A Stochastic Wave Model Interpretation of Correlation Functions for Turbulent Shear Flows.
Interim rept. 1970-1971,
STANFORD UNIV CALIF THERMOSCIENCES DIV
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The classical difficulties in synthesizing the velocity fluctuation field from turbulence data are discussed, including the closure problem, consequent non-uniqueness of the representation, and the loss of information due to averaging. In the present work the inverse approach is used, that is, several analytical models of the velocity fluctuation field, suggested by the flow visualization data, are compared with the existing space-time correlation function data. This approach effectively eliminates the closure problem, but due to its inductive nature, causes some difficulties in disclosing the underlying physics. Using the most promising model, the turbulent flow field has been decomposed, by modeling the velocity fluctations as non-deterministic travelling waves with random phase angles. It is found that this phenomenological model correctly represents the observed trends in the narrow band frequency filtered correlation function data. Next, the power spectral density function is identified as the appropriate frequency weighting function with which to synthesize the broad band unfiltered from the narrow band correlation functions. The functional form of the power spectral density function which agrees with the observed data is taken to be the superposition of a strong, unorganized background turbulence Markoff noise and an organized turbulent structure. The derived broad band correlation functions agree very well with a wide range of turbulent correlation function measurements.
- Statistics and Probability
- Fluid Mechanics