A small closed box of fluid heated from below is run at four steadily increasing…
PHYSICS · Multi-part · Fermi University Physics · Fluids & Continuum Physics · Instability, transition and turbulence · Instability, transition and turbulence
Fluid Dynamics, Ch Transition to turbulence
Problem
A small closed box of fluid heated from below is run at four steadily increasing temperature differences, and the power spectrum of the temperature at one point is recorded each time. Spectrum 1 is flat, at the noise floor. Spectrum 2 has one sharp peak at a frequency f1, with its harmonics 2f1,3f1,…. Spectrum 3 keeps those peaks and adds new ones at f1/2, 3f1/2, 5f1/2,…. Spectrum 4 keeps all of these and adds peaks at f1/4, 3f1/4, 5f1/4,….
((a)) Name the route to chaos this sequence follows, and say how it differs from the route Gollub and Swinney recorded in Taylor-Couette flow.
((b)) If the sequence continues, at what frequency does the lowest new peak of the next spectrum appear?
((c)) A different experiment shows two sharp peaks at f1 and f2, together with peaks at f1+f2 and f1−f2. Combination peaks like these can appear on either route. Which property of the ratio f2/f1 decides which route the flow is on?