Columnar eddy formation in freely decaying homogeneous rotating turbulence

2011 ◽  
Vol 677 ◽  
pp. 154-178 ◽  
Author(s):  
K. YOSHIMATSU ◽  
M. MIDORIKAWA ◽  
Y. KANEDA
Keyword(s):  
Coriolis Force ◽  
Stokes Equations ◽  
Fluid Motion ◽  
Navier Stokes ◽  
Length Scale ◽  
Rotational Axis ◽  
Navier Stokes Equation ◽  
Direction Parallel ◽  
Substantial Growth ◽  
Rotating Turbulence

The roles of the Coriolis force and the convection associated with the fluid motion in the formation of columnar eddies in freely decaying homogeneous rotating turbulence at a moderate Rossby number are studied by direct numerical simulation of the Navier–Stokes equations in a periodic box. The simulated field is compared with a series of artificial fields generated by switching off the nonlinear and viscous terms in the Navier–Stokes equation at given instants. The comparison shows that, without the nonlinear convection effect, the Coriolis force cannot sustain the substantial growth in the direction parallel to the rotational axis of the length scale defined on the basis of the two-point correlation of the square of the vorticity, i.e. cannot sustain the formation of the columnar eddies. The length scale characterizes well the intuitive impression from visualization of flow obeying the dynamics with or without the nonlinear effect. It is shown that the lack of substantial growth is insensitive to the scale of the eddies, the box size and viscosity, at least in the case studied here.

scholarly journals Generalized Navier–Stokes Equations and Dynamics of Plane Molecular Media

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 288
Author(s):  
Alexei Kushner ◽  
Valentin Lychagin
Keyword(s):  
Carbon Dioxide ◽  
Internal Structure ◽  
Stokes Equation ◽  
Hydrogen Cyanide ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations

The first analysis of media with internal structure were done by the Cosserat brothers. Birkhoff noted that the classical Navier–Stokes equation does not fully describe the motion of water. In this article, we propose an approach to the dynamics of media formed by chiral, planar and rigid molecules and propose some kind of Navier–Stokes equations for their description. Examples of such media are water, ozone, carbon dioxide and hydrogen cyanide.

Numerical Integration of the Navier-Stokes Equations for a Disk Rotating in a Housing

1985 ◽  
Vol 40 (8) ◽  
pp. 789-799 ◽  
Author(s):  
A. F. Borghesani
Keyword(s):  
Boundary Layer ◽  
Cylindrical Cavity ◽  
Boundary Layer Thickness ◽  
Stokes Equations ◽  
Fluid Motion ◽  
Rotating Disk ◽  
Infinite Medium ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Viscous Torque

The Navier-Stokes equations for the fluid motion induced by a disk rotating inside a cylindrical cavity have been integrated for several values of the boundary layer thickness d. The equivalence of such a device to a rotating disk immersed in an infinite medium has been shown in the limit as d → 0. From that solution and taking into account edge effect corrections an equation for the viscous torque acting on the disk has been derived, which depends only on d. Moreover, these results justify the use of a rotating disk to perform accurate viscosity measurements.

A note on the solution of the Navier-Stokes equations for a spherically symmetric expansion into a very low pressure

1973 ◽  
Vol 59 (2) ◽  
pp. 391-396 ◽  
Author(s):  
N. C. Freeman ◽  
S. Kumar
Keyword(s):  
Shock Wave ◽  
Reynolds Number ◽  
Stokes Equation ◽  
Stokes Equations ◽  
Low Pressure ◽  
Navier Stokes ◽  
Spherically Symmetric ◽  
Navier Stokes Equation ◽  
Navier Stokes Equations ◽  
Type Flow

It is shown that, for a spherically symmetric expansion of a gas into a low pressure, the shock wave with area change region discussed earlier (Freeman & Kumar 1972) can be further divided into two parts. For the Navier–Stokes equation, these are a region in which the asymptotic zero-pressure behaviour predicted by Ladyzhenskii is achieved followed further downstream by a transition to subsonic-type flow. The distance of this final region downstream is of order (pressure)−2/3 × (Reynolds number)−1/3.

scholarly journals CAUCHY PROBLEM FOR VISCOUS SHALLOW WATER EQUATIONS WITH A TERM OF CAPILLARITY

2010 ◽  
Vol 20 (07) ◽  
pp. 1049-1087 ◽  
Author(s):  
BORIS HASPOT
Keyword(s):  
Shallow Water ◽  
Existence Of Solutions ◽  
Stokes Equations ◽  
Variable Viscosity ◽  
Water System ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Viscosity Coefficients ◽  
Global Existence Of Solutions ◽  
Dependent Viscosity

In this paper, we consider the compressible Navier–Stokes equation with density-dependent viscosity coefficients and a term of capillarity introduced formally by van der Waals in Ref. 51. This model includes at the same time the barotropic Navier–Stokes equations with variable viscosity coefficients, shallow-water system and the model introduced by Rohde in Ref. 46. We first study the well-posedness of the model in critical regularity spaces with respect to the scaling of the associated equations. In a functional setting as close as possible to the physical energy spaces, we prove global existence of solutions close to a stable equilibrium, and local in time existence of solutions with general initial data. Uniqueness is also obtained.

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

<p>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.</p><p>[1] U. Frisch, Z.S. She and P. L. Sulem, “Large-Scale Flow Driven by the Anisotropic Kinetic Alpha Effect,” Physica D, Vol. 28, No. 3, 1987, pp. 382-392.</p>

Numerical Solutions of the Viscous Flow Equations for a Class of Closed Flows

1965 ◽  
Vol 69 (658) ◽  
pp. 714-718 ◽  
Author(s):  
Ronald D. Mills
Keyword(s):  
Moving Boundary ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Fluid Motion ◽  
Navier Stokes ◽  
Steady Flows ◽  
Flow Equations ◽  
Steady Streaming ◽  
Difference Formula ◽  
Surface Passing

The Navier-Stokes equations are solved iteratively on a small digital computer for the class of flows generated within a rectangular “cavity” by a surface passing over its open end. Solutions are presented for depth/breadth ratios ƛ=0.5 (shallow), 10 (square), 20 (deep) and Reynolds number 100. Flow photographs ore obtained which largely confirm the predicted flows. The theoretical velocity profiles and pressure distributions through the centre of the vortex in the square cavity are calculated.In an appendix an improved finite difference formula is given for the vorticity generated at a moving boundary.Since Thorn began his pioneering work some thirty-five years ago the number of numerical solutions which have been obtained for the equations of incompressible viscous fluid motion remains small (see bibliographies of Thom and Apelt, Fromm). The known solutions are principally for steady streaming flows, although two methods have now been used with success for non-steady flows (Payne jets and Fromm flow past obstacles). By contrast this paper is concerned with the class of closed flows generated in a rectangular region of varying depth/breadth ratio by a surface passing over an open end. This problem has been considered for a number of reasons.

Pulsatile Waterhammer Subject to Laminar Friction

1972 ◽  
Vol 94 (2) ◽  
pp. 467-472 ◽  
Author(s):  
D. A. P. Jayasinghe ◽  
H. J. Leutheusser
Keyword(s):  
Stokes Equations ◽  
Fluid Motion ◽  
Present Theory ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
One Dimensional ◽  
Arbitrary Velocity ◽  
Velocity Input ◽  
Special Case ◽  
Signalling Problem

This paper deals with elastic waves which may be generated in a fluid by the sudden movement of a flow boundary. In particular, an analysis of the classical piston, or signalling problem is presented for the special case of arbitrary velocity input into a stationary fluid contained in a circular, semi-infinite waveguide. The decay of the pulse, as well as the resulting flow development in the inlet region of the pipe are analyzed by means of an asymptotic expansion of the suitably nondimensionalized Navier-Stokes equations for a compressible, nonheat-conducting Newtonian fluid. The results differ significantly from those of the more conventional one-dimensional approach based on the so-called telegrapher’s equation of mathematical physics. The present theory realistically predicts the growth of a boundary layer both in time and position and, hence, it appears to represent the transient fluid motion in a manner which is physically more appealing.

scholarly journals NUMERICAL CALCULATION OF VELOCITY FIELDS FOR VISCO-ELASTIC MATERIALS IN CYLINDRICAL CHANNELS

2019 ◽  
pp. 19-28
Author(s):  
Ekaterina Valer'evna Fomenko ◽  
Albert Hamed-Harisovich Nugmanov ◽  
Thi Sen Nguyen ◽  
Aleksanyan Igor Yuryevich Aleksanyan
Keyword(s):  
Mass Transfer ◽  
Heat And Mass Transfer ◽  
Stokes Equations ◽  
Radiation Power ◽  
Wheat Gluten ◽  
Internal Heat ◽  
Velocity Fields ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Suggested Approach

The article touches upon the application of the numerical finite difference method for solving Navier-Stokes equation in case of one-dimensional problem of passing a cooled viscoelastic material inside circular nozzles. There have been analyzed the specific features of using the method and presented the results of its application. The object of study was not chosen at random, because viscous properties of raw gluten are variable and depend on the temperature, chemical composition and properties of the feedstock. Working not properly with the object of research (phenomenon, process), but with its model helps to characterize its properties and behavior in various situations relatively quickly and without significant costs. The need to identify patterns of internal heat and mass transfer, which is based on studying the kinetics of the process, is obvious for physic-mathematical modeling of heat and mass transfer processes of wheat gluten granulation, in particular, analyzing the mechanism of moisture removal during its drying under radiation power supply. The results of the conducted research are consistent with the available data on the subject, and the suggested approach to solving the problem of choosing rational hydrodynamic regimes has been applied due to the difficulty of experimental determining the velocity fields and problematic analyzing the system of hydrodynamic differential Navier-Stokes equations with variable proportionality ratios.

scholarly journals Simulation of aeromechanics of the grinding process in a centrifugal mill

2020 ◽  
Vol 8 (2) ◽  
pp. 59-66
Author(s):  
I.A. Ostashko ◽  
◽  
A.P. Naumenko ◽  
Keyword(s):  
Gas Dynamics ◽  
Heterogeneous Medium ◽  
Stokes Equations ◽  
Flow Path ◽  
Navier Stokes ◽  
Maximum Diameter ◽  
Navier Stokes Equation ◽  
Crushed Material ◽  
Centrifugal Mill

The article discusses aeromechanical processes in a centrifugal mill at different speeds of rotation in order to establish the regularities of the kinematics of the flow of a heterogeneous medium in the grinding chamber of the mill, its interaction with the working body and the classification of the crushed material when removed from the grinding chamber. The study of gas dynamics of processes in the flow path of a centrifugal mill has been carried out. The trajectories of streams, velocity and pressure fields were investigated. The influence of various factors on the efficiency of the classification and the maximum diameter of particles removed from the grinding chamber was revealed. The regularities of the movement of a heterogeneous medium, its interaction with the working body and the classification of the crushed material when removed from the grinding chamber were established, the gas dynamics of processes in the flow path of a centrifugal mill was studied. The main way to increase the speed of air flows is to increase the flow of transport air, which in turn affects the aerodynamics of the processes in the grinding chamber of the mill, productivity and grinding time of the material. Processes of gas dynamics in a compressed medium of the flow path of a centrifugal mill were described by a system of non-stationary Navier-Stokes equations of continuity, energy and equation of state in approximation of the turbulence model. Analysis of the results of mathematical modeling of processes in the working chamber showed that the air flow carries out a complex rotational movement in the transverse and longitudinal sections with the formation of local zones of increased turbulence. As a result of numerical modeling and analysis of the results, factors have been identified that make it possible to intensify the process of material grinding. The flows have a pronounced ballistic trajectory. They start their movement from the center of the bottom of the grinding chamber and move along the walls of the chamber while rotating in a spiral and moving down the wall of the hollow shaft. It is observed that the point of separation of the flows rotating in the lower part of the grinding chamber and the flows moving in the upper part is on 60% of the height of the chamber. Keywords: modeling, centrifugal mill, finite element method, Navier-Stokes equation.

scholarly journals Solutions of Navier-Stokes Equations with Coriolis Force in the Rotational Framework

2021 ◽  
Vol 31 (5) ◽  
pp. 54-57
Keyword(s):  
Coriolis Force ◽  
Existence And Uniqueness ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Mixed Norm ◽  
Uniqueness Of Solutions ◽  
Navier Stokes Equations ◽  
Interpolation Inequalities ◽  
Stokes Problems ◽  
Point Argument

In this article, for 0 ≤m<∞ and the index vectors q=(q_1,q_2 ,q_3 ),r=(r_1,r_2,r_3) where 1≤q_i≤∞,1<r_i<∞ and 1≤i≤3, we study new results of Navier-Stokes equations with Coriolis force in the rotational framework in mixed-norm Sobolev-Lorentz spaces H ̇^(m,r,q) (R^3), which are more general than the classical Sobolev spaces. We prove the existence and uniqueness of solutions to the Navier-Stokes equations (NSE) under Coriolis force in the spaces L^∞([0, T]; H ̇^(m,r,q) ) by using topological arguments, the fixed point argument and interpolation inequalities. We have achieved new results compared to previous research in the Navier-Stokes problems.

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