Titlebook: Navier-Stokes Turbulence; Theory and Analysis Wolfgang Kollmann Textbook 2024Latest edition The Editor(s) (if applicable) and The Author(s)

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sented over subsequent chapters, is devoted to mapping methods, homogeneous turbulence based upon the hypotheses of Kolmogorov and Onsager, intermittency, structural features of turbulent shear flows and their 978-3-031-59580-6978-3-031-59578-3

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Flow Domains and Bases,ted 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.

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Integral Transforms and Spectra,e wavenumber vector and is eliminated from the transformed momentum balances. The result is a system of three integro-differential equations for the velocity modes, and the nonlinear interactions emerge as the convolution of velocity modes.

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The Lewis-Kraichnan Equation for the Space-Time Functional,eneralized Laplacians are defined as standard and Levy types and related within the framework of an ONS basis. The last section is devoted to the definition and analysis of Hessian and Laplacian operators on the functional level and the Hopf fde in the material description, which is shown to be of a type different than the spatial description.

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Properties and Construction of Mappings,haracteristic functionals are considered for the case of nuclear definition and image spaces and restrictions are established to insure that the image of a characteristic function is also a characteristic function. Methods for the construction of local and global mappings are covered and illustrated with examples.

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