Theory of turbulence

Chandrasekhar , S. (1956) Theory of turbulence Physical Review, 102 (4). pp. 941-952. ISSN 0031-899X

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It is pointed out if there are aspects of the turbulence phenomenon which are truly universal, then they should be capable of being characterized in terms of the two parameters ε and ν which denote the constant rate of dissipation of energy per unit mass and the kinemetic viscosity respectively and these two parameters only without reference either to the mean square velocity <μ12>Av or to the size of the largest energy containing eddies. This is a slight modification of Kolmogoroff's similarity principles as currently formulated. It appears that χ=∂ψ(r, t)/∂r, where ψ(r, t)=½<(μ1'-μ1'')2Av, and μ1' and μ1'' are the velocities in the x-direction (say) at two points on the x-axis separated by a distance r and at times an interval t apart, can be so specified. The similarity principles require that if this is the case, χ should be of the form χ≡(ε3/ν)¼X(r(ε/ν3)¼, t(ε/ν)½), where X is a universal function of the arguments specified. In the limit of zero viscosity, χ must have the more special form χ→ Γσ(t/r) (ν→0). The boundary conditions on σ(x) are that σ=σ0(>0) and dσ/dx=0 at x=0 and σ→0 as x→∞. It is shown that with a slight modification of the premises of the theory described in an earlier paper, an equation for χ can be derived which is compatible with the requirements of the similarity principles as formulated. In particular the ordinary differential equation for σ to which the theory leads can be solved. The solution for σ which is found satisfies all the boundary conditions of the problem and is unique, apart from adjustable scale factors. The predicted evolutions of χ and the vorticity correlations are illustrated.

Item Type:Article
Source:Copyright of this article belongs to The American Physical Society.
ID Code:70313
Deposited On:16 Nov 2011 04:09
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