Bounds for second order structure functions and energy spectrum in turbulence

Journal Article · Sun Aug 01 04:00:00 EDT 1999 · Physics of Fluids (1994)

DOI:https://doi.org/10.1063/1.870086· OSTI ID:351860

Constantin, P ^[1]; Nie, Q ^[1]; Tanveer, S ^[2]

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1. Department of Mathematics, The University of Chicago, Chicago, Illinois 60637 (United States)
2. Department of Mathematics, The Ohio State University, Columbus, Ohio 43210 (United States)

In this paper we derive upper bounds for the second order structure function as well as for the Littlewood{endash}Paley energy spectrum {emdash} an average of the usual energy spectrum E(k). While the upper bound results are consistent with a Kolmogorov type dependence on wave number {ital k}, the bounds do not involve the usual dissipation rate {epsilon}. Instead the bounds involve a dissipative quantity {cflx {epsilon}} similar to {epsilon} but based on the L{sup 3} average of {nabla}u. Numerical computations for a highly symmetric flows with Taylor microscale Reynolds numbers up to R{sub {lambda}}=155 are found to be consistent with the proposition that a relation in the inertial regime of the type E(k){approximately}{cflx C}{cflx {epsilon}}{sup 2/3}k{sup {minus}5/3} holds with constant {cflx C}. {copyright} {ital 1999 American Institute of Physics.}

• OSTI ID: 351860
• Journal Information: Physics of Fluids (1994), Journal Name: Physics of Fluids (1994) Journal Issue: 8 Vol. 11; ISSN PHFLE6; ISSN 1070-6631
• Country of Publication: United States
• Language: English

Related Subjects

66 PHYSICS
DISSIPATION FACTOR
ENERGY SPECTRA
NUMERICAL SOLUTION
STRUCTURE FUNCTIONS
TURBULENCE