Homogeneous, isotropic turbulence and its collapse in stratified and rotating fluids

Autor: Robert R. Long
Rok vydání: 1998
Předmět:
Zdroj: Dynamics of Atmospheres and Oceans. 27:471-483
ISSN: 0377-0265
DOI: 10.1016/s0377-0265(97)00025-0
Popis: We derive properties of turbulence in a homogeneous, incompressible, Newtonian fluid. The discussion features au invariant N (characteristic circulation in material circuits containing vorticity but imbedded in nearly irrotational masses of fluid). The key to closure is to see that the turbulence is immature for a while after creation of the vorticity in that friction, important in the creation of the vorticity, is subsequently unimportant for a period τ such that N τ d 2 = γ o R 1 4 (d is an initial length, R = N ν and γo is a constant). After t = τ, any statistical property can be expressed to within certain undetermined constants by a known function of N, t and R. Thus u 2 = A u ( N t )R case1 4 , where t is time, u is r.m.s. (root-mean-square) velocity and Au is a constant. The theory predicts that the dissipation is weakly R-dependent as R −1 4 a behavior conjectured long ago by Saffman as both theoretically possible and not inconsistent with the data. The theory may be applied to find the collapse time Ts when rotation and stratification are present but at lesser times are unimportant. We find γT s = βR 2 5 where β is a constant and γ is the Brunt-Vaisala frequency.
Databáze: OpenAIRE