High frequency energy cascades in inviscid hydrodynamics

Adam Smith N. Costa, J.M. de Araújo, Nir Cohen, Liacir S. Lucena and G.M. Viswanathan

Physica A: Statistical Mechanics and its Applications, 2014, vol. 399, issue C, 137-146

Abstract: With the aim of gaining insight into the notoriously difficult problem of energy and vorticity cascades in high dimensional incompressible flows, we take a simpler and very well understood low dimensional analog and approach it from a new perspective, using the Fourier transform. Specifically, we study, numerically and analytically, how kinetic energy moves from one scale to another in solutions of the hyperbolic or inviscid Burgers equation in one spatial dimension (1D). We restrict our attention to initial conditions which go to zero as x→±∞. The main result we report here is a Fourier analytic way of describing the cascade process. We find that the cascade proceeds by rapid growth of a crossover scale below which there is asymptotic power law decay of the magnitude of the Fourier transform.

Keywords: Burgers equation; Hydrodynamics; Singularity formation (search for similar items in EconPapers)
Date: 2014
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378437113011436
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:399:y:2014:i:c:p:137-146

DOI: 10.1016/j.physa.2013.12.019

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 ().