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Session: Lagrangian aspects of turbulence 4

Session starts: Friday 28 August, 10:30

Presentation starts: 12:15

Room: Room F

*Mahendra K. Verma (Department of Physics, Indian Institute of Technology Kanpur, Kanpur, 208016, India)*

Abhishek Kumar (Department of Physics, Indian Institute of Technology Kanpur, Kanpur, 208016, India)

Abstract:

We perform renormalization group analysis (RG) of the Navier-Stokes equation in the presence of constant mean velocity field $\mathbf U_0$, and show that the renormalized viscosity is unaffected by $\mathbf U_0$, thus negating the ``sweeping effect", proposed by Kraichnan [Phys. Fluids {\bf 7}, 1723 (1964)] using random Galilean invariance. Using direct numerical simulation, we show that the correlation functions $\langle {\mathbf u} ({\mathbf k}, t){\mathbf u}({\mathbf k}, t+\tau) \rangle$ for $\mathbf U_0 =0$ and $\mathbf U_0 \ne 0$ differ from each other, but the renormalized viscosity for the two cases are the same. Our numerical results are consistent with the RG calculations.

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*Mahendra K. Verma, Abhishek Kumar*

12:15

15 mins

Sweeping has no effect on renormalized turbulent viscosity
15 mins

Session starts: Friday 28 August, 10:30

Presentation starts: 12:15

Room: Room F

Abhishek Kumar (Department of Physics, Indian Institute of Technology Kanpur, Kanpur, 208016, India)

Abstract:

We perform renormalization group analysis (RG) of the Navier-Stokes equation in the presence of constant mean velocity field $\mathbf U_0$, and show that the renormalized viscosity is unaffected by $\mathbf U_0$, thus negating the ``sweeping effect", proposed by Kraichnan [Phys. Fluids {\bf 7}, 1723 (1964)] using random Galilean invariance. Using direct numerical simulation, we show that the correlation functions $\langle {\mathbf u} ({\mathbf k}, t){\mathbf u}({\mathbf k}, t+\tau) \rangle$ for $\mathbf U_0 =0$ and $\mathbf U_0 \ne 0$ differ from each other, but the renormalized viscosity for the two cases are the same. Our numerical results are consistent with the RG calculations.