Laminar streak growth above a spanwise oscillating wall

Abstract

Accepted for publication in Journal of Fluid MechanicsThe use of spanwise wall oscillations to attenuate the growth of laminar streaks within the incompressible Blasius boundary layer is investigated. As in the case of the flow above a stationary flat plate, studied by Leib et al. (J. Fluid Mech. vol. 380, 1999, p. 169), free-stream convected gusts interact with the boundary layer to drive the streak growth. Spanwise wall oscillations can either reduce or increase the total energy of the laminar streaks, depending upon the wall oscillation amplitude and frequency, as well as the free-stream gust properties. Reductions in streak energies of up to 90% are obtained, indicating that spanwise wall oscillations are an effective technique for attenuating the laminar streak growth. Therefore they may suppress secondary boundary-layer instabilities and delay transition.The laminar boundary-layer base flow matches the Blasius profile in the streamwise and wall-normal directions, while in the spanwise direction a generalized version of the classical Stokes layer profile (generated by a wall oscillating beneath a quiescent fluid) occurs, which evolves downstream due to non-parallel flow effects. Via a Wentzel-KramersBrillouin-Jeffreys (WKBJ) analysis this generalized Stokes layer is shown to approach the classical Stokes layer in the limit of large downstream distances or high-frequency plate oscillations. The laminar streaks forced by the generalized and the classical Stokes flows differ significantly, which implies that the choice of the spanwise base flow may affect the secondary instability and transition in this flow. The analysis also proves that the use of the classical Stokes layer as spanwise base flow, as employed by Hack & Zaki (Phys. Fluids. vol 24. 2012), is inappropriate.

A review of turbulent skin-friction drag reduction by near-wall transverse forcing

“…Open transitional boundary layers subjected to free-stream vortical disturbances have also been stabilized by steady and time-periodic spanwise wall oscillations [Ricco, 2011, Hack and Zaki, 2012, Hicks and Ricco, 2015a,b, Hack and Zaki, 2015. The simulations by Hack and Zaki [2014] with uniform spanwise oscillations, Negi et al [2015] with steady sinusoidal spanwise-velocity waves, Negi et al [2019] with both temporal and spatial oscillations demonstrated a delayed onset of transition and a lengthened transition region.…”

Wall Oscillation Induced Drag Reduction Zone in a Turbulent Boundary Layer

“…Hence, when comparing simulation data and theory, the spatial transient may be neglected. In addition, note that the exact laminar solution would need to take the non-parallel effect into account, which was done by Hicks & Ricco [14] who studied the oscillating wall beneath the Blasius boundary layer. Hence, the exact solution in the present case would be a combination of the solutions provided by Zeng & Weinbaum and Hicks & Ricco.…”

Exact coherent states in plane Couette flow under spanwise wall oscillation

“…In particular, their linear analysis revealed that there is a short time interval in the oscillation period during which the optimal perturbation resulting in the streaks with a certain angle grows strongly, and this angle remains dominant for almost half of the entire wall oscillation period, consistent with the observation from DNS. In a similar context, Hicks & Ricco (2015) examined the evolution of streaks driven by a free-stream noise in a laminar boundary layer. They found that the energy of laminar streaks can be reduced by due to the spanwise wall oscillation.…”