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The background of this work is the problem of reducing the aerodynamicturbulent friction drag, which is an important source of energy waste ininnumerable technological fields. We develop a theoretical framework aimed atpredicting the behaviour of existing drag reduction techniques when used at thelarge values of Re which are typical of applications. We focus on one recentlyproposed and very promising technique, which consists in creating at the wallstreamwise-travelling waves of spanwise velocity. A perturbation analysis ofthe Navier-Stokes equations that govern the fluid motion is carried out, forthe simplest wall-bounded flow geometry, i.e. the plane channel flow. Thestreamwise base flow is perturbed by the spanwise time-varying base flowinduced by the travelling waves. An asymptotic expansion is then carried outwith respect to the velocity amplitude of the travelling wave. The analysis,although based on several assumptions, leads to predictions of drag reductionthat agree well with the measurements available in literature and mostlycomputed through DNS of the full Navier-Stokes equations. New DNS data areproduced on purpose in this work to validate our method further. The method isthen applied to predict the drag-reducing performance of thestreamwise-travelling waves at increasing Re, where comparison data are notavailable. The current belief, based on a Re-range of about one decade onlyabove the transitional value, that drag reduction obtained at low Re is deemedto decrease as Re is increased is fully confirmed by our results. From aquantitative standpoint, however, our outlook based on several decades ofincrease in Re is much less pessimistic than other existing estimates, andmotivates further, more accurate studies on the present subject.

A perturbative model for predicting the high-Reynolds-number behaviour of the streamwise travelling waves technique in turbulent drag reduction