London SW7 2BZ, United Kingdom
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    Dipartimento di Ingegneria Aerospaziale, Politecnico di Milano,\
    via La Masa, 34 - 20156 Milano, Italy
author:
- Pierre Ricco
- Maurizio Quadrio
title: 'Wall-oscillation conditions for drag reduction in turbulent channel flow'
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Turbulent channel flow ,turbulent drag reduction ,spanwise wall oscillation ,direct numerical simulation

Introduction
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This paper presents a numerical investigation of a turbulent channel flow with sinusoidal spanwise oscillations of the walls. The flow over the oscillating walls results from the combination of two simpler flows, i.e. a canonical turbulent channel flow in the streamwise direction and an oscillating boundary-layer-type flow in the transversal (spanwise) direction. The most relevant characteristic of this modified turbulent flow is the time-sustained reduction of the streamwise wall-shear stress, first pointed out by @jung-mangiavacchi-akhavan-1992. The drag reduction effect is caused by the weakening of the relevant turbulence-producing events in the vicinity of the wall [@akhavan-etal-1993; @dhanak-si-1999; @choi-clayton-2001; @dicicca-etal-2002; @iuso-etal-2003; @ricco-2004; @xu-huang-2005; @zhou-ball-2006], but the precise details are still poorly understood. It has also been established [@baron-quadrio-1996; @quadrio-ricco-2004b] that a net energetic saving of the order of 10% (determined by taking into account the power spent to move the walls against the viscous resistance of 