Energy and Helicity Dissipation Rates of the Ns-alpha and Ns-alpha-deconvolution Models
نویسنده
چکیده
We consider the NS-alpha and the family of high accuracy, NS-alpha-deconvolution models of turbulence on Ω = [0, LΩ] 3 subject to periodic boundary conditions. For body force driven turbulence, we prove directly from the model equations of motion the following bounds on the time averaged modified energy dissipation rate, 〈εα,N(wα,N)〉, and unmodified helicity dissipation rate, 〈γ(wα,N)〉, for the Nth model (N = 0, 1, 2, . . . ) 〈εα,N(wα,N)〉 ≤ C1(1 + N) U3 N LN , and | 〈γ(wα,N)〉 | ≤ C2(1 + N) U3 N LN . Here, N is the degree of the approximate deconvolution operator, UN and LN are global velocity and length scales, and C1 and C2 are constants that don’t depend on UN .
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