Transition to turbulence of the Batchelor flow in a rotor/stator device

Abstract

This experimental study is devoted to the transition to turbulence of the flow confined between a stationary and a rotating disk. Using visualization and video image analysis, we describe the different transitions occurring in the flow as the rotating velocity of the disk is varied. The space-time behavior of the wave patterns is analyzed using the BiOrthogonal Decomposition (BOD) technique. This decomposition of the experimental signals on proper modes permits to project the dynamics of the waves in a reduced embedding phase space. By this means, a torus doubling bifurcation is revealed before its complete destruction during the transition to a weak turbulence. Finally, a more classical 2D-Fourier analysis completes our description of the transition and shows for higher rotation rates, the appearance of a more developed turbulence issued from the former chaotic waves.

A 3D pseudospectral method for cylindrical coordinates. Application to the simulations of rotating cavity flows

“…10a), the highest Reynolds number considered in this study, the flow is fully turbulent characterized by thin structures that tend to be circular and extend to the vicinity of the axis in agreement with experimental observations [38]. On the rotor side, turbulence appears at the periphery of the disc between Re ¼ 2 Â 10 5 and Re ¼ 2:5 Â 10 5 .…”

A statistical study of spots in torsional Couette flow

“…As already described, the torsional Couette flow is formed when the rotating boundary layer (the Kármán layer) and the stationary disc layer (the Bödewadt layer) merge. Note that this is only possible (at the considered Reynolds numbers) when the stationary and the rotating disc are sufficiently close to one another, otherwise another transition that involves circular and spiral waves takes place (14). Because of rotation, the velocity field is threedimensional and a centrifugal flow takes place in the Karman layer.…”

An energy analysis of convective instabilities of the Bödewadt and Ekman boundary layers over rough surfaces

“…Many studies have been performed to reveal the similarities in the stability characteristics across the entire BEK class (see, for example, the theoretical and experimental studies discussed in papers [9][10][11][12][13][14] for the Bödewadt layer; papers [15,16] for the Ekman layer; and papers [17][18][19][20] for the von Kármán flow). These studies have shown the existence of two main flow instability mechanisms, commonly referred to as the Type I and the Type II modes.…”