Canuto and Dubovikov 1997

Canuto, V.M., and M.S. Dubovikov, 1997: A dynamical model for turbulence. V. The effect of rotation. Phy. Fluids, 9, 2132-2140, doi:10.1063/1.869332.

We study turbulence undergoing rapid rotation. We show that there exist two different regimes divided by the new number N = K/νΩ. N < 1: rotation is so strong that it suppresses the energy cascade process and no inertial regime can develop. In the freely decaying case, only viscosity operates; an initailly isotropic three-dimensional (3-D) turbulence remains so and never tends toward a 2-D state. N > 1: the energy cascade, though inhibited, allows an inertial regime in which 3-D and a quasi 2-D state exist in equilibrium. The latter is restricted to a narrow band of values δk_z ~ k_Ω^-1K², where k_Ω = (Ω³/ε)^1/2. For k > k_Ω, the Kolmogorov spectrum sets in, while k < k_Ω, the spectrum exhibits a new form, E(k) ~ (εΩ)^1/2/k². A freely decaying turbulence within a time scale τ_Ω ~ (Ω/ε)^1/2L tends to a 2-D—3-D regime: K ~ t^-n while horizontal length scales grow as t^m, where (m,n) are half the values of the Ω = 0 case. As for the vertical length scales, one grows as the horizontal scales, while the other grows much faster, deomonstrating the existence of the 2-D mode. The nonlinear interactions, though weakened, are the main cause of two-dimensionalization, which, however, is not of the Proudman-Taylor type since the latter requires negligible nonlinearities. We also derive the dynamic equation for the dissipation rate ε. All the results are shown to be in agreement with numerical simulation and experimental data.

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Canuto, V.M., and Dubovikov, M.S.: A dynamical model for turbulence. V. The effect of rotation, Phy. Fluids, 9, 2132-2140, doi:10.1063/1.869332, 1997.

Canuto, V.M., and M.S. Dubovikov (1997), A dynamical model for turbulence. V. The effect of rotation, Phy. Fluids, 9, 2132-2140, doi:10.1063/1.869332.

Canuto, V.M., and M.S. Dubovikov, 1997: A dynamical model for turbulence. V. The effect of rotation. Phy. Fluids, 9, 2132-2140, doi:10.1063/1.869332.

Canuto, V.M., & Dubovikov, M.S. 1997, Phy. Fluids, 9, 2132, doi:10.1063/1.869332.

Canuto VM, Dubovikov MS. A dynamical model for turbulence. V. The effect of rotation, Phy Fluids 1997;9:2132-2140. doi:10.1063/1.869332.

V.M. Canuto, M.S. Dubovikov, Phy. Fluids 9, 2132-2140, doi:10.1063/1.869332 (1997).