Kicked Burgers turbulence

被引:42
作者
Bec, J
Frisch, U
Khanin, K
机构
[1] Observ Cote Azur, Lab GD Cassini, F-06304 Nice 4, France
[2] Heriot Watt Univ, Dept Math, Edinburgh EH14 4AS, Midlothian, Scotland
[3] Isaac Newton Inst Math Sci, Cambridge CB3 0EH, England
[4] LD Landau Theoret Phys Inst, Moscow 117332, Russia
关键词
D O I
10.1017/S0022112000001051
中图分类号
O3 [力学];
学科分类号
08 ; 0801 ;
摘要
Burgers turbulence subject to a force f(x,t) = Sigma(i)f(j)(x)delta(t - t(j)), where the t(j) are 'kicking times' and the 'impulses' f(j)(x) have arbitrary space dependence, combines features of the purely decaying and the continuously forced cases. With large-scale forcing this 'kicked' Burgers turbulence presents many of the regimes proposed by E et al. (1997) for the case of random white-noise-in-time forcing. It is also amenable to efficient numerical simulations in the inviscid limit, using a modification of the fast Legendre transform method developed for decaying Burgers turbulence by Noullez & Vergassola (1994). For the kicked case, concepts such as 'minimizers' and 'main shock', which play crucial roles in recent developments for forced Burgers turbulence become elementary since everything can be constructed from simple two-dimensional area-preserving; Euler-Lagrange maps. The main results are for the case of identical deterministic kicks which are periodic and analytic in space and are applied periodically in time. When the space integrals of the initial velocity and of the impulses vanish, it is proved and illustrated numerically that a space- and time-periodic solution is achieved exponentially fast. In this regime, probabilities can be defined by averaging over space and time periods. The probability densities of large negative velocity gradients and of (not-too-large) negative velocity increments follow the power law with -7/2 exponent proposed by E et al. (1997) in the inviscid limit, whose existence is still controversial in the case of white-in-time forcing, This power law, which is seen very clearly in the numerical simulations, is the signature of nascent shocks (preshocks) and holds only when at least one new shock is born between successive kicks. It is shown that the third-order structure function over a spatial separation Delta x is analytic in dr although the velocity field is generally only piecewise analytic (i.e. between shocks). Structure functions of order p not equal 3 are non-analytic at Delta x = 0. For even p there is a leading-order term proportional to \Delta x \ and for odd p > 3 the leading-order term cc proportional to Delta x has a non-analytic correction proportional to Delta x \Delta x \ stemming from shock mergers.
引用
收藏
页码:239 / 267
页数:29
相关论文
共 37 条
[1]  
[Anonymous], 1990, DISSIPATIVE STRUCTUR, DOI DOI 10.1016/B978-0-08-092445-8.50011-0
[2]   THE TWIST MAP, THE EXTENDED FRENKEL-KONTOROVA MODEL AND THE DEVILS STAIRCASE [J].
AUBRY, S .
PHYSICA D, 1983, 7 (1-3) :240-258
[3]  
Barabasi A-Ls, 1995, FRACTAL CONCEPTS SUR, DOI [10.1017/CBO9780511599798, DOI 10.1017/CBO9780511599798]
[4]   Probability distribution functions of derivatives and increments for decaying Burgers turbulence [J].
Bec, J ;
Frisch, U .
PHYSICAL REVIEW E, 2000, 61 (02) :1395-1402
[5]  
BEC J, 2000, IN PRESS PHYSICA D
[6]  
Belitskii G. R., 1973, FUNCTIONAL ANAL APPL, V7, P268
[7]   Velocity-difference probability density functions for Burgers turbulence [J].
Boldyrev, SA .
PHYSICAL REVIEW E, 1997, 55 (06) :6907-6910
[8]   SCALING AND INTERMITTENCY IN BURGERS TURBULENCE [J].
BOUCHAUD, JP ;
MEZARD, M ;
PARISI, G .
PHYSICAL REVIEW E, 1995, 52 (04) :3656-3674
[9]   KOLMOGOROV TURBULENCE IN A RANDOM-FORCE-DRIVEN BURGERS-EQUATION - ANOMALOUS SCALING AND PROBABILITY DENSITY-FUNCTIONS [J].
CHEKHLOV, A ;
YAKHOT, V .
PHYSICAL REVIEW E, 1995, 52 (05) :5681-5684
[10]   ON A QUASI-LINEAR PARABOLIC EQUATION OCCURRING IN AERODYNAMICS [J].
COLE, JD .
QUARTERLY OF APPLIED MATHEMATICS, 1951, 9 (03) :225-236