Nonlinear wave-number selection in gradient-flow systems

Hsueh-Chia Chang, Evgeny A. Demekhin, Dmitry I. Kopelevich, and Yi Ye
Phys. Rev. E 55, 2818 – Published 1 March 1997
PDFExport Citation

Abstract

The selection of a final periodic state (wave pattern), out of a family of such states, is shown to be governed generically by defects for the lowest order gradient-flow model, the generalized Kuramoto-Sivashinsky equation. Such defects arise when the nonlinear dispersion relationship of the periodic states couples with the flow-inducing Galilean zero mode, in a manner unique to gradient dynamics, to trigger a modulation instability and a self-similar, finite-time evolution toward jumps in the local wave-number gradient and mean thickness. This coupled modulation instability is much stronger than the classical phase modulation instability. The jumps at these defects then serve as wave sinks whose strength relaxes in time. Due to such consumption of wave peaks (nodes) at the relaxing defects, the bulk wave number away from the defects decreases in time until a unique stable periodic state is reached whose speed is equal to its differential flow rate with respect to change in thickness. We estimate the defect formation dynamics and the final relaxation toward equilibrium analytically, and compare them favorably to numerical results.

  • Received 23 September 1996

DOI:https://doi.org/10.1103/PhysRevE.55.2818

©1997 American Physical Society

Authors & Affiliations

Hsueh-Chia Chang, Evgeny A. Demekhin, Dmitry I. Kopelevich, and Yi Ye

  • Department of Chemical Engineering, University of Notre Dame, Notre Dame, Indiana 46556

References (Subscription Required)

Click to Expand
Issue

Vol. 55, Iss. 3 — March 1997

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review E

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×