Interdisciplinary Seminar in Nonlinear Science

Title: New Structures in a Shaking Fluid
Speaker: Professor J. Fineberg
Speaker Info: Hebrew U., Israel
Brief Description:
Special Note:

We describe experimental studies of two types of nonlinear structures that appear on the surface of a fluid when, like the well-known Faraday instability, a thin fluid layer is subjected to a spatially uniform, periodic acceleration. When a fluid is sufficiently dissipative, the dominant fluid state observed for single frequency excitation is that of highly localized, soliton-like structures that propagate along the two dimensional surface. These structures, harmonically coupled to the external driving frequency, are observed above a critical intrinsic "dissipation" in the system (i.e. the ratio of the viscous boundary layer height to the depth of the fluid layer) for a wide range of fluid viscosities and system parameters. These highly localized nonlinear states, unlike classical solitons, propagate at a single constant velocity for given fluid parameters and their existence is dependent on the highly dissipative character of the system. The properties of these states are discussed. A different type of nonlinear state is excited when the fluid is made less dissipative and driven via two simultaneous frequencies. Nonlinear waves with basic wavenumbers, k1 and k2, are then simultaneously excited via two-frequency parametric excitation of a fluid surface. Three new multi-wave states are observed: (1) a superlattice state composed of k1 and k2 whose relative orientation is governed by a temporal resonance condition, (2) a superlattice built entirely of wavenumbers k1 and k1/2, and (3) a state is composed of wavenumbers of lengths k1 and k2, that are uncorrelated in both space and time. The three states exhibit interesting temporal as well as spatial behavior and are observed in a variety of frequency combinations.

Date: Friday, October 9, 1998
Time: 2:00pm
Where: Tech M416
Contact Person: Prof. Riecke
Contact email: h-riecke@nwu.edu
Contact Phone: 847-491-8316
Copyright © 1997-2024 Department of Mathematics, Northwestern University.