Experimental assessment of Taylor’s hypothesis and its applicability to dissipation estimates in turbulent flows

Abstract

Results are presented from an assessment of the applicability of Taylor’s hypothesis for approximating streamwise derivatives and obtaining dissipation estimates in turbulent flows. These are based on fully resolved measurements of a conserved scalar field ζ(x,t) throughout a four-dimensional spatio-temporal volume in a turbulent flow. The data allow simultaneous evaluation of all three components of the true gradient vector field ∇ζ(x,t) and the time derivative field (∂/∂t)ζ(x,t) at the small scales of a turbulent shear flow. Streamwise derivatives obtained from Taylor’s frozen flow hypothesis yield a correlation of 0.74 with the true streamwise derivative field at the present measurement location in the self-similar far field of an axisymmetric turbulent jet. Direct assessments are also presented of approximations invoking Taylor’s hypothesis to estimate energy dissipation rates in turbulent flows. The classical single-point time series approximation yields a correlation of 0.56 with the true scalar energy dissipation rate, while a mixed estimate that combines one spatial derivative and the time derivative gives a correlation of 0.72. A general analytical formulation is presented for assessing various dissipation estimates, and for determining the optimal dissipation estimate that maximizes the correlation with the true dissipation rate. The resulting optimal mixed dissipation estimate yields a correlation of 0.82 at the point of maximum turbulence intensity in a jet, and a value of 0.92 on the jet centerline.