A note on the onset of recirculation in a 2D Couette flow over a wavy bottom

作者：Esquivelzeta Rabell F M^*; Figueroa Espinoza B; Legendre D; Salles P

来源：Physics of Fluids, 2015, 27(1): 014108.

DOI：10.1063/1.4906153

Laminar Couette flow over a fixed wavy surface was studied with direct numerical simulation in a 2D periodic numerical domain. The mesh was generated by a conformal transformation that sets horizontal flow at the top of the domain, where a constant velocity boundary condition is given. The bottom of the domain is a wavy sinusoidal surface of wave slope 2 pi a/lambda. The combined effect of bottom shape, inertia, and viscosity was explored using different Reynolds numbers (Re) and two dimensionless parameters in terms of channel width h, wavelength lambda, and the amplitude of the wavy bottom a. Even if the Reynolds number was large, the simulations were not perturbed so the regime was always laminar. However, a recirculation appeared at the vicinity of the trough. The horizontal location of the eddy center was reported as a function of 2 pi a/lambda and Re lambda/h. The conditions for the onset of this recirculation were studied and compared with results from the literature. Two regimes can be clearly identified from the numerical results; a viscous regime with a weak dependence between 2 pi a/lambda and Re lambda/h for small Reynolds numbers and an inertial regime with an exponential dependence between 2 pi a/lambda and Re lambda/h for large Reynolds numbers, which presents an approximate slope of -1/3. Almost all results collapse in one single curve that characterizes the phenomenon (with the exception of some points where the flow is confined due to a large lambda/h ratio).

• 出版日期2015-1