Instabilities of Decaying Flow in a Rectangular Channel

Abstract

Instabilities near the wall of a rectangular water channel in decaying freestream flow is investigated experimentally. A sliding piston imparts trapezoidal velocity variation (constant acceleration from rest, constant velocity, and constant deceleration to rest) onto the freestream in the channel. With the onset of deceleration, a space invariant unsteady wall jet like velocity profiles develop opposite to the flow direction as evident from particle image velocimetry (PIV) measurements. Strong shear and decaying velocity profiles with reverse flow are observed in the deceleration phase and after piston stops. Velocity profiles at this stage are found to be highly inflectional. Dye visualization shows that the outer layer becomes unstable resulting in the formation of array of vortices similar to Kelvin–Helmholtz vortices in shear layer instability. Secondary vortices of opposite sign evolve in the inner layer close to the wall due to the adverse pressure gradient induced by the primary vortices. Vortex formation is not observed below a critical value of Reynolds number. Due to decaying nature of the base flow, i.e., decreasing Reynolds number, the instability vortices do not break down to turbulent flow. The wavelength of instability vortices ($\lambda$) scales with the average boundary-layer thickness ${\bar{\delta }}$, the average being taken from start of reverse flow to appearance of a vortex. The ratio $\lambda /{{\bar{\delta }}}$ is $\sim 2.6$. The vortex formation time scales with the average convective time scale and is $\sim 16/ (\overline{ \Delta u/ \delta })$, where $\Delta u = u_{max} - u_{min}$ and $u_{max}, u_{min}$, $\delta$ are maximum velocity, minimum velocity, and boundary-layer thickness respectively of the base flow at any instant. Visualization in the transverse plane reveals vortical structures appear at later times after vortex formation in stream-wise direction indicating three dimensional flow.