Spectral Transfer of Concentration Correlation with Photochemical Reaction for Inhomogeneous Turbulence in Planetary Boundary Layer

Very recently, in the air pollution modeling, the usual practice of neglecting the concentration correlation in the atmospheric photochemical reaction has been recognized as a source of serious error and it is shown that in the case of pure mixing (without chemical reaction) the concentration of air pollution decays in a natural manner but if the concentration selected is the chemical reactant of the first order, then the effect is that the decomposition of the concentration fluctuation is much more rapid (Kumar and Patel 1974, 1975; Patel 1974,1976, 1983, 1984, 1992,1998). Also, the study of formation and destruction of photochemical smog is increasing at both small and large scale (Wanner et al., 1993). So, it is important to study the various aspects of the concentration fluctuation with photochemical reaction. In this study a correlation equation between velocity and concentration (with chemical reaction) fluctuation is constructed and it is shown that even for a general inhomogeneous turbulence with chemical reaction, certain terms in the two-point correlation spectrum equation can be interpreted as a transfer term. In fact, several terms in the two point correlation 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 interpretion apply when the turbulence is not homogeneous. In particular one might question the interpretation for the terms associated with turbulence self interation, since the condition of homogeneity is usually used in making the interpretation (Batchelor 1953). So, in this study a two point correlation equation for concentration of air pollution with photochemical reaction is constructed and using the method of Deissler (1981), it is shown that even for a general inhomogeneous turbulence with photochemical reaction, certain terms in the two-point correlation spectrum equation can be interpreted as a transfer term.