Solution of Howells’ model of the scalar spectrum and comparison with experiment

Abstract

Howells’ model of the scalar spectrum for isotropic turbulent flow is simplified using a restriction to large Péclet number and statistically stationary turbulence at high wavenumbers, and is generalized by introducing Batchelor's constant as a free parameter. The resulting model is compared with data from the atmospheric surface layer, ocean, and liquid mercury. It is found that Howells’ model, which is applicable for arbitrary Prandtl number (Pr), does not compare well with data for large and intermediate Pr at wavenumbers higher than those in the inertial-convective range. The model implies that the inertial-diffusive range asymptotic form, , cannot appear even for Pr as small as that of mercury (Pr = 0·018).