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

Mahendra K. Verma

Physica A: Statistical Mechanics and its Applications, 2000, vol. 277, issue 3, 359-388

Abstract: 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 σ of the noise variance of the Burgers equation (variance ∝k−2σ) exceeds 3/2, large shocks appear in the velocity profile leading to 〈|u(k)|2〉∝k−2, and structure function 〈|u(x+r,t)−u(x,t)|q〉∝r suggesting that the Burgers equation is intermittent for this range of σ. For −1⩽σ⩽0, the profile is dominated by noise, and the spectrum 〈|h(k)|2〉 of the corresponding KPZ equation is in close agreement with the Medina et al. renormalization group predictions. In the intermediate range 0<σ<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 σ, while P(u′) is Gaussian for σ=−1, but steadily becomes non-Gaussian for larger σ; for negative u′, P(u′)∝exp(−ax) for σ=0, and approximately ∝u′−5/2 for σ>1/2. We have also calculated the energy cascade rates for all σ and found a constant flux for all σ⩾1/2.

Date: 2000
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378437199005440
Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:277:y:2000:i:3:p:359-388

DOI: 10.1016/S0378-4371(99)00544-0

Access Statistics for this article

Physica A: Statistical Mechanics and its Applications is currently edited by K. A. Dawson, J. O. Indekeu, H.E. Stanley and C. Tsallis

More articles in Physica A: Statistical Mechanics and its Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().