Flow Domains and Bases

The flow domain for homogeneous turbulence domain and its approximations are summarized. The turbulent flow through straight, circular pipes is one of the central examples discussed throughout the book. Compact and non-compact domains are considered and the construction of a solenoidal Schauder basis for scalar and vector fields is developed in detail for the case of flow periodic in the direction of the pipe axis. The Schauder bases are constructed with the aid of Fourier and modified Jacobi polynomials. The Gram-Schmidt orthogonalization is introduced to construct an ONS basis. Non-compact flow domains are discussed in terms of analytic mappings for boundary layer and free shear layers.