Abstract
Some new perspectives are offered on the spectral and spatial structure of turbulent flows, in the context of conservation principles and entropy. In recent works, we have shown that the turbulence energy spectra are derivable from the maximum entropy principle, with good agreement with experimental data across the entire wavenumber range. Dissipation can also be attributed to the Reynolds number effect in wall-bounded turbulent flows. Within the global energy and dissipation constraints, the gradients (d/dy+ or d2/dy+2) of the Reynolds stress components neatly fold onto respective curves, so that function prescriptions (dissipation structure functions) can serve as a template to expand to other Reynolds numbers. The Reynolds stresses are fairly well prescribed by the current scaling and dynamical formalism so that the origins of the turbulence structure can be understood and quantified from the entropy perspective.
Highlights
The ultimate in numerics is the direct numerical simulation (DNS), which produces an abundance of turbulence data [2,3]
The principal constraint is the energy principle: The kinetic energy is dissipated by the viscosity effect progressively at large wavenumbers [20]
If we depart from the conventional turbulence theories and view this phenomenon from the entropy perspective, clear and logical explanations of the observed structure can be discovered
Summary
The ultimate in numerics is the direct numerical simulation (DNS), which produces an abundance of turbulence data [2,3] These are very useful, but should be concurrent with fundamental attempts to theoretically solve the problem. The flux dynamics encapsulated by this alternative dynamical theory provide complete and succinct prescriptions of the turbulence structure, in canonical flow geometries. During this analysis, a spin-off idea of scaling the gradients has been inspired, leading to the self-similarity in the dissipation structure of the Reynolds stress tensor components, u0 2 , v0 2 , and u0 v0 [11].
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