Abstract
The analytical theory of a turbulent scalar, developed in previous papers [Phys. Fluids 28 (1985) 1299; J. Fluid Mech. 217 (1990) 203], is extended to the case of large Prandtl number. The fluctuation character of the least principal rate of strain γ has an important effect upon the scalar spectrum. The scalar variance spectrum in the viscous range is F(k) = 4.472 ( ν ε ) 1 2 χk −1 H(x) , x ≡ ( k k b ) 2 ; H( x) is a dimensionless universal function and is determined by solving numerically the closed spectral dynamical equations. A simple fitting formula of the numerical result is H( x) = 0.7687 exp(−3.79 x) + 0.2313 exp(−11.13 x), which corresponds a two-values fluctuation model of γ. Here ν is the kinematic viscosity, k b ≡ ( ε νμ 2 ) 1 4 is the Batchelor wavenumber, μ is the scalar diffusivity, and ε and ≡ are respectively the energy and variance dissipation rates.
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