Abstract
In this paper we derive upper bounds for the second order structure function as well as for the Littlewood-Paley energy spectrum - an average of the usual energy spectrum E(k). While the upper bound results are consistent with a Kolmogorov type dependence on wave number k, the bounds do not involve the usual dissipation rate e. Instead the bounds involve a dissipative quantity ∈̂ similar to ∈ but based on the L3 average of Δu. Numerical computations for a highly symmetric flows with Taylor microscale Reynolds numbers up to R-λ- 155 are found to be consistent with the proposition that a relation in the inertial regime of the type E(k) ∼ Ĉ∈̂2/3k-5/3 holds with constant Ĉ.
Original language | English (US) |
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Pages (from-to) | 2251-2256 |
Number of pages | 6 |
Journal | Physics of Fluids |
Volume | 11 |
Issue number | 8 |
DOIs | |
State | Published - Aug 1999 |
All Science Journal Classification (ASJC) codes
- Computational Mechanics
- Condensed Matter Physics
- Mechanics of Materials
- Mechanical Engineering
- Fluid Flow and Transfer Processes