A diagnostic scale-interaction study employing a horizontal filtering technique

The present paper is a continuation of the paper by Holopainen and Nurmi (1979), in which an example of a scale-interaction study employing a horizontal filtering technique was reported. Here we apply the same technique to large material (upper wind observations at 300 mb from the British Isles in 1961–65) to investigate some statistical properties of the horizontal “sub-grid” (L < L_f ~ 400 km) force A^H. To illustrate the effect qualitatively the technique is also applied to some schematic flow patterns.

The results show that A^H cannot be parametrized in terms of the smoothed flow with expressions (Fickian scheme, Smagorinsky’s (1963) scheme, Leith’s (1969) scheme) commonly used in the numerical models for the lateral frictional force.

The mean effect of A^H on the kinetic energy of the smoothed flow (“lateral dissipation”) turns out to be practically zero, whereas all the three parametrization schemes indicate an energy cascade from resolved to unresolved scales. The correlation between the 3464 instantaneous values of observed and parametrized “dissipation” is almost zero.