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...

unsteady hydromagnetic generalised couette flow of a viscous, incompressible and electrically conducting fluid between two horizontal parallel porous plates darcian channel in the presence of a uniform transverse magnetic field taking hall current and ion-slip into account in a rotating system is investigated. an exact solution of the governing equations is obtained by laplace transform techniq...

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 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...

We prove the instability of Couette flow if disturbances is less smooth than Gevrey space class 2. This shows that this critical regularity for problem since it was proved in [5] stability and inviscid damping hold which are smoother A big novelty due to an mechanism completely nonlinear some energy cascade. © 2023 Wiley Periodicals LLC.