Cospectral similarity of pressure terms in the budgets of TKE and horizontal heat flux in the atmospheric surface layer

During the 1994 Risoe Air Sea Experiment (RASEX), turbulence measurements, including pressure, were taken at three levels on an off-shore mast in the Baltic Sea. A previous analysis of the horizontal heat flux (uT) budget using this data set demonstrated that the pressure gradient-temperature covariance term Tdp/dx is the largest term in the budget, and closely balances the combined shear and stratification production terms phim and phih. Similarly, an analysis of the TKE budget found that the pressure transport term d(pw)/dz was a significant source term, and that in the RASEX data set the overall TKE budget, including pressure transport, was balanced to within approximately 10% accuracy.

In the present analysis we evaluate the cospectral characteristics of the Tdp/dx term from the horizontal heat flux budget, and the pw term from the TKE budget. In addition, we also examine the term udp/dx that is present in the budget of the streamwise velocity component of the TKE budget (u2). Monin-Obhukov scaling arguments are used to derive the wavenumber dependence of each of the three terms in the inertial subrange: k-7/3 for Tdp/dx; k-8/3 for pw; and k-5/3 for udp/dx. These predictions are then evaluated using the RASEX cospectra. Following the methodology of Kaimal et al., formulae are derived for the cospectral values at a fixed frequency value in the inertial subrange, and these are used to collapse the cospectra in the inertial subrange. The cospectrum of udp/dx is unusual in that it changes signs at nz/U ~ 0.1 under unstable stratification, with it being a loss term at higher frequencies (consistent with return to isotropy arguments) but a gain at lower frequencies.