will be the torus T2 or the whole plane R2. We shall use, as in the previous chapters, the following notation: if u is a vector field on Ω we state u = (uh, u3). In all that follows, we shall assume that on the boundary ∂Ω, uε0 · n = uε,30 = 0, and that div uε0 = 0. The condition u30 = 0 on the boundary implies the following fact: for any vector field u ∊ H(Ω), the function ∂3u3 is L2(]0, 1[) with respect to the variable x3 with values in H−1(Ωh) due to the divergence-free condition.

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