Pressure-strain correlations in curved wall boundary layers
Pressure-strain correlations represent a redistribution of turbulence energy in shear flows and, therefore, are often included in modeling as some part of production and dissipation of Reynolds stress. It is then of interest to establish what portion of the energy spectrum contributes to pressure-stra in correlations. Considering wall- bounded flows, the correlations have been determined, utilizing the large-eddy interaction model (LEIM), for the cases of boundary-layer flows past convex, concave, and flat walls, the latter also in a case where the flat wall follows a convex wall. The LEIM also provides a means of determining the contribution from different parts of turbulence spectra to the correlations in different regions across the boundary layer. RESSURE-STRAIN correlations present a problem in closure of describing equations for turbulent flows. Several models have been suggested in the literature.1"7 Measurement is not entirely trustworthy in the body of flows. Corrsin and Kollman8 had made an important and successful attempt at evolving a method of obtaining pressure-strain correlations by computational experimenta- tion and demonstrated the applicability of the method in the case of uniform shear flow. In a discussion of Ref. 8, Brad- shaw raised an interesting question concerning pressure- strain correlations, namely, what portion of the energy spec- trum contributes to the pressure-strain correlations that is represented in modeling as some part of production and dissipation of Reynolds stresses. The large-eddy interaction model (LEIM)9 n provides a framework for the determination of the contribution by a wavenumber range of spectra to various turbulence-related quantities including the pressure-strain correlations. Within that framework the pressure-strain correlations are expressed in terms of large-eddy spectra that are obtained by solving dynamical equations for large eddies. The equations describe interactions of large eddies with mean flow and all of the ed- dies in the mixed (x,k) space where x space corresponds to coordinate(s) containing inhomogeneity of turbulence and k is the wavenumber space. The LEIM thus not only permits a determination of the contribution of different parts of the turbulence spectrum to any chosen turbulence process parameter, but also provides a means of testing the validity of any model that may be developed for the parameter under consideration. When an incompressibl e, wall boundary layer is subjected to an additional strain such as curvature, there arises a special opportunity (based also on practical needs) for establishing and explaining the changes in the relative con- tribution of different parts of the spectrum to pressure-strain correlations compared to the flat-plate case and for deter- mining the applicability and implications of current models. Thus, it can be shown that for different types of curvatures