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Geometric realization of the two-point velocity correlation tensor for isotropic turbulence. (English) Zbl 1213.53024
Summary: A new geometric view of homogeneous isotropic turbulence is studied employing the two-point velocity correlation tensor of the velocity fluctuations. We show that this correlation tensor generates a family of pseudo-Riemannian metrics. This enables us to specify the geometry of a singled out Eulerian fluid volume in a statistical sense. We expose the relationship of some geometric constructions with statistical quantities arising in turbulence.
MSC:
53B21Methods of Riemannian geometry
53B30Lorentz metrics, indefinite metrics
76F05Isotropic turbulence; homogeneous turbulence
53B50Applications of local differential geometry to physics