Spectral-rans Method: for Turbulent Shear Flows

Direct numerical simulation of turbulence is usually carried out using spectral-Chebyshev method. However, Chebyshev basis are not optimal in any sense, therefore, one has to use a certain number of modes to obtain reasonable results and this number of modes increases as Reynolds number increase. This would have never been an obstacle if there exist a set of functions that are ordered in turbulent kinetic energy sense, i.e, the lower mode contains most of the energy and so forth. The only available mathematical method to extract such an optimal basis is the POD method. However, POD method needs the two-point correlation of the entire flow field to be implemented. This book introduces a new method to extract such optimal basis from spectral equations that govern the flow field. Moreover, the book describes how this method can be used to model turbulence. This book will interest mechanical, chemical, aerospace, civil, and environmental engineers. Applied mathematicians and physicists who are interested in turbulence will find the book helpful as well.