The velocity field of second-order Rivlin–Ericksen fluid between two parallel porous plates rotating around two different axes but with the same angular velocity

2000 ◽  
Vol 38 (8) ◽  
pp. 939-955 ◽  
Author(s):  
N.Aydin Unverdi
Keyword(s):  
Velocity Field ◽  
Angular Velocity ◽  
Second Order

Finite difference code for velocity and surface traction of a Fluid between Two Eccentric Spheres

2015 ◽  
Vol 11 (1) ◽  
pp. 2960-2971
Author(s):  
M.Abdel Wahab
Keyword(s):  
Velocity Field ◽  
Angular Velocity ◽  
Finite Difference ◽  
Numerical Study ◽  
Outer Sphere ◽  
Equation Of Motion ◽  
Annular Region ◽  
Surface Traction ◽  
Angular Velocities ◽  
Axis Passing

The Numerical study of the flow of a fluid in the annular region between two eccentric sphere susing PHP Code isinvestigated. This flow is created by considering the inner sphere to rotate with angular velocity 1  and the outer sphererotate with angular velocity 2  about the axis passing through their centers, the z-axis, using the three dimensionalBispherical coordinates (, ,) .The velocity field of fluid is determined by solving equation of motion using PHP Codeat different cases of angular velocities of inner and outer sphere. Also Finite difference code is used to calculate surfacetractions at outer sphere.

scholarly journals Some solutions of Einstein's gravitational equations for systems with axial symmetry

1930 ◽  
Vol 126 (803) ◽  
pp. 592-602 ◽  
Keyword(s):  
Angular Velocity ◽  
Axial Symmetry ◽  
Second Order ◽  
Newtonian Potential ◽  
Static Distribution ◽  
Gravitational Equations

§1. In this paper we find solutions of Einstein’s gravitational equations G μν = 0 which give the field due to any static distribution of matter sym­metrical about an axis; in the later part of the paper an angular velocity about the axis is introduced. We take the ground form ds 2 = - e λ ( dx 2 + dr 2 ) - e -ρ r 2 d θ 2 + e ρ dt 2 , (1) where λ, ρ are functions of x and r . Further we take ρ to be the Newtonian potential of an auxiliary distribution of matter of density σ ( x, r ), the potential being calculated as though our co-ordinates were Euclidean. We find that it is then possible to determine λ, so that the equations G μν = 0 are exactly satisfied everywhere outside the auxiliary body. λ is nearly equal to —ρ, the quantity μ = λ + ρ being of the second order in terms of σ.

scholarly journals The influence of circulation on the stability of vortices to mode-one disturbances

1995 ◽  
Vol 451 (1943) ◽  
pp. 747-755 ◽  
Keyword(s):  
Velocity Field ◽  
Angular Velocity ◽  
Initial Value Problem ◽  
Large Time ◽  
Asymptotic Methods ◽  
Two Dimensional ◽  
Initial Value ◽  
The Stability ◽  
Ultimate Fate ◽  
Solution Behaviour

The initial value problem for the two-dimensional inviscid vorticity equation, linearized about an azimuthal basic velocity field with monotonic angular velocity, is solved exactly for mode-one disturbances. The solution behaviour is investigated for large time using asymptotic methods. The circulation of the basic state is found to govern the ultimate fate of the disturbance: for basic state vorticity distributions with non-zero circulation, the perturbation tends to the steady solution first mentioned in Michalke & Timme (1967), while for zero circulation, the perturbation grows without bound. The latter case has potentially important implications for the stability of isolated eddies in geophysics.

Evaluation and Comparison of Bounding Techniques for Convection-Diffusion Problems

1993 ◽  
Vol 115 (1) ◽  
pp. 33-40 ◽  
Author(s):  
M. A. R. Sharif ◽  
A. A. Busnaina
Keyword(s):  
Velocity Field ◽  
Second Order ◽  
Upwind Scheme ◽  
Numerical Dispersion ◽  
Test Problems ◽  
Analytical Treatment ◽  
Numerical Diffusion ◽  
Convection Diffusion ◽  
Uniform Velocity ◽  
Flux Corrected Transport

The effects of bounding the skew upwind and the second-order upwind discretization schemes for the convection terms in convection-diffusion transport equations have been studied. Earlier studies indicated that these two schemes produce less numerical diffusion but introduce unacceptable numerical dispersion or oscillations in the solution if not bounded. A simplified analytical treatment exploring the reason for this behavior is presented. Two bounding techniques, the flux-corrected transport and the filtering remedy and methodology were evaluated. Test problems used in the evaluation are (i) one-dimensional convection of a rectangular pulse, (ii) transport of a scalar step in a uniform velocity field at an angle to the grid lines, (iii) Smith and Hutton problem, (iv) two-dimensional convection of a square scalar pulse in a uniform velocity field at an angle to the grid lines, and (v) two interacting parallel streams moving at an angle to the grid lines. The results indicate that the flux-corrected transport eliminates the oscillations in the solution without introducing any additional numerical diffusion when used with both schemes. The filtering remedy and methodology also eliminates the oscillation when used with the skew upwind scheme. This technique, however, is not effective in reducing the over-shoots when used with the second-order upwind scheme.

scholarly journals NUMERICAL SIMULATION OF TURBULENT WAVE BOUNDARY LAYERS

1986 ◽  
Vol 1 (20) ◽  
pp. 119 ◽  
Author(s):  
J.H. Trowbridge ◽  
C.N. Kanetkar ◽  
N.T. Wu
Keyword(s):  
Velocity Field ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Boundary Layers ◽  
Second Order ◽  
Minor Role ◽  
Steady Streaming ◽  
Stokes Waves ◽  
A Minor ◽  
Wave Boundary

This paper reports numerical computations of fully rough turbulent boundary layers produced by first and second order Stokes waves. The computations are based on a mixing length turbulence closure and on a slightly more sophisticated turbulent kinetic energy closure. The first order results compare well with existing laboratory results. Reversal of the second order steady streaming under relatively long waves, which has been predicted analytically, is also predicted in the numerical results, The steady second order velocity field is found to become fully established only after a development time on the order of a few hundred wave periods. Both the first and second order results indicate that advection and diffusion of turbulent kinetic energy play a minor role in determining the Reynolds averaged velocity field.

scholarly journals Dynamics of eye movements under time varying stimuli

2018 ◽  
Vol 11 (1) ◽  
Author(s):  
Verica Radisavljevic-Gajic
Keyword(s):  
Mathematical Model ◽  
Eye Movements ◽  
Time Delay ◽  
Angular Velocity ◽  
Second Order ◽  
Time Varying ◽  
First Order ◽  
Linear Dynamic ◽  
Delay Elements ◽  
Range Of Values

In this paper we study the pure-slow and pure-fast dynamics of the disparity convergence of the eye movements second-order linear dynamic mathematical model under time varying stimuli. Performing simulation of the isolated pure-slow and pure-fast dynamics, it has been observed that the pure-fast component corresponding to the eye angular velocity displays abrupt and very fast changes in a very broad range of values. The result obtained is specific for the considered second-order mathematical model that does not include any saturation elements nor time-delay elements. The importance of presented results is in their mathematical simplicity and exactness. More complex mathematical models can be built starting with the presented pure-slow and pure-fast first-order models by appropriately adding saturation and time-delay elements independently to the identified isolated pure-slow and pure-fast first-order models.

Note on the inviscid stability of flow over a compliant wall

1994 ◽  
Vol 279 ◽  
pp. 165-168 ◽  
Author(s):  
K. S. Yeo
Keyword(s):  
Velocity Field ◽  
Simple Form ◽  
Second Order ◽  
Parallel Flow ◽  
Order Derivative ◽  
Necessary Condition ◽  
Zero Velocity ◽  
Type Criterion ◽  
Compliant Wall ◽  
Flexible Wall

This paper is concerned with the linear inviscid stability of parallel flow over a compliant or flexible wall. A Fjørtoft-type criterion providing a necessary condition for instability in terms of the basic velocity field and its second-order derivative is established. This criterion assumes a simple form for basic flows with zero velocity at the wall. For the latter flows, another necessary condition for stability is given. The results are helpful in the search for unstable modes in flow over a compliant wall.

The forced flow of a rotating viscous liquid which is heated from below

1953 ◽  
Vol 246 (907) ◽  
pp. 81-112 ◽  
Keyword(s):  
Velocity Field ◽  
Angular Velocity ◽  
Viscous Liquid ◽  
Opposite Direction ◽  
Equations Of Motion ◽  
Cylindrical Vessel ◽  
Central Axis ◽  
Forced Flow ◽  
Outer Portion ◽  
Non Linear

A liquid is contained in a cylindrical vessel and is subject to heating on the horizontal base of the vessel. The problem of the forced flow arising from the heating has been investigated in the case when the heating function is symmetrically arranged about the central axis. It is found that the relative forced flow tends to become zonal in character when the vessel rotates at a sufficiently high angular velocity. This relative zonal motion is principally in the direction of the rotation except near the outer portion of the fluid where it is in the opposite direction, the former being ‘westerlies’, the latter ‘easterlies’. The easterlies are due to the non-linear inertia terms in the equations of motion. This description of the velocity field is used because the experiment described above has considerable meteorological significance.

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.

Sign in / Sign up

Export Citation Format

Share Document