The stability of compressible plane Couette flow, which is a simple case of hypersonic wall-bounded shear flows, is not well understood even though incompressible Couette flow has been studied extensively by linear stability analysis and shown to be stable to linear disturbances. As a first step in studying the stability of three-dimensional hypersonic boundary layers, this paper studies the te...

In this paper, the Ritz-Galerkin method in Bernstein polynomial basis is applied for solving the nonlinear problem of the magnetohydrodynamic (MHD) flow of third grade fluid between the two plates. The properties of the Bernstein  polynomials together with the Ritz-Galerkin method are used to reduce the solution of the MHD Couette flow of non-Newtonian fluid in a porous medium to the solution o...

The statistical properties of fully developed planar turbulent Couette–Poiseuille flow result from the simultaneous imposition of a mean wall shear force together with a mean pressure force. Despite the fact that pure Poiseuille flow and pure Couette flow are the two extremes of Couette–Poiseuille flow, the statistical properties of the latter have proved resistant to scaling approaches that co...

Synovial joints are loaded by weight bearing, stretching, and fluid-driven shear. To simulate in vitro fluid-driven shear, we developed an "oscillating Couette flow mechanical shear loader". Oscillating Couette flow mimics relative motion of articular surfaces; hence, characterizing flow-induced shear by the loader enhances understanding of mechanotransduction in the joint tissue. Here, the ana...

The motivation underpinning this work is the need to understand bubble generation mechanisms due to interactions between free surface and turbulent boundary layers as commonly seen near ship walls. As a canonical problem, we consider a turbulent plane Couette flow with vertical parallel sidewalls and an air-water interface established by gravity in the vertical direction. Two-phase Couette flow...

Sommerfeld paradox roughly says that mathematically Couette shear flow is linearly stable for all Reynolds number, but experimentally it is unstable to any size perturbation when the Reynolds number is large enough. Our study here focuses upon a sequence of 2D oscillatory shears which are the Couette linear shear plus small amplitude and high frequency sinusoidal shear perturbations. The sequen...

A flow transition in a coaxial rotating cylinder with only inner cylinder rotation was investigated using ultrasonic Doppler method for a wide range of Reynolds number up to 40 times critical Reynolds number (Rc). By analysing spatio-temporal velocity profiles, excitation functions of various transition modes such as wavy and modulated wavy modes were obtained using space-time Fourier expansion...

In this article using the inverse Laplace transform, we show analytical solutions for the generalized mass transfers with (and without) a chemical reaction. These transfers have been expressed as the Couette flow with the fractional derivative of the Caputo sense. Also, using the Hankel contour for the Bromwich's integral, the solutions are given in terms of the generalized Airy functions.

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...