Using a nonlinear projection operator technique, the Markovian stochastic dynamics of a classical Brownian particle is derived in the case that the effective temperature is not constant. After recapitulating the general formalism and its application to isothermal Brownian motion, an isolated...

The leading anomalous Kolmogorov scaling exponent μθ in the inertial range of temperature spectra is calculated on the basis of a recent theory involving a 4D spectral analysis of fully developed Navier–Stokes–Boussinesq turbulence.

Using a self-consistent 4D spectral analysis of fully developed Navier–Stokes–Boussinesq turbulence (involving the dynamical response on small scale isotropic configurations) leads to a manyfold ℘(k) for the second-order scaling exponent. Plots of both energy and Reynolds stress spectra...