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- W133987886 abstract "By using the space-time scaling invariance of the Navier-Stokes equations, the spatio-temporal structure of fully developed turbulence, in the homogeneous or inhomogeneous cases, can be understood in terms of a spatio-temporal self-similarity. The latter consists in a hierarchy of spatial and temporal modes which are all similar, namely related to each other through a dilation symmetry group. Our analysis uses biorthogonal decompositions which decompose the flow into spatial and temporal orthogonal modes for which there is a one-to-one correspondence. It also permits the derivation of (exponential) spectrum laws which, for the kinetic energy of the flow, coincide with Kolmogorov’s k−5/3 power law when the flow is both homogeneous and incompressible. Such self-similarity, or fractal structure in a spatio-temporal sense, originates in the space-time dynamics of the flow and is unlikely to be observed from the analysis of a one-dimensional signal (obtained by a single point measurement or an instantaneous picture of the flow). It is, however, recovered by the spatial and temporal two-point correlations and therefore should appear in the structure of the eigenvectors and eigenvalues of the Proper Orthogonal Decomposition in which the ensemble average is a time average. The analysis of spatial two-point correlations, experimentally measured in a turbulent far-wake flow, supports the previous theory.KeywordsParticle Image VelocimetryProper Orthogonal DecompositionProper Orthogonal Decomposition ModeProper Orthogonal Decomposition TechniqueInhomogeneous DirectionThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves." @default.
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- W133987886 date "1993-01-01" @default.
- W133987886 modified "2023-09-27" @default.
- W133987886 title "Detection of Self-Similar Modes in Turbulence: Application to a Wake Flow" @default.
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- W133987886 doi "https://doi.org/10.1007/978-94-011-2098-2_19" @default.
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