Structure of the Dissipation Range in Homogeneous Turbulence

The structure of dissipation range in homogeneous turbulence is examined by the use of two fundamental equations for the velocity covariance and the response which are derived from the Direct-Interaction formalism. The entrance wavenumber k_D denoting the smallest wavenumber of the dissipation range is taken as a multiple of the usual dissipation wavenumber k_d({=}({\varepsilon}/ν³)^1/4, \varepsilon is the energy dissipation and ν the kinematic viscosity). The form of velocity spectrum is assumed in an appropirate manner, under the constraint that it takes the so-called inertial-range form and vanishes, respectively, as k/k_d tends to zero and infinity (k is the wavenumber). The entrance wavenumber k_D and the velocity spectrum as well as the response time are determined so that they should give the correct estimate of the energy dissipation and be consistent with the two fundamental equations. It is also shown that the results obtained do not depend critically on the choice of spectral form.