Evaluation of a Turbulence Pressure Instrument using the budget of horizontal heat flux

Direct measurements of each of the terms in the budget of the streamwise horizontal heat flux, including pressure-gradient interaction, were measured during the Risoe Air-Sea Experiment (RASEX). The measurements were taken at an off-shore tower, at three heights. The horizontal heat flux budget is of interest because the shear and buoyant production terms in this budget are just Phi-m and Phi-h (the familiar non-dimensional shear and buoyant production terms also present in the TKE budget). Also present is a third-order moment representing turbulent transport, and a term due to a pressure-gradient and temperature correlation (Tdp/dx). The turbulent transport term is found to be small (but not entirely negligible). This means that the pressure-gradient interaction term must be a large sink to essentially balance the net production due to Phi-m and Phi-h. This provides a rigorous test for any instrument that claims to be able to measure turbulent pressure fluctuations. We find that for the RASEX data set the pressure-gradient interaction term Tdp/dx balances the sum of the shear and stratification production terms and turbulent transport to within approximately 10%. The closure of the budget to this degree also places limits on the uncertainties in the formulations of Phi-m and Phi-h.

In addition, the stability dependence of the Tdp/dx co-spectrum is presented in the non-dimensional form suggested by Monin-Obhukov similarity theory. Finally, the sign of Tdp/dx in stable and unstable conditions is related to coherent ramp structures in the turbulent flow. Because of the relative simplicity of measuring the pressure-gradient interaction term in the streamwise horizontal heat flux budget (only a single sonic anemometer and pressure sensor are needed), and because the shear and stratification production terms as functions of stability are now well known, we propose that this budget be used as a benchmark for assessing the quality of pressure measurements in future surface layer field experiments.