A model for homogeneous anisotropic incompressible turbulence is proposed. The model generalizes the GISS model of homogeneous isotropic turbulence; the generalization involves the solution of the GISS equations along a set of integration paths in wavenumber (k-) space. In order to make the problem tractable, these integration paths (“cascade lines”) must be chosen in such a way that the behavi...

Axisymmetric stability of viscous resistive magnetized Couette flow is re-examined, with emphasis on flows that would be hydrodynamically stable according Rayleigh’s criterion: opposing gradients of angular velocity and specific angular momentum. In this regime, magnetorotational instability (MRI) may occur. The governing system in cylindrical coordinates is of tenth order. It is proved, by met...

This paper examines the bifurcation and structure of the bifurcated solutions of the two-dimensional infinite Prandtl number convection problem. The existence of a bifurcation from the trivial solution to an attractor ΣR was proved by Park [14]. We prove in this paper that the bifurcated attractor ΣR consists of only one cycle of steady state solutions and that it is homeomorphic to S1. By thor...

A linear stability analysis is performed on a thermal, stratified liquid layer with a deformable thermocapillary surface. The objective is to investigate the possibility and conditions for existence of oscillatory cellular convection in the linear thermocapillary system. In general, the principle of the exchange of stabilities for the onset of cellular convection in liquid layers with deformabl...

We present measurements of the Nusselt number N as a function of the Rayleigh number R and the Prandtl number sigma in cylindrical cells with aspect ratios gamma = 0.5 and 1.0. We used acetone, methanol, ethanol, and 2-propanol with Prandtl numbers sigma = 4.0, 6.5, 14.2, and 34.1, respectively, in the range 3x10(7) less, similarR less, similar10(11). At constant R, N(R,sigma) varies with sigma...

For the understanding of planetary and stellar dynamos an overview of the major parameter dependences of convection driven dynamos in rotating spherical fluid shells is desirable. Although the computationally accessible parameter space is limited, earlier work is extended with emphasis on higher Prandtl numbers and uniform heat flux condition at the outer boundary. The transition from dynamos d...

a = mean speed of sound, R T 1=2 aw = mean speed of sound at the wall, RTw 1=2 C = turbulent viscosity parameter, T= Lk cp = specific heat at constant pressure, R= 1 ; 1004:5 J= kg K cv = specific heat at constant volume, R= 1 ; 717:5 J= kg K f = uniform body force, w=h h = half channel height hw = wall length scale, h=Re i = turbulence intensity, 2k=3 = U1 k = turbulent kinetic energy, uiui=2 ...

Effect of the capillary meniscus on the instability of large Prandtl number Czochralski melt flow is studied experimentally. The measurements are conducted in two experimental facilities by two independent non-intrusive optical techniques. The quantitative results are presented as dependencies of the critical Grashof number (critical temperature difference) on the meniscus height for different ...

Convection refers to fluid motion that is induced by buoyancy. In thermal convection buoyancy is due to temperature differences and one of the interesting questions is how much of the total heat transfer is due to convection. The natural measure of this quantity is the Nusselt number, N , and many experiments and numerical simulations have been performed to discern the relationship between N an...