Elliptic approximation of the space-time temperature correlation function thaws turbulence with random sweeps

Abstract:

The space-time correlation function encodes basic properties of turbulent flows at variable spatial locations and variable time instants. Its quantification has been the subject of active research for more than 7 decades now, with no signs of abatement today. In the case of velocity fluctuations, celerity has been computed and linked to partial derivatives of the correlation contours with respect to both space- and time-lags. The variation of the computed celerity with respect to mean velocity has been documented as a function of distance from the wall and turbulence intensity, forming the basis of Taylor's frozen eddy hypothesis (FEH). FEH is routinely used in laboratory and field studies to estimate the spatial scales of turbulence. Theoretical and simulation studies suggest that FEH may be applicable for flows that are stationary, locally homogeneous, and of low turbulence intensity. The requirements for application of FEH can be unnecessarily restrictive, particularly for real-world atmospheric flows that are complicated by the presence of complex terrain, vegetation, and non-neutral conditions. For this reason, there are a number of approximation methods available for the extension of FEH to non-ideal conditions. Attention has, however, been disproportionately focused on velocity, leaving the extension of approximation methods to active and passive scalars a subject of inquiry. These knowledge gaps motivate the work here.

A space-time array of thermocouple measurements over a sloped vineyard are used to explore the space-time correlation function of temperature. A recently proposed ellipse approximation (EA) method is employed to analyze the data. The relations between (i) the convection velocity and mean flow velocity, and (ii) the sweeping velocity and turbulence intensity, are presented at differing heights, atmospheric stability conditions, and turbulent intensities for the first time in the roughness sublayer. This work is not only the first to apply the EA approach to measurements in the roughness sublayer of vegetated canopies at very high Reynolds numbers, it also provides a unique perspective into the scalar space-time correlation within and above plant canopies covering complex terrain.