The transition to turbulence in pipe and plane Couette flow differs from the better understood situation of Taylor-Couette or Rayleigh-Bénard flow in that the laminar profile is stable against infinitesimal perturbations for all Reynolds numbers. Moreover, even when turbulent flow is established, it can spontaneously return to laminar flow. These observations are compatible with the formation o...

1 Chandrasekhar, S., "The Stability of Non-Dissipative Couette Flow in Hydromagnetics," these PROCEEDINGS, 46, 253-257 (1960); see also Velikhov, E. P., "Stability of an ideally conducting liquid flowing between cylinders rotating in a magnetic field," Soviet Phys.-JETP, 36, 995-998 (1959). 2 Reid, W. H., "Inviscid modes of instability in Couette flow," J. Math. Anal. and Applications (to appea...

In turbulent Taylor-Couette flow, the injection of bubbles reduces the overall drag. On the other hand, rough walls enhance the overall drag. In this work, we inject bubbles into turbulent Taylor-Couette flow with rough walls (with a Reynolds number up to 4 x 10(5), finding an enhancement of the dimensionless drag as compared to the case without bubbles. The dimensional drag is unchanged. As in...

entropy generation in an unsteady hydromagnetic couette flow of a viscous incompressible electrically conducting fluid between two infinite horizontal parallel plates in a rotating system have been analyzed. both the lower and upper plates of the channel are subjected to asymmetric convective heat exchange with the ambient following the newton's law of cooling. a numerical solution for governin...

This paper discusses my work through December 2004 to implement Johnston and Liu’s Pressure Poisson Equation (PPE) method[1] for Plane Couette flow. Also, I discuss some results and plans for implementing a periodic orbit search. The advantage of this method is that it decouples the computation of velocity and pressure at each time step by treating the pressure term explicitly in time. The proj...

Matched asymptotic solutions for the steady banded flow of the diffusive Johnson-Segalman model in various geometries ⋆ Abstract We present analytic solutions for steady flow of the Johnson-Segalman (JS) model with a diffusion term in various geometries and under controlled strain rate conditions , using matched asymptotic expansions. The diffusion term represents a singular perturbation that l...

Starting from stationary bifurcations in Couette-Dean flow, we compute nontrivial stationary solutions in inertialess viscoelastic circular Couette flow. These solutions are strongly localized vortex pairs, exist at arbitrarily large wavelengths, and show hysteresis in the Weissenberg number, similar to experimentally observed "diwhirl" patterns. Based on the computed velocity and stress fields...

Plane Couette flow of viscoelastic fluids is shown to exhibit a purely elastic subcritical instability at a very small-Reynolds number in spite of being linearly stable. The mechanism of this instability is proposed and the nonlinear stability analysis of plane Couette flow of the Upper-Convected Maxwell fluid is presented. Above a critical Weissenberg number, a small finite-size perturbation i...

The Ω phase of the liquid sodium α-Ω dynamo experiment at New Mexico Institute of Mining and Technology in cooperation with Los Alamos National Laboratory has demonstrated a high toroidal field B(ϕ) that is ≃8×B(r), where B(r) is the radial component of an applied poloidal magnetic field. This enhanced toroidal field is produced by the rotational shear in stable Couette flow within liquid sodiu...

This article looks at the case of a large, flat-bottomed ship, such as a bulk carrier, moving in close proximity to a flat sea floor. It is shown that the flow beneath the ship can be modeled as a shear flow between two parallel plates, one of which is moving. The resulting flow can be represented using laminar Couette flow at low Reynolds numbers (possible at model scale) or the very different...