TRANSITIONS TOWARD TURBULENCE IN A CURVED CHANNEL

A numerical study of the transitions that occur with increasing Reynolds number in a curved channel with radius ratio-eta = 0.875 is performed using spectral simulations of the three-dimensional, incompressible, time-dependent Navier-Stokes equations. Periodic boundary conditions are used in the spanwise and streamwise directions. At Reynolds number Re = 6.31 Re(c) temporally periodic wavy (twisting) Dean vortices occur (Re(c) is the Reynolds number for the transition from laminar curved channel Poiseuille flow to steady, streamwise-oriented Dean vortices). At Re = 8.84 Re(c), a three-frequency flow is discovered in which two new incommensurate frequencies modulate the wavy vortices. At Re = 10.10 Re(c) the two modulation frequencies are phase locked producing a two-frequency modulated wavy vortex flow that is similar in some ways to that seen in Taylor-Couette flow. The spatial and temporal characteristics of the modulation frequencies are discussed.