Spectral Transfer of Velocity—Temperature Correlation for Inhomogeneous Turbulence for Atmosphere-Land Interaction

The Monin-Obukhov theory is one of the most powerful tools in describing the phyical properties of the atmospheric boundary layer and now it is applied not only to the surface layer but also to the well mixed layers (Deardorff 1970), free convection layers (Wyngaard et al., 1971) and stable layers (Nieuwstadt 1984). Similarity relationships apply not only to the mean profiles of the meteorological parameters, but also to the statistical quantities and spectral behaviour of turbulence (Kaimal et al., 1972). There are several studies of similarity principle for horizontal homogeneous boundary layers but very few for horizontally inhomogeneous surfaces because of their obvious difficulties.To avoid these problems most fields experiments have been performed in carefully chosen homogeneous conditions. But in fact the atmosphere-land interactions occur in inhomogeneous surfaces. So, it is important to study the various aspects of the turbulent characteristics of atmmosphere-land interactions. In this study a correlation equation between velocity and temperature is constructed and it is shown that even for a general inhomogeneous turbulence certain terms can be interpreted as a transfer term. In fact, several terms in the two-point spectral equation for homogeneous turbulence can be interpreted as spectral transfer terms. That is, they represent the net rate of energy transfer into a wavenumber region from all other wavenumbers. This is true for terms associated with both turbulence self-interaction (Batchelor 1953) and interaction between turbulence and mean gradients (Deissler 1961). However, it does not seem obvious that similar interpretation apply when the turbulence is not homogeneous. In particular one might question the interpretation for the terms associated with turbulent self interaction, since the condition of homogeneity is generally used in making the interpretation (Batchelor 1953). So, in this study a two-point correlation equation for velocity and temperature is constructed and using the method of Deissler (1981), it is shown that even for a general inhomogeneous turbulence certain terms in the two-point correlation spectrum equation can be interpreted as a transfer term.