On the origin of super-rotating layers in magnetohydrodynamic flows

An asymptotic analysis has been performed for the magnetohydrodynamic flow between perfectly conducting concentric cylindrical shells. The flow in the model geometry exhibits all the features which had been discovered in the past for the case of differentially rotating spherical shells considered in the context of geophysical analyses. For strong magnetic fields, the flow domain splits into distinct subregions and exhibits two different types of cores which are separated from each other by a tangent shear layer. The fluid in the inner core flows similar to a solid-body rotation and the outer core is entirely stagnant. With increasing magnetic fields the shear layer becomes thinner and, since the flow rate carried by the layer asymptotes to a finite value, the velocity in the layer increases as the layer thickness decreases. Moreover, the flux carried by the layer rotates in opposite direction compared with the rotation of the body. It is shown that the rotating jet is driven by the electric potential difference between the edges of the inner and the outer core.     

Convective stability of a nonisothermal fluid in a rotating horizontal coaxial gap

The thermal fluid convection in a coaxial horizontal gap uniformly rotating about its axis is investigated. The threshold above which convective flows are excited and the structure of these flows are studied. It is found that convection ensues irrespective of whether the inner or outer boundary temperature is higher. Convection manifests itself in the threshold development of rolls elongated in the direction of the rotation axis and is determined by two different mechanisms. If the layer is heated from outside, the centrifugal convection mechanism plays a leading part and the diameter of the convective rolls is comparable with the layer thickness. If the higher is the temperature of the inner boundary of the layer, the centrifugal inertia force has a stabilizing effect and convection development is related with the action of thermal vibrational mechanism. The latter is determined by gravity-generated oscillations of the nonisothermal fluid relative to the cavity. The wave number of the vibrational convective structures is several times smaller than under centrifugal convection. The results obtained broaden our understanding of thermal convection in systems rotating in external static force fields.     

Time-dependent stagnation-point flow over rotating disk impinging oncoming flow

The unsteady stagnation point flow of an incompressible viscous fluid over a rotating disk is investigated numerically in the present study.The disk impinges the oncoming flow with a time-dependent axial velocity.The three-dimensional axisymmetric boundary-layer flow is described by the Navier-Stokes equations.The governing equations are solved numerically,and two distinct similarity solution branches are obtained.Both solution branches exhibit different flow patterns.The upper branch solution exists for all values of the impinging parameter β and the rotating parameter.However,the lower branch solution breaks down at some moderate values of β.The involvement of the rotation at disk allows the similarity solution to be transpired for all the decreasing values of β.The results of the velocity profile,the skin friction,and the stream lines are demonstrated through graphs and tables for both solution branches.The results show that the impinging velocity depreciates the forward flow and accelerates the flow in the tangential direction.     

On the orbital motion of a rotating inner cylinder in annular flow

In this paper, numerical calculations have been performed to analyse the influence of the orbital motion of an inner cylinder on annular flow and the forces exerted by the fluid on the inner cylinder when it is rotating eccentrically. The flow considered is fully developed laminar flow driven by axial pressure gradient. It is shown that the drag of the annular flow decreases initially and then increases with the enhancement of orbital motion, when it has the same direction as the inner cylinder rotation. If the eccentricity and rotation speed of the inner cylinder keep unchanged (with respect to the absolute frame of reference), and the orbital motion is strong enough that the azimuthal component (with respect to the orbit of the orbital motion) of the flow‐induced force on the inner cylinder goes to zero, the flow drag nearly reaches its minimum value. When only an external torque is imposed to drive the eccentric rotation of the inner cylinder, orbital motion may occur and, in general, has the same direction as the inner cylinder rotation. Under this condition, whether the inner cylinder can have a steady motion state with force equilibrium, and even what type of motion state it can have, is related to the linear density of the inner cylinder. Copyright © 2006 John Wiley & Sons, Ltd.     

Generation of a magnetic field by convective flows in a rotating horizontal layer

The generation of a magnetic field by convective flows of a conducting fluid in a rotating plane layer is investigated numerically. The problem is considered in the complete three-dimensional nonlinear formulation. The sequence of temporal regimes that ensue as the Taylor number Ta increases from 0 (no rotation) to 2000 (the fluid motion is suppressed by rapid rotation) when the other parameters are fixed is studied. The Ta intervals on which bifurcations occur are found, and the breakdown and onset of symmetries in the attractors that arise is investigated.     

Rotationally symmetric flow over a rotating disk

The rotationally symmetric flow over a rotating disk in an incompressible viscous fluid is analyzed by a new method when the fluid at infinity is in a state of rigid rotation (in the same or in the opposite sense) about the same axis as that of the disk. Asymptotic expansions for the velocity field over the entire flow field are obtained for the general class of one-parameter rotationally symmetric flows. This method is further extended to the case when a uniform suction or injection is assumed at the rotating disk. Fluid motion induced by oscillatory suction of small amplitude at the rotating disk is also discussed.An initial-value analysis reveals that resonance is possible only when the angular velocity of the rotating fluid is greater than that of the rotating disk.     

Convective heat transfer from a rotating or nonrotating axisymmetric body

An analysis of steady laminar mixed-convection heat transfer from a rotating or nonrotating axisymmetric body is presented. A mixed-convection parameter is proposed to serve as a controlling parameter that determines the relative importance of the forced and the free convection. In addition, a rotation parameter is introduced to indicate the relative contributions of the flow forced convection and the rotational forced convection. The values of both these two parameters lie between 0 and 1. Furthermore, the coordinates and dependent variables are transformed to yield computationally efficient numerical solutions that are valid over the entire range of mixed convection from the forced-convection limit (rotating or nonrotating bodies) to the pure free-convection limit (non-rotating bodies) and the entire regime of forced convection from the pure flow forced-convection limit (nonrotating bodies) to pure rotational forced-convection limit (rotating bodies). The effects of mixed-convection intensity, body rotation, fluid suction or injection, and fluid Prandtl number on the velocity profiles, the temperature profiles, the skin-friction parameter, and heat transfer parameter are clearly illustrated for both cases of buoyancy assisting and opposing flow conditions.     

Flow structures,nonlinear inertial waves and energy transfer in rotating spheres

We investigate flow structures, nonlinear inertial waves and energy transfer in a rotating fluid sphere, using a Galerkin spectral method based on helical-wave decomposition (HWD). Numerical simulations of flows in a sphere are performed with different system rotation rates, where a large-scale forcing is employed. For the case without system rotation, the intense vortex structures are tube-like. When a weak rotation is introduced, small-scale structures are reduced and vortex tubes tend to align with the rotation axis. As the rotation rate increases, a large-scale anticyclonic vortex structure is formed near the rotation axis. The structure is shown to be led by certain geostrophic modes. When the rotation rate further increases, a cyclone and an anticyclone emerge from the top and bottom of the boundary, respectively, where two quasi-geostrophic equatorially symmetric inertial waves dominate the flow. Based on HWD, effects of spherical confinement on rotating turbulence are systematically studied. It is found that the forward cascade becomes weaker as the rotation increases. When the rotation rate becomes larger than some critical value, dual energy cascades emerge, with an inverse cascade at large scales and a forward cascade at small scales. Finally, the flow behavior near the boundary is studied, where the average boundary layer thickness gets smaller when system rotation increases. The flow behavior in the boundary layer is closely related to the interior flow structures, which create significant mass flux between the boundary layer and the interior fluid through Ekman pumping.     

Time-dependent MHD Couette flow of rotating fluid with Hall and ion-slip currents

The unsteady magnehydrodynamics (MHD) Couette flow of an electrically conducting fluid in a rotating system is investigated by taking the Hall and ion-slip currents into consideration.The derived fundamental equations on the assumption of a small magnetic Reynolds number are solved analytically with the well-known Laplace transform technique.The unified closed-form expressions are obtained for the velocity and the skin friction in the two different cases of the magnetic field being fixed to either the fluid or the moving plate.The effects of various parameters on the velocity and the skin friction are discussed by graphs.The results reveal that the primary and secondary velocities increase with the Hall current.An increase in the ion-slip parameter also leads to an increase in the primary velocity but a decrease in the secondary velocity.It is also shown that the combined effect of the rotation,Hall,and ion-slip parameters determines the contribution of the secondary motion in the fluid flow.     

Vibrational Dynamics of a Centrifuged Fluid Layer

The dynamics of a low-viscosity fluid layer inside a rotating cylinder under transverse translational vibration relative to the rotation axis is investigated experimentally. A novel vibrational effect, the generation of intense azimuthal fluid flows with velocities comparable with the cavity rotation velocity, is revealed. The structure and intensity of the vibrational flows and the flow transformation with variation of the determining dimensionless parameters (frequency and vibrational acceleration) are studied.__________Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, 2005, pp. 147–156.Original Russian Text Copyright © 2005 by Ivanova, Kozlov, and Polezhaev.