Spatial and temporal resonances in a periodically forced hydrodynamic system

The occurrence of a Naimark-Sacker bifurcation in a periodically forced spa tially extended system is analyzed with Floquet theory. The basic periodic state of the flow in an annular region consists of the superposition of cir cular Couette flow, driven by the constant rotation of the inner cylinder, and annular Stokes how, driven by the harmonic oscillation of the inner cyl inder in the axial direction. Windows in parameter space where onset of ins tability is via Naimark-Sacker correspond to forcing frequencies close to t he natural frequencies of the unforced system when the forcing amplitude is sufficiently large. In these windows, not only have strong temporal resona nces been identified, but also competition and resonances between various s patial modes that are simultaneously excited take place. An excitation diag ram mapping out these windows and loci of resonance points is produced, pro viding a guide for future explorations into the nonlinear regime by either experimental or computational techniques. (C)2000 Elsevier Science B.V. All rights reserved.