有哪些信誉好的足球投注网站Shock Structures and Velocity Fluctuations in the Noisy Burgers and KdV-Burgers Equations.pdf
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Shock Structures and Velocity Fluctuations in the Noisy Burgers and KdV-Burgers Equations
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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
February 2, 2008
abstract
Statistical properties of the noisy Burgers and KdV-Burgers equations are nu-
merically studied. It is found that shock-like structures appear in the time-
averaged patterns for the case of stepwise fixed boundary conditions. Our re-
sults 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.
1 Introduction
The Burgers equation and the KdV-Burgers equation are well-known model
equations used in the study of shock waves in fluids and plasmas.[1, 2] Spatial
integration of the noisy Burgers equation yieldsthe Kardar-Parisi-Zhang equa-
tion. The KPZ equation has been intensively studied in the context of growing
rough interfaces.[3] The Kuramoto-Sivashinsky equation is one of the simplest
partial differential equations that exhibit spatiotemporal chaos. There is a con-
jecture that the statistical properties of the Kuramoto-Sivashinsky equation on
large scales are closely related to those of the noisy Burgers equation.[4, 5] In
previous studies, we have found shock structures in the time averaged patterns
of the Kuramoto-Sivashinsky equation with fixed boundary conditions, where
the boundary values are set as u(0) = ?U0, u(L) = U0.[6, 7] In this paper, we
study some statistical properties of the noisy KdV-Burgers equation and the
noisy Burgers equation with stepwise fixed boundary conditions.
1
2 Time-averaged shock structure and velocity
fluctuations
The noisy
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