Our concern is with the evolution of large amplitude Tollmien-Schlichting waves in boundary layer ows. In fact the disturbances we consider are of a comparable size to the unperturbed state. We shall describe two-dimensional disturbances which are locally periodic in time and space. This is achieved using a phase equation approach of the type discussed by Howard and Kopell (1977) in the context...

A numerical approach called “SIMPLER” is used to investigate the  flow and heat transfer characteristics in a square driven cavity. The two-dimensional incompressible Navier-Stokes equations were solved and the results are depicted as contour plots of stream function, vorticity, and total pressure for Reynolds numbers from 1 to 10000. At the higher values of Reynolds number, an inviscid core re...

A comprehensive method of theoretical analysis for finite Squeeze Film Damper using finite element method is presented. The modified Reynolds equation in the film is solved using the finite element discretization. A Galerkin variational method is applied for solving modified Reynolds equation to determine the pressures as well as load carrying capacities. The pressure distribution and load carr...

A small parameter technique is used to derive Reynolds' lubrication equation from the Stokes equation. The error associated with the approximation is estimated in suitable norms.

Stokes Paradox, Fluid dynamics, Stokes flow, Stream function, Biharmonic equation, Helmholtz equation, Low Reynolds number This paper proposes a solution to Stokes’ paradox for asymptotically uniform viscous flow around a cylinder. The existence of a global stream function satisfying a perturbative form of the two-dimensional Navier–Stokes equations for low Reynolds number is established. This ...

We study the linearized stability of shear flow satisfying Navier slip boundary conditions. The Orr-Sommerfeld equation for the plane Poiseuille flow with Navier slip boundary conditions is solved numerically by the Chebyshev collocation method. Our numerical results show that slip at the boundary increases the critical Reynolds number Rc for instability. The dependence of the this critical Rey...

The dynamics of the Reynolds stress tensor is given by an evolution equation coupling geometrical effects and turbulent source terms. The effects of the mean flow geometry are shown up when the source terms are neglected. In this case, the Reynolds stress tensor is expressed as the sum of three tensor products of vector fields only associated with the mean flow. The vector fields are governed b...

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 ...