Influence of a longitudinally compressed elastic plate on stream wave perturbation development for a homogeneous fluid with vertical velocity shift

1981 ◽  
Vol 22 (1) ◽  
pp. 102-107 ◽  
Author(s):  
A. E. Bukatov ◽  
V. I. Mordashev
Keyword(s):  
Vertical Velocity ◽  
Elastic Plate ◽  
Wave Perturbation ◽  
Homogeneous Fluid ◽  
Velocity Shift

Shear layers in a rotating fluid

1967 ◽  
Vol 29 (1) ◽  
pp. 165-175 ◽  
Author(s):  
D. James Baker
Keyword(s):  
Velocity Field ◽  
Angular Velocity ◽  
Shear Layer ◽  
Vertical Velocity ◽  
Vertical Shear ◽  
Geometrical Parameters ◽  
Homogeneous Fluid ◽  
Rotating System ◽  
Layer Flow ◽  
Good Agreement

A homogeneous fluid of viscosityvis confined between two co-axial disks (vertical separationH) which rotate relative to a rotating system (angular velocity Ω). The resulting velocity field is studied for values of the parameterv/2ΩH2in the range 1·6 × 10−2to 1·8 × 10−3. The Rossby number, defined as the ratio of the relative angular velocity of the disks to the angular velocity of the system, ranged from 0·038 to 0·0041. The dependence of the resulting velocity field (interior and boundary-layer flow) on geometrical parameters, imposed surface and bottom velocities, and Ω, is in good agreement with the calculations of Stewartson and Carrier. In particular, when the two disks rotate with the same angular velocity, the width of the vertical shear layer at the edge of the disks is found to be proportional to Ω−0·25±0·02. When the disks rotate in opposite senses, a shear layer in the vertical velocity is observed which transports fluid from one disk to the other and whose width is proportional to Ω−0·40±0·10. The magnitude and shape of the observed vertical velocity is in fair agreement with a numerical integration of the theoretical results.

scholarly journals Water entry of a flat elastic plate at high horizontal speed

2013 ◽  
Vol 724 ◽  
pp. 123-153 ◽  
Author(s):  
M. Reinhard ◽  
A. A. Korobkin ◽  
M. J. Cooker
Keyword(s):  
Free Surface ◽  
Boundary Conditions ◽  
Vertical Velocity ◽  
Elastic Plate ◽  
Velocity Component ◽  
Plate Motion ◽  
Beam Equation ◽  
Hydrodynamic Loads ◽  
Elastic Deflection ◽  
The Impact

AbstractThe two-dimensional problem of an elastic-plate impact onto an undisturbed surface of water of infinite depth is analysed. The plate is forced to move with a constant horizontal velocity component which is much larger than the vertical velocity component of penetration. The small angle of attack of the plate and its vertical velocity vary in time, and are determined as part of the solution, together with the elastic deflection of the plate and the hydrodynamic loads within the potential flow theory. The boundary conditions on the free surface and on the wetted part of the plate are linearized and imposed on the initial equilibrium position of the liquid surface. The wetted part of the plate depends on the plate motion and its elastic deflection. To determine the length of the wetted part we assume that the spray jet in front of the advancing plate is negligible. A smooth separation of the free-surface flow from the trailing edge is imposed. The wake behind the moving body is included in the model. The plate deflection is governed by Euler’s beam equation, subject to free–free boundary conditions. Four different regimes of plate motion are distinguished depending on the impact conditions: (a) the plate becomes fully wetted; (b) the leading edge of the plate touches the water surface and traps an air cavity; (c) the free surface at the forward contact point starts to separate from the plate; (d) the plate exits the water. We could not detect any impact conditions which lead to steady planing of the free plate after the impact. It is shown that a large part of the total energy in the fluid–plate interaction leaves the main bulk of the liquid with the spray jet. It is demonstrated that the flexibility of the plate may increase the hydrodynamic loads acting on it. The impact loads can cause large bending stresses, which may exceed the yield stress of the plate material. The elastic vibrations of the plate are shown to have a significant effect on the fluid flow in the wake.

THEORY OF BRILLOUIN SCATTERING BY AN ISOTROPIC ELASTIC PLATE

1984 ◽  
Vol 45 (C5) ◽  
pp. C5-103-C5-107
Author(s):  
D. R. Tilley ◽  
E. L. Albuquerque ◽  
M. C. Oliveros
Keyword(s):  
Elastic Plate ◽  
Brillouin Scattering

Combining SAR interferometry and the equation of continuity to estimate the three-dimensional glacier surface-velocity vector

1999 ◽  
Vol 45 (151) ◽  
pp. 533-538 ◽  
Author(s):  
Niels Reeh ◽  
Søren Nørvang Madsen ◽  
Johan Jakob Mohr
Keyword(s):  
Steady State ◽  
Mass Balance ◽  
Vertical Velocity ◽  
Velocity Vector ◽  
Thickness Distribution ◽  
Vertical Surface ◽  
Horizontal Velocity ◽  
Sar Interferometry ◽  
Surface Velocity ◽  
Ice Thickness

AbstractUntil now, an assumption of surface-parallel glacier flow has been used to express the vertical velocity component in terms of the horizontal velocity vector, permitting all three velocity components to be determined from synthetic aperture radar interferometry. We discuss this assumption, which neglects the influence of the local mass balance and a possible contribution to the vertical velocity arising if the glacier is not in steady state. We find that the mass-balance contribution to the vertical surface velocity is not always negligible as compared to the surface-slope contribution. Moreover, the vertical velocity contribution arising if the ice sheet is not in steady state can be significant. We apply the principle of mass conservation to derive an equation relating the vertical surface velocity to the horizontal velocity vector. This equation, valid for both steady-state and non-steady-state conditions, depends on the ice-thickness distribution. Replacing the surface-parallel-flow assumption with a correct relationship between the surface velocity components requires knowledge of additional quantities such as surface mass balance or ice thickness.

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