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• W3016875885 abstract "We consider three-dimensional stochastically forced Navier-Stokes equations subjected to white-in-time (colored-in-space) forcing in the absence of boundaries. Upper and lower bounds of the mean value of the time-averaged energy dissipation rate, $mathbb{E} [langlevarepsilon rangle] $, are derived directly from the equations. First, we show that for a weak (martingale) solution to the stochastically forced Navier-Stokes equations, [ mathbb{E} [langlevarepsilon rangle] leq G^2 + (2+ frac{1}{Re})frac{U^3}{L},] where $G^2$ is the total energy rate supplied by the random force, $U$ is the root-mean-square velocity, $L$ is the longest length scale in the applied forcing function, and $Re$ is the Reynolds number. Under an additional assumption of energy equality, we also derive a lower bound if the energy rate given by the random force dominates the deterministic behavior of the flow in the sense that $G^2 > 2 F U$, where $F$ is the amplitude of the deterministic force. We obtain, [frac{1}{3} G^2 - frac{1}{3} (2+ frac{1}{Re})frac{U^3}{L} leq mathbb{E} [langlevarepsilon rangle] leq G^2 + (2+ frac{1}{Re})frac{U^3}{L},.] In particular, under such assumptions, we obtain the zeroth law of turbulence in the absence of the deterministic force as, [mathbb{E} [langlevarepsilon rangle] = frac{1}{2} G^2.] Besides, we also obtain variance estimates of the dissipation rate for the model." @default.
• W3016875885 created "2020-04-24" @default.
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• W3016875885 date "2020-04-18" @default.
• W3016875885 modified "2023-09-27" @default.
• W3016875885 title "On the zeroth law of turbulence for the stochastically forced Navier-Stokes equations" @default.
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