A stochastic model of torque in von Karman swirling flow

Nicolas Leprovost (1) , Louis Marié (1) , Bérengère Dubrulle (1)

1 SPEC - UMR3680 - Service de physique de l'état condensé

A stochastic model is derived to predict the turbulent torque produced by a swirling flow. It is a simple Langevin process, with a colored noise. Using the unified colored noise approximation, we derive analytically the PDF of the fluctuations of injected power in two forcing regimes: constant angular velocity or constant applied torque. In the limit of small velocity fluctuations and vanishing inertia, we predict that the injected power fluctuates twice less in the case of constant torque than in the case of constant angular velocity forcing. The model is further tested against experimental data in a von Karman device filled with water. It is shown to allow for a parameter-free prediction of the PDF of power fluctuations in the case where the forcing is made at constant torque. A physical interpretation of our model is finally given, using a quasi-linear model of turbulence.

Mots clés: convection and heat transfer; Turbulence modeling; Turbulent flows

Domaines: Dynamique des Fluides [physics.flu-dyn]; Autre [cond-mat.other]

Nicolas Leprovost, Louis Marié, Bérengère Dubrulle. A stochastic model of torque in von Karman swirling flow. The European Physical Journal B: Condensed Matter and Complex Systems, 2004, 39, pp.121-129. ⟨10.1140/epjb/e2004-00177-x⟩. ⟨hal-00004132⟩