Turbulent fluxes and entropy production rate

The entropy production rate is calculated for an interchange driven turbulence both in fluid and kinetic regimes. This calculation provides a rigorous way to define thermodynamical forces and fluxes. It is found that the forces are the gradients of density and temperature normalized to their “canonical” values, which are Lagrangian invariants of the flow. This formulation is equivalent to expressing the fluxes in terms of “curvature pinches,” where the curvature pinches are proportional to the logarithmic gradient of canonical profiles. Off diagonal terms in the transport matrix are found, which correspond to thermodiffusion and its Onsager symmetrical contribution to the heat flux. Hence, if thermodiffusion is significant, a heat pinch due to the density gradient also exists. The entropy production rate is found to be minimum when the profiles are equal to their canonical values. This property yields a generalized form of profile stiffness. However, a state where all profiles match their canonical values is not attainable because it is linearly stable.