Forcing-dependent stability of steady states in a turbulent swirling
  flow

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Abstract

We study the influence of the forcing on the steady turbulent states of a von K\'arm\'an swirling flow, at constant impeller speed, or at constant torque. We find that the different forcing conditions change the nature of the stability of the steady states and reveal dynamical regimes that bear similarities with low-dimensional systems. We suggest that this forcing dependence may be an out- of-equilibrium analogue of the ensemble inequivalence, valid for long-range interacting statistical systems, and that it may be applicable to other turbulent systems.

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Is Open Access

A turbulent model of torque in von Karman swirling flow

Nicolas Leprovost, Louis Marié, Bérengère Dubrulle (2007)

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.