The ideal velocity field of ship waves on a viscous fluid

The results of an earlier paper are extended. The elastic field outside an inclusion or inhomogeneity is treated in greater detail. For a general inclusion the harmonic potential of a certain surface distribution may be used in place of the biharmonic potential used previously. The elastic field outside an ellipsoidal inclusion or inhomogeneity may be expressed entirely in terms of the harmonic potential of a solid ellipsoid. The solution gives incidentally the velocity field about an ellipsoid which is deforming homogeneously in a viscous fluid. An expression given previously for the strain energy of an ellipsoidal region which has undergone a shear transformation is generalized to the case where the region has elastic constants different from those of its surroundings. The Appendix outlines a general method of calculating biharmonic potentials.

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Wave Motion of a Compressible Viscous Fluid Contained in a Cylindrical Shell

Journal of Pressure Vessel Technology ◽

10.1115/1.2929532 ◽

1993 ◽

Vol 115 (3) ◽

pp. 302-312 ◽

Cited By ~ 1

Author(s):

J. H. Terhune ◽

K. Karim-Panahi

Keyword(s):

Velocity Field ◽

Viscous Fluid ◽

Imaginary Part ◽

Fluid Velocity ◽

Wave Number ◽

Mode Shapes ◽

Infinite Length ◽

Complex Frequency ◽

Compressible Viscous Fluid ◽

Fluid Velocity Field

The free vibration of cylindrical shells filled with a compressible viscous fluid has been studied by numerous workers using the linearized Navier-Stokes equations, the fluid continuity equation, and Flu¨gge ’s equations of motion for thin shells. It happens that solutions can be obtained for which the interface conditions at the shell surface are satisfied. Formally, a characteristic equation for the system eigenvalues can be written down, and solutions are usually obtained numerically providing some insight into the physical mechanisms. In this paper, we modify the usual approach to this problem, use a more rigorous mathematical solution and limit the discussion to a single thin shell of infinite length and finite radius, totally filled with a viscous, compressible fluid. It is shown that separable solutions are obtained only in a particular gage, defined by the divergence of the fluid velocity vector potential, and the solutions are unique to that gage. The complex frequency dependence for the transverse component of the fluid velocity field is shown to be a result of surface interaction between the compressional and vortex motions in the fluid and that this motion is confined to the boundary layer near the surface. Numerical results are obtained for the first few wave modes of a large shell, which illustrate the general approach to the solution. The axial wave number is complex for wave propagation, the imaginary part being the spatial attenuation coefficient. The frequency is also complex, the imaginary part of which is the temporal damping coefficient. The wave phase velocity is related to the real part of the axial wave number and turns out to be independent of frequency, with numerical value lying between the sonic velocities in the fluid and the shell. The frequency dependencies of these parameters and fluid velocity field mode shapes are computed for a typical case and displayed in non-dimensional graphs.

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On characteristic functionals of a random velocity field of helical motions of a viscous fluid

Journal of Applied Mathematics and Mechanics ◽

10.1016/0021-8928(75)90161-6 ◽

1975 ◽

Vol 39 (2) ◽

pp. 357-359

Author(s):

N.V. Derendiaev

Keyword(s):

Velocity Field ◽

Viscous Fluid ◽

Random Velocity

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On the Torsional Oscillations of a Solid Sphere in a Viscous Fluid

Journal of Applied Mechanics ◽

10.1115/1.4011406 ◽

1956 ◽

Vol 23 (4) ◽

pp. 601-605

Author(s):

G. F. Carrier ◽

R. C. Di Prima

Keyword(s):

Velocity Field ◽

Viscous Fluid ◽

Angular Displacement ◽

Solid Sphere ◽

Circumferential Velocity ◽

Torsional Oscillations ◽

Viscosity Measurements ◽

First Approximation ◽

Viscous Torque ◽

Solid Bodies

Abstract Most treatments of the torsional oscillations of solid bodies assume that the velocity field is circumferential. In this paper the motion in planes containing the axis of oscillation is also considered. An expansion in terms of the angular displacement ϵ (assumed small) is made. The first approximation to the circumferential velocity is computed, and then used in computing the first approximation to the pumping motion. This is used to compute the correction to the circumferential velocity and, in particular, the correction to the viscous torque. For the range of parameters considered it is found that the correction to the torque is of the order of 0.04ϵ2|N0|, where N0 is the classical viscous torque. This problem is of interest in practical viscosity measurements.

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Ship waves on a viscous fluid of finite depth

Physics of Fluids ◽

10.1063/1.869189 ◽

1997 ◽

Vol 9 (4) ◽

pp. 940-944 ◽

Cited By ~ 3

Author(s):

Andy T. Chan ◽

Allen T. Chwang

Keyword(s):

Viscous Fluid ◽

Finite Depth ◽

Ship Waves

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MHD FLOWS DUE TO NON-COAXIAL ROTATIONS OF POROUS DISK AND A VISCOUS FLUID AT INFINITY: GRAPHICAL SOLUTIONS USING MATLAB

Advances in Mathematics: Scientific Journal ◽

10.37418/amsj.9.11.33 ◽

2020 ◽

Vol 9 (11) ◽

pp. 9287-9301

Author(s):

R. Lakshmi ◽

Santhakumari

Keyword(s):

Velocity Field ◽

Analytical Solution ◽

Viscous Fluid ◽

Stokes Equations ◽

Daily Life ◽

Vital Role ◽

Navier Stokes ◽

Porous Disk ◽

Navier Stokes Equations ◽

Complex Phenomena

Fluids play a vital role in many aspects of our daily life. We drink water, breath air, fluids run through our bodies and it controls the weather. The study of motion of fluids is a complex phenomena. The equations which govern the flows of Newtonian fluids are Navier-Stokes equations. In this paper, the flows which are due to non – coaxial rotations of porous disk and a fluid at infinity are considered. Analytical solution for the velocity field using Laplace transform is derived. MATLAB coding is written to get the graphical solutions. The results are compared with the existing results. MATLAB software provides accurate results depending on the solution we obtained.

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