Physical interpretation of unstable modes of a linear shear flow in shallow water on an equatorial beta-plane

2006 ◽  
Vol 567 ◽  
pp. 1 ◽  
Author(s):  
HIROSHI TANIGUCHI ◽  
MASAKI ISHIWATARI
Keyword(s):  
Shear Flow ◽  
Shallow Water ◽  
Physical Interpretation ◽  
Beta Plane ◽  
Linear Shear

Over-reflection and shear instability in a shallow-water model

1992 ◽  
Vol 236 ◽  
pp. 259-279 ◽  
Author(s):  
Shin-Ichi Takehiro ◽  
Yoshi-Yuki Hayashi
Keyword(s):  
Shear Flow ◽  
Shallow Water ◽  
Water Waves ◽  
Shear Instability ◽  
Water Model ◽  
Shallow Water Waves ◽  
Wave Amplification ◽  
Linear Shear ◽  
Conservation Of Momentum ◽  
The Relationship

The characteristics of shallow-water waves in a linear shear flow are studied, and the relationship between waves and unstable modes is examined. Numerical integration of the linear shallow-water equations shows that over-reflection occurs when a wave packet is incident at the turning surface. This phenomenon can be explained by the conservation of momentum as discussed by Acheson (1976). The unstable modes of linear shear flow in a shallow water found by Satomura (1981) are described in terms of the properties of wave propagation as proposed by Lindzen and others. Ripas's (1983) theorem, which is the sufficient condition for stability of flows in shallow water, is also related to the wave geometry. The Orr mechanism, which is proposed by Lindzen (1988) as the primary mechanism of wave amplification, cannot explain the over-reflection of shallow-water waves. The amplification of these waves occurs in the opposite sense to that of Orr's solution.

scholarly journals Fluid-Structure Energy Transfer of a Tensioned Beam Subject to Vortex-Induced Vibrations in Shear Flow

2011 ◽  
Author(s):  
Remi Bourguet ◽  
Michael S. Triantafyllou ◽  
Michael Tognarelli ◽  
Pierre Beynet
Keyword(s):  
Energy Transfer ◽  
Shear Flow ◽  
Cross Flow ◽  
Reynolds Numbers ◽  
Structural Vibrations ◽  
Fluid Structure ◽  
Vortex Induced Vibrations ◽  
Linear Shear ◽  
Structural Responses ◽  
Lock In

The fluid-structure energy transfer of a tensioned beam of length to diameter ratio 200, subject to vortex-induced vibrations in linear shear flow, is investigated by means of direct numerical simulation at three Reynolds numbers, from 110 to 1,100. In both the in-line and cross-flow directions, the high-wavenumber structural responses are characterized by mixed standing-traveling wave patterns. The spanwise zones where the flow provides energy to excite the structural vibrations are located mainly within the region of high current where the lock-in condition is established, i.e. where vortex shedding and cross-flow vibration frequencies coincide. However, the energy input is not uniform across the entire lock-in region. This can be related to observed changes from counterclockwise to clockwise structural orbits. The energy transfer is also impacted by the possible occurrence of multi-frequency vibrations.

A Balanced Approximation of the One-Layer Shallow-Water Equations on a Sphere

2009 ◽  
Vol 66 (6) ◽  
pp. 1735-1748 ◽  
Author(s):  
W. T. M. Verkley
Keyword(s):  
Shallow Water ◽  
Potential Vorticity ◽  
Shallow Water Equations ◽  
Rossby Waves ◽  
Coriolis Parameter ◽  
Beta Plane ◽  
Propagating Waves ◽  
Barotropic Vorticity Equation ◽  
Barotropic Vorticity ◽  
The One

Abstract A global version of the equivalent barotropic vorticity equation is derived for the one-layer shallow-water equations on a sphere. The equation has the same form as the corresponding beta plane version, but with one important difference: the stretching (Cressman) term in the expression of the potential vorticity retains its full dependence on f 2, where f is the Coriolis parameter. As a check of the resulting system, the dynamics of linear Rossby waves are considered. It is shown that these waves are rather accurate approximations of the westward-propagating waves of the second class of the original shallow-water equations. It is also concluded that for Rossby waves with short meridional wavelengths the factor f 2 in the stretching term can be replaced by the constant value f02, where f0 is the Coriolis parameter at ±45° latitude.

ON VORTEX LOCKING-ON PHENOMENON FOR A CABLE IN LINEAR SHEAR FLOW

1984 ◽  
pp. 289-300
Author(s):  
H.G.C. Woo ◽  
J.E. Cermak ◽  
J.A. Peterka
Keyword(s):  
Shear Flow ◽  
Linear Shear

The motion of a droplet subjected to linear shear flow including the presence of a plane wall

1995 ◽  
Vol 302 ◽  
pp. 45-63 ◽  
Author(s):  
W. S. J. Uijttewaal ◽  
E. J. Nijhof
Keyword(s):  
Shear Flow ◽  
Flow Field ◽  
Theoretical Models ◽  
Boundary Integral ◽  
Plane Wall ◽  
Time Dependent ◽  
Fluid Inertia ◽  
Linear Shear ◽  
Material Element ◽  
Migration Velocities

A fluid droplet subjected to shear flow deforms and rotates in the flow. In the presence of a wall the droplet migrates with respect to a material element in the undisturbed flow field. Neglecting fluid inertia, the Stakes problem for the droplet is solved using a boundary integral technique. It is shown how the time-dependent deformation, orientation, circulation and droplet viscosity. The migration velocities are calculated in the directions parallel and perpendicular to the wall, and compared with theoretical models and expeeriments. The results reveal some of the shortcomings of existiong models although not all diserepancies between our calculations and known experiments could be clarified.

Stability of linear shear flows in shallow water

1995 ◽  
Vol 303 ◽  
pp. 203-214 ◽  
Author(s):  
Charles Knessl ◽  
Joseph B. Keller
Keyword(s):  
Shallow Water ◽  
Shear Flows ◽  
Special Functions ◽  
Rigid Wall ◽  
Eigenvalue Equation ◽  
Reflection And Transmission ◽  
Transmission Coefficients ◽  
Linear Shear ◽  
The Stability ◽  
Rigid Walls

The stability or instability of various linear shear flows in shallow water is considered. The linearized equations for waves on the surface of each flow are solved exactly in terms of known special functions. For unbounded shear flows, the exact reflection and transmission coefficients R and T for waves incident on the flow, are found. They are shown to satisfy the relation |R|2= 1+ |T|2, which proves that over reflection occurs at all wavenumbers. For flow bounded by a rigid wall, R is found. The poles of R yield the eigenvalue equation from which the unstable mides can be found. For flow in a channel, with two rigid walls, the eigenvalue equation for the modes is obtained. The results are compared with previous numerical results.

Some problems concerning the production of a linear shear flow using curved wire-gauze screens

1976 ◽  
Vol 76 (4) ◽  
pp. 689-709 ◽  
Author(s):  
I. P. Castro
Keyword(s):  
Shear Flow ◽  
Incompressible Fluid ◽  
Experimental Work ◽  
Arbitrary Shape ◽  
Practical Problem ◽  
Analytic Solution ◽  
Linear Shear ◽  
Wire Gauze ◽  
The Common ◽  
Small Shear

The flow of an incompressible fluid through a curved wire-gauze screen of arbitrary shape is reconsidered. Some inconsistencies in previously published papers are indicated and the various approximations and linearizations (some of which are necessary for a complete analytic solution) are discussed and their inadequacies demonstrated. Attention is concentrated on the common practical problem of calculating the screen shape required to produce a linear shear flow and experimental work is presented which supports the contention that the theoretical solutions proposed by Elder (1959)–subsequently discussed by Turner (1969) and Livesey & Laws (1973)-and Lau & Baines (1968) are inadequate, although, for the case of small shear, Elder's theory appears to be satisfactory. Since, in addition, there are inevitable difficulties concerning both the value of the deflexion coefficient appropriate to any particular screen and inhomogeneities in the screen itself, it is concluded that the preparation of a curved screen to produce the commonly required moderate to large linear shear flow is bound to be somewhat empirical and should be attempted with caution.

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