Abstract
The CCK map** method is extended to velocity-scalar Pdfs in the spatial description and to position- scalar Pdfs in the material description. The starting point is the Leray version of the Navier-Stokes pdes assuming Green’s function exists to express the pressure in terms of velocity; the result is a system of three integrodifferential equations for the velocity field. The domain of definition of this system is defined as the velocity-scalar phase space \(v_{\alpha }(\mathbf {x}),\Phi _i(\mathbf {x}),i=1(1)N\), ad the space spanned by the possible range of values is denoted by \(\Omega _{loc}\). Local map**s \(\chi :R^{N+3}\rightarrow \Omega _{loc}\) are constructed with the aid of the Jacobian of the map** thus leading to map** equations. Single-point and multipoint map** equations are developed in the spatial and material description.
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Kollmann, W. (2024). \(\mathcal {M}_1(N)\): Map**s for Velocity-Scalar and Position-Scalar Pdfs. In: Navier-Stokes Turbulence. Springer, Cham. https://doi.org/10.1007/978-3-031-59578-3_16
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DOI: https://doi.org/10.1007/978-3-031-59578-3_16
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