ISSN:
1573-1472
Source:
Springer Online Journal Archives 1860-2000
Topics:
Geosciences
,
Physics
Notes:
Abstract In a recent paper, the author introduced a new viscous boundary layer, called the mesolayer, in turbulent shear flow. Its importance stems from its location between the inner and outer regions which are controlled by the law of the wall and Reynolds number similarity, respectively. This intrusion prevents the classical overlap assumption which appears to be fundamental in the derivation of the classical logarithmic behavior. The mesolayer has a thickness proportional to Taylor's microscale λ. This, and the analogy between the energy equation for the spectrum function of isotropic turbulence and the momentum equation for shear flow, suggest the existence of a similar region in wavenumber space with wavenumber k ~ λ-1. This mesoregion separates the inner region k ~ k s(where k sη-1 and η is the Kolmogorov length) and the outer region k k e(where k e -1 and l is the energy-containing eddy size) and again invalidates the overlap assumption which appears to be fundamental in the derivation of the classical k -5/3-behavior of the ‘inertial subrange’. Incorporation of the mesoregion into the argument leads to a new theory with k -5/3-behavior in two regions (λ-1 ≪ k ≪ k s) and (k e≪ k ≪ λ-1) although with two different coefficients of proportionality (Kolmogorov constants). This leads to a ‘wandering’ of the spectrum curve about the classical k -5/3 line similar to a ‘wandering’ in turbulent shear flow about the logarithmic curve. This is clearly indicated by the data for the variation of the Kolmogorov ‘constant’. Other data support the new theory. In particular, the location of the point k mwhere the curve of the nonlinear energy-transfer function goes through zero shows agreement with the theory, i.e., k mλ-1.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00121665
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