Quick Search:
Prog. Theor. Phys. Vol. 110 No. 2 (2003) pp. 187-194
Shock Structures and Velocity Fluctuations in the Noisy Burgers and KdV-Burgers Equations
Hidetsugu Sakaguchi
Department of Applied Science for Electronics and Materials,
Interdisciplinary Graduate School of Engineering Sciences,
Kyushu University, Kasuga 816-8580, Japan
(Received May 12, 2003)
Abstract:
Statistical properties of the noisy Burgers and KdV-Burgers
equations are numerically studied. It is found that
shock-like structures appear in the time-averaged patterns
for the case of stepwise fixed boundary conditions.
Our results show that the shock structure for the noisy KdV-Burgers equation
has an oscillating tail,
even for the time-averaged pattern. Also, we find that
the width of the shock and the intensity of the velocity fluctuations in the
shock region increase with system size.
URL :
http://ptp.ipap.jp/link?PTP/110/187/
DOI : 10.1143/PTP.110.187
References:
- V. I. Karpman, Nonlinear Waves in Dispersive Media (Pergamaon Press, 1975).
- R. Z. Sagdeev, D. A. Usikov and G. M. Zaslavsky, Nonlinear Physics: From Pendulum to Turbulence and Chaos (Harwood Academic Publishers, Chur, 1988).
-
M. Kardar, G. Parisi and Y. C. Zhang, Phys. Rev. Lett. 56 (1986), 889[APS].
-
V. Yakhot, Phys. Rev. A 24 (1981), 642[APS].
-
K. Sneppen, J. Krug, M. H. Jensen, C. Jayaprakash and T. Bohr, Phys. Rev. A 46 (1992), R7351[APS].
-
H. Sakaguchi, Phys. Rev. E 62 (2000), 8817[APS].
- H. Sakaguchi, Prog. Theor. Phys. 107 (2002), 879[PTP].
-
S. A. Janowsky and J. L. Lebowitz, Phys. Rev. A 45 (1992), 618[APS].
-
A. B. Kolomeisky, G. M. Schütz, E. B. Kolomeisky and J. P. Straley, J. of Phys. A 31 (1998), 6911[CrossRef].
- D. J. Evans and G. P. Morris, Statistical Mechanics of Nonequilibrium Liquids (Academic Press, London, 1990).
- J. Lebowitz, E. Presutti and H. Spohn, J. Stat. Phys. 51 (1988), 841.
