Effect of condensation and evaporation on the viscous-convective subrange

Abstract

The effect of condensation and evaporation on the viscous-convective subrange is investigated using a general mean-field approximation that is consistent with the nonhomogeneous vertical structure of the condensate’s first and second moments and experimental observations of mean vertical flux in a condensation cloud. Expressions for the scalar density in the Batchelor limit are derived and used to reproduce the spectral behavior of new atmospheric measurements that exhibit anomalous scaling of cloud liquid water in the near inertial-convective regime. Good agreement between the model and data are obtained when axisymmetric Kraichnan transfer of scalar variance is balanced by axisymmetric production by condensation/evaporation resulting in an isotropic contribution to the real (homogeneous) part of the spectrum. The model also assumes a significant imaginary (nonhomogeneous) component to the spectrum that is indicative of a strong vertical coherence in condensation clouds. A “production subrange” is predicted in which the scalar dissipation rate increases with increasing wave number and the usual −1 viscous-convective scaling evolves into an anomalous −3 regime. The strongly nonhomogeneous (anisotropic) character of the predicted scalar spectrum is in stark contrast with atmospheric models of inertial-convective regime cloud inhomogeneity that are used in radiative transfer calculations and are typically isotropic.