Estimation of mean turbulent kinetic energy and temperature variance dissipation rates using a spectral chart method

A method aimed at estimating ek and eθ, respectively, the mean dissipation rates of turbulent kinetic energy k and half the temperature variance θ2/2, is developed for slightly heated turbulent flows of air. It is limited to a Prandtl number near unity and applicable to flows where temperature can be treated as a passive scalar. A significant advantage of the method is that ek and eθ can both be estimated from the measurement of a temperature frequency spectrum, Gθθ(f). The method relies on the collapse in the dissipative range of one-dimensional temperature spectra, ϕθ(k1η), when normalized with eθ, ek, and ν. This collapse ensues from a similarity analysis of scale-by-scale budgets of the second-order structure function for the temperature. A generic spectrum ϕθG(k1η), defined in the wavenumber range 0.07 ≤ k1η ≤ 0.7, is used to construct a spectral chart. The method has been tested in several flows and found to be reliable. In particular, it is tested on the axis of a slightly heated round jet, where e...