We identify a benchmark problem simple enough that it can be solved both by an eddy-viscosity model and by direct numerical simulation: this is the linear response of a turbulent flow's mean-velocity profile to an external volume force. An example of such a force was found in a study of the perturbation induced by bottom topography by Luchini & Charru (J. ) 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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