Abstract
AbstractNon-normal transient growth of disturbances is considered as an essential prerequisite for subcritical transition in shear flows, i.e. transition to turbulence despite linear stability of the laminar flow. In this work we present numerical and analytical computations of linear transient growth covering all linearly stable regimes of Taylor–Couette flow. Our numerical experiments reveal comparable energy amplifications in the different regimes. For high shear Reynolds numbers$\mathit{Re}$, the optimal transient energy growth always follows a$\mathit{Re}^{2/3}$scaling, which allows for large amplifications even in regimes where the presence of turbulence remains debated. In co-rotating Rayleigh-stable flows, the optimal perturbations become increasingly columnar in their structure, as the optimal axial wavenumber goes to zero. In this limit of axially invariant perturbations, we show that linear stability and transient growth are independent of the cylinder rotation ratio and we derive a universal$\mathit{Re}^{2/3}$scaling of optimal energy growth using Wentzel–Kramers–Brillouin theory. Based on this, a semi-empirical formula for the estimation of linear transient growth valid in all regimes is obtained.
Highlights
The flow of viscous fluid between two coaxial independently and uniformly rotating cylinders, Taylor–Couette flow, is a paradigmatic system to study the stability and dynamics of rotating shear flows
Davey 1973; Romanov 1973; Drazin & Reid 1981), certain Taylor–Couette flows may undergo subcritical transition to turbulence in the absence of unstable eigenvalues
For a Taylor–Couette flow configuration given by the parameters Rei, Reo and η, the optimal transient growth is defined by Gmax := supt,n,k G(t)
Summary
The flow of viscous fluid between two coaxial independently and uniformly rotating cylinders, Taylor–Couette flow, is a paradigmatic system to study the stability and dynamics of rotating shear flows. The transition from regime II to III defines the Rayleigh line where Rayleigh’s stability criterion ceases to be fulfilled and a centrifugal (linear) instability of the laminar flow emerges In experiments, this results in the formation of a new stationary flow, characterized by the famous toroidal Taylor vortices (Taylor 1923). To plane Couette and Poiseuille flow (cf Davey 1973; Romanov 1973; Drazin & Reid 1981), certain Taylor–Couette flows may undergo subcritical transition to turbulence in the absence of unstable eigenvalues This phenomenon has been observed both by Coles (1965) in the Rayleigh-unstable counter-rotating regime IV as well as by Wendt (1933) and Taylor (1936) for a stationary inner cylinder (i.e. at the lower boundary of the Rayleigh-stable regime I; see figure 1b).
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
