Inspired by P. Luchini \& F. Charru's\footnote{Luchini, P., Charru, F., The phase lead of shear stress in shallow-water flow over a perturbed bottom, \textit{J. Fluid Mech.} \textbf{665}, 516-539 (2010)} analysis of the phase lead of the wall-shear stress at a channel's perturbed bottom, we identified a benchmark problem simple enough that it can be solved both by an eddy-viscosity model, similar to those typically used in shallow-water flow calculations, and by direct numerical simulation. This is the linear response of a turbulent flow's mean-velocity profile to an external volume force. Such a force, of unspecified origin in the present context, was found in $^1$ to be representative of the perturbation induced by bottom topography, and its consequences were analysed by means of an eddy-viscosity model. On the other hand, a modification of Luchini, Quadrio \& Zuccher's\footnote{Luchini, P., Quadrio, M., Zuccher, S., The phase-locked mean impulse response of a turbulent channel flow, \textit{Phys. Fluids} \textbf{18}, 121702 (2006).} method to compute the linear impulse response of a wall­-bounded turbulent flow allows the response to a volume force to be computed directly. The comparison exhibits significant differences and suggests that there might be fundamental obstacles to designing an eddy-viscosity model that provides the correct result.

### A comparison between eddy-viscosity models and direct numerical simulation: the response of turbulent flow to a volume force

#### Abstract

Inspired by P. Luchini \& F. Charru's\footnote{Luchini, P., Charru, F., The phase lead of shear stress in shallow-water flow over a perturbed bottom, \textit{J. Fluid Mech.} \textbf{665}, 516-539 (2010)} analysis of the phase lead of the wall-shear stress at a channel's perturbed bottom, we identified a benchmark problem simple enough that it can be solved both by an eddy-viscosity model, similar to those typically used in shallow-water flow calculations, and by direct numerical simulation. This is the linear response of a turbulent flow's mean-velocity profile to an external volume force. Such a force, of unspecified origin in the present context, was found in $^1$ to be representative of the perturbation induced by bottom topography, and its consequences were analysed by means of an eddy-viscosity model. On the other hand, a modification of Luchini, Quadrio \& Zuccher's\footnote{Luchini, P., Quadrio, M., Zuccher, S., The phase-locked mean impulse response of a turbulent channel flow, \textit{Phys. Fluids} \textbf{18}, 121702 (2006).} method to compute the linear impulse response of a wall­-bounded turbulent flow allows the response to a volume force to be computed directly. The comparison exhibits significant differences and suggests that there might be fundamental obstacles to designing an eddy-viscosity model that provides the correct result.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11386/4027927
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