Steady-state Burgers turbulence with large-scale forcing

Journal Article · Sun Nov 01 04:00:00 EST 1998 · Physics of Fluids (1994)

DOI:https://doi.org/10.1063/1.869807· OSTI ID:662207

Gotoh, T ^[1]; Kraichnan, R H ^[2]

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1. Department of Systems Engineering, Nagoya Institute of Technology, Showa-ku, Nagoya 466 (Japan)
2. 369 Montezuma 108, Santa Fe, New Mexico 87501-2626 (United States)

Steady-state Burgers turbulence supported by white-in-time random forcing at low wave numbers is studied analytically and by computer simulation. The peak of the probability distribution function (pdf) Q({xi}) of velocity gradient {xi} is at {xi}=O({xi}{sub f}), where {xi}{sub f} is a forcing parameter. It is concluded that Q({xi}) displays four asymptotic regimes at Reynolds number R{gt}1: (A) Q({xi}){approximately}{xi}{sub f}{sup {minus}2}{xi}exp({minus}{xi}{sup 3}/3{xi}{sub f}{sup 3}) for {xi}{gt}{xi}{sub f} (reduction of large positive {xi} by stretching); (B) Q({xi}){approximately}{xi}{sub f}{sup 2}{vert_bar}{xi}{vert_bar}{sup {minus}3} for {xi}{sub f}{lt}{minus}{xi}{lt}R{sup 1/2}{xi}{sub f} (transient inviscid steepening of negative {xi}); (C) Q({xi}){approximately}{vert_bar}R{xi}{vert_bar}{sup {minus}1} for R{sup 1/2}{xi}{sub f}{lt}{minus}{xi}{lt}R{xi}{sub f} (shoulders of mature shocks); (D) very rapid decay of Q for {minus}{xi}{ge}O(R{xi}{sub f}) (interior of mature shocks). The typical shock width is O(1/Rk{sub f}). If R{sup {minus}1/2}{gt}rk{sub f}{gt}R{sup {minus}1}, the pdf of velocity difference across an interval r is found to be P({Delta}u,r){proportional_to}r{sup {minus}1}Q({Delta}u/r) throughout regimes A and B and into the middle of C. {copyright} {ital 1998 American Institute of Physics.}

• OSTI ID: 662207
• Journal Information: Physics of Fluids (1994), Journal Name: Physics of Fluids (1994) Journal Issue: 11 Vol. 10; ISSN PHFLE6; ISSN 1070-6631
• Country of Publication: United States
• Language: English

Related Subjects

42 ENGINEERING
COMPUTERIZED SIMULATION
DISTRIBUTION FUNCTIONS
PROBABILITY
REYNOLDS NUMBER
SHOCK WAVES
STEADY-STATE CONDITIONS
TURBULENCE
VELOCITY