Spectral Transfer of Velocity-Salinity Correlation for Inhomogeneous Turbulence for Marine Atmospheric Boundary Layer

The Monin-Obukhov similarity theory is one of the most powerful tools in describing the physical 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 (Nieuwstad 1984). Similarity relationship 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 field experiments have been performed in carefully chosen homogeneous conditions. But in fact marine atmospheric boundary layers occur in inhomogeneous surfaces. So, it is important to study the various aspects of the turbulent characteristics in marine atmospheric boundary layers. In this study a correlation equation between velocity and salinity fluctuations 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 (Deissler1961). 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 turbulence 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 salinity 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.