Intermittency exponents and energy spectrum of the Burgers and KPZ equations with correlated noise

Details Intermittency exponents and energy spectrum of the Burgers and KPZ equations with correlated noise Intermittency exponents and energy spectrum of the Burgers and KPZ equations with correlated noise

1999-04-12

arxiv.org/abs/chao-dyn/9904020v2

Physica A277 (2000) 359-388

Physics

Condensed Matter

Revised version combining chao-dyn/9904020v1 & chao-dyn/9904021, To appear in Physica A

Scientific paper

10.1016/S0378-4371(99)00544-0

We numerically calculate the energy spectrum, intermittency exponents, and probability density $P(u')$ of the one-dimensional Burgers and KPZ equations with correlated noise. We have used pseudo-spectral method for our analysis. When $\sigma$ of the noise variance of the Burgers equation (variance $\propto k^{-2 \sigma}$) exceeds 3/2, large shocks appear in the velocity profile leading to $<|u(k)|^2> \propto k^{-2}$, and structure function $<|u(x+r,t)-u(x,t)|^q> \propto r$ suggesting that the Burgers equation is intermittent for this range of $\sigma$. For $-1 \le \sigma \le 0$, the profile is dominated by noise, and the spectrum $<|h(k)|^{2}>$ of the corresponding KPZ equation is in close agreement with Medina et al.'s renormalization group predictions. In the intermediate range $0 < \sigma <3/2$, both noise and well-developed shocks are seen, consequently the exponents slowly vary from RG regime to a shock-dominated regime. The probability density $P(h)$ and $P(u)$ are gaussian for all $\sigma$, while $P(u')$ is gaussian for $\sigma=-1$, but steadily becomes nongaussian for larger $\sigma$; for negative $u'$, $P(u') \propto \exp(-a x)$ for $\sigma=0$, and approximately $\propto u'^{-5/2}$ for $\sigma > 1/2$. We have also calculated the energy cascade rates for all $\sigma$ and found a constant flux for all $\sigma \ge 1/2$.

Affiliated with

Also associated with

No associations

Rating

Intermittency exponents and energy spectrum of the Burgers and KPZ equations with correlated noise does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Intermittency exponents and energy spectrum of the Burgers and KPZ equations with correlated noise, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Intermittency exponents and energy spectrum of the Burgers and KPZ equations with correlated noise will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-346086