scholarly journals Some remarks on a quasi-steady-state approximation of the Navier-Stokes equation

1988 ◽  
Vol 29 (4) ◽  
pp. 440-447
Author(s):  
John R. Cannon ◽  
George H. Knightly
Keyword(s):  
Steady State ◽  
Stokes Equation ◽  
Small Body ◽  
Navier Stokes ◽  
Quasi Steady State ◽  
Navier Stokes Equation ◽  
State Approximation ◽  
Steady State Approximation ◽  
The Difference ◽  
Image Position

AbstractA quasi-steady-state apprcncimation to the Navier-Stokes equation is the corresponding equation with nonhomogeneous forcing term f(x, t), but with the term Vt deleted. For solutions that are zero on the boundary, the difference z between the solution of the Navier-Stokes equation and the solution of this quasi-steady-state approximation is estimated in the L2 norm ║z║ with respect to the spatial variables. For sufficiently large viscosity or sufficiently small body force f, the inequalityholds for 0 < t ≤ T and certain real numbres C, β > 0.

The Quasi-Steady-State Approximation: Numerical Validation

1998 ◽  
Vol 75 (9) ◽  
pp. 1158 ◽  
Author(s):  
Richard A. B. Bond ◽  
Bice S. Martincigh ◽  
Janusz R. Mika ◽  
Reuben H. Simoyi
Keyword(s):  
Steady State ◽  
Quasi Steady State ◽  
Numerical Validation ◽  
State Approximation ◽  
Steady State Approximation

Coriolis force influence on the AKA effect

2021 ◽  
Author(s):  
Peter Rutkevich ◽  
Georgy Golitsyn ◽  
Anatoly Tur
Keyword(s):  
Steady State ◽  
Stokes Equation ◽  
Nonlinear Equations ◽  
Coriolis Force ◽  
Large Scale ◽  
Fluid Velocity ◽  
Navier Stokes ◽  
Basic Solution ◽  
Navier Stokes Equation ◽  
Alpha Effect

&lt;p&gt;Large-scale instability in incompressible fluid driven by the so called Anisotropic Kinetic Alpha (AKA) effect satisfying the incompressible Navier-Stokes equation with Coriolis force is considered. The external force is periodic; this allows applying an unusual for turbulence calculations mathematical method developed by Frisch et al [1]. The method provides the orders for nonlinear equations and obtaining large scale equations from the corresponding secular relations that appear at different orders of expansions. This method allows obtaining not only corrections to the basic solutions of the linear problem but also provides the large-scale solution of the nonlinear equations with the amplitude exceeding that of the basic solution. The fluid velocity is obtained by numerical integration of the large-scale equations. The solution without the Coriolis force leads to constant velocities at the steady-state, which agrees with the full solution of the Navier-Stokes equation reported previously. The time-invariant solution contains three families of solutions, however, only one of these families contains stable solutions. The final values of the steady-state fluid velocity are determined by the initial conditions. After account of the Coriolis force the solutions become periodic in time and the family of solutions collapses to a unique solution. On the other hand, even with the Coriolis force the fluid motion remains two-dimensional in space and depends on a single spatial variable. The latter fact limits the scope of the AKA method to applications with pronounced 2D nature. In application to 3D models the method must be used with caution.&lt;/p&gt;&lt;p&gt;[1] U. Frisch, Z.S. She and P. L. Sulem, &amp;#8220;Large-Scale Flow Driven by the Anisotropic Kinetic Alpha Effect,&amp;#8221; Physica D, Vol. 28, No. 3, 1987, pp. 382-392.&lt;/p&gt;

scholarly journals The Rise and Fall of α-Model Viscosity

1996 ◽  
Vol 158 ◽  
pp. 111-114
Author(s):  
F. V. Hessman ◽  
C. Obach
Keyword(s):  
Steady State ◽  
Stokes Equation ◽  
Accretion Disks ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Averaged Models

AbstractFor nearly two decades, our only useful model for the viscosity in accretion disks has been the so-called ‘α-model’. However, it has become clear that the simplest models –in which α is constant – are inadequate to explain the range of behaviours seen in real disks. We show that the properties of steady-state, vertically-averaged models can be determined without any assumptions other than that the disks obey the classical Navier-Stokes equation. These solutions have derived values of α which vary with radius by many orders of magnitude even in small CV disks.

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