Further Generalization of Onsager's Cascade Model for Turbulent Spectra

Onsager's conservative cascade model used to deduce the turbulent energy spectrum in the isotropic ``inertial range,'' is generalized in three different ways, with examples taken from the turbulent mixing problem. (a) Extension to a nonconservative cascade, mixing with a first-order isothermal chemical reaction, is presented more compactly than an earlier treatment and is applied to a new case. (b) Application to mixing at wavenumbers in the viscous range is indicated briefly. (c) Extension is made to a dual cascade, a model for turbulent mixing with a second-order isothermal reaction. The nonlinearity of the reaction causes spectral transfer.