Viscous incompressible fluid motion on a rotating sphere in the central newtonian attraction field

1995 ◽  
Vol 30 (2) ◽  
pp. 267-274
Author(s):  
M. G. Sal'nikova ◽  
V. A. Samsonov
Keyword(s):  
Incompressible Fluid ◽  
Viscous Incompressible Fluid ◽  
Fluid Motion ◽  
Rotating Sphere

scholarly journals Waves in Two Coaxial Elastic Cubically Nonlinear Shells with Structural Damping and Viscous Fluid Between Them

Symmetry ◽  
2020 ◽  
Vol 12 (3) ◽  
pp. 335
Author(s):  
Lev Mogilevich ◽  
Sergey Ivanov
Keyword(s):  
Exact Solution ◽  
Incompressible Fluid ◽  
Difference Scheme ◽  
Viscous Incompressible Fluid ◽  
Initial Conditions ◽  
Numerical Study ◽  
Fluid Motion ◽  
Structural Damping ◽  
The Difference ◽  
The Mathematical Model

This article investigates longitudinal deformation waves in physically nonlinear coaxial elastic shells containing a viscous incompressible fluid between them. The presence of a viscous incompressible fluid between the shells, as well as the influence of the inertia of the fluid motion on the amplitude and velocity of the wave, are taken into account. The mathematical model phenomenon is constructed by means of the method of two-scale asymptotic expansion. Structural damping in the shells and surrounding elastic media did not allow discovery of the exact solution of the problem of the deformation waves propagation. This leads to the need for numerical methods. A numerical study of the model constructed in the course of this work is carried out by using a difference scheme for the equation similar to the Crank–Nicholson scheme for the heat equation. In the absence of the structural damping and surrounding media influences, and under the similar initial conditions for both shells, the velocity and amplitude of the wave do not change. The result of the numerical experiment coincides with the exact solution, which is found in the case of the absence of the structural damping and surrounding media influences; therefore, the difference scheme is adequate to the generalized modified Korteweg–de Vries equations system. There is energy is transferred in the presence of the fluid, between the shells. The presence of inertia of the fluid motion leads to a decrease in the velocity of the deformation wave.

scholarly journals Asymptotic behavior of solutions to barotropic vorticity equation on a sphere

2020 ◽  
Vol 5 (2) ◽  
pp. 229-238
Author(s):  
Yuri N. Skiba
Keyword(s):  
Asymptotic Behavior ◽  
Incompressible Fluid ◽  
Viscous Incompressible Fluid ◽  
Sufficient Conditions ◽  
Vorticity Equation ◽  
Asymptotic Behavior Of Solutions ◽  
Rotating Sphere ◽  
Bounded Set ◽  
Barotropic Vorticity Equation ◽  
Barotropic Vorticity

AbstractThe behavior of a viscous incompressible fluid on a rotating sphere is described by the nonlinear barotropic vorticity equation (BVE). Conditions for the existence of a bounded set that attracts all BVE solutions are given. In addition, sufficient conditions are obtained for a BVE solution to be a global attractor. It is shown that, in contrast to the stationary forcing, the dimension of the global BVE attractor under quasiperiodic forcing is not limited from above by the generalized Grashof number.

scholarly journals On the existence of an exact solution of the Navier-Stokes equation pertaining to certain vortex motion

1972 ◽  
Vol 13 (4) ◽  
pp. 456-460
Author(s):  
K. Kuen Tam
Keyword(s):  
Exact Solution ◽  
Incompressible Fluid ◽  
Stokes Equation ◽  
Viscous Incompressible Fluid ◽  
Fluid Motion ◽  
Vortex Motion ◽  
Polar Coordinates ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Cylindrical Polar Coordinates

In 1942, Burgers [1] observed that in cylindrical polar coordinates, the steady Navier-Stokes equation governing viscous incompressible fluid motion can be reduced to a set of ordinary differential equations if the velocity components vr, vo and vz are assumed to have a special form.

Free convection from a disk rotating in a vertical plane

1983 ◽  
Vol 126 ◽  
pp. 307-313 ◽  
Author(s):  
S. S. Chawla ◽  
A. R. Verma
Keyword(s):  
Convective Flow ◽  
Energy Equation ◽  
Viscous Incompressible Fluid ◽  
Fluid Motion ◽  
Axisymmetric Flow ◽  
Vertical Plane ◽  
Cross Flow ◽  
Accurate Solution ◽  
Free Convective Flow ◽  
Heated Disk

An exact solution of the free convective flow of a viscous incompressible fluid from a heated disk, rotating in a vertical plane, is obtained. The non-axisymmetric fluid motion consists of two parts; the primary von Kármán axisymmetric flow and the secondary buoyancy-induced cross-flow. A highly accurate solution of the energy equation is also derived for its subsequent use in the analysis of the cross-flow.

Slender-body theory for slow viscous flow

1976 ◽  
Vol 75 (4) ◽  
pp. 705-714 ◽  
Author(s):  
Joseph B. Keller ◽  
Sol I. Rubinow
Keyword(s):  
Integral Equation ◽  
Incompressible Fluid ◽  
Viscous Incompressible Fluid ◽  
Unit Length ◽  
The Body ◽  
Slender Body ◽  
Slow Flow ◽  
Slender Body Theory ◽  
Slow Viscous Flow ◽  
Body Theory

Slow flow of a viscous incompressible fluid past a slender body of circular crosssection is treated by the method of matched asymptotic expansions. The main result is an integral equation for the force per unit length exerted on the body by the fluid. The novelty is that the body is permitted to twist and dilate in addition to undergoing the translating, bending and stretching, which have been considered by others. The method of derivation is relatively simple, and the resulting integral equation does not involve the limiting processes which occur in the previous work.

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