New solutions of an amplitude equation describing transition in a laminar shear flow
In order to better understand the process of laminar-turbulent transition in parallel shear flows, study of the stability of viscous flow between parallel plates, known as plane Poiseuille flow, is found to be a good prototype. For Reynolds number near the critical value at which a linear instability first appears, Stewartson and Stuart (1971) developed a weakly nonlinear theory for which an amplitude equation is derived describing the evolution of a disturbance in plane Poiseuille flow in two space dimensions. Solutions describe modulations to the wave of primary instability, with amplitude which is steady in an appropriate coordinate system. The ordinary differential equation describing the spatial structure of quasi-steady solutions is viewed as a low-dimensional dynamical system. Using numerical continuation and perturbation techniques, new spatially periodic and quasi-periodic solutions are found which bifurcate from the laminar state and undergo a complex series of bifurcations. Moreover, solitary waves and other solutions suggestive of laminar transition are found numerically for Reynolds number on either side of Re/sub c/, connecting the laminar state to finite-amplitude states, some of the latter corresponding to known solutions of the full fluid equations.
- Research Organization:
- California Inst. of Tech., Pasadena (USA)
- OSTI ID:
- 6948967
- Country of Publication:
- United States
- Language:
- English
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