Apparent counter-gradient heat fluxes generated by atmospheric waves

In studies of turbulence, tower data are used to measure vertical fluxes of momentum and heat generated by correlations in the fluctuating fields. Similar time averages of wu and w may be computed for an interval of wave activity observed at an instrumented tower. However, it is shown that such measurements do not necessarily correspond to the conventional Reynold's stresses or vertical heat fluxes. And waves can appear to have non-zero and even countergradient fluxes when proper averages show no fluxes at all.These spurious fluxes are generated by the method of analysis, a Fourier series performed on a finite time interval. Any background disturbance that is not strictly confined to the interval will generate a spurious wave spectrum. In particular, long-period waves will generate terms that interfere with the true high frequency waves to give false wave fluxes. The theoretical findings of this paper provide a ready explanation of tower data that would otherwise appear to conflict with conventional wave theory.