A low-dimensional model for turbulent shear flows
By Jeff Moehlis, Holger Faisst, Bruno Eckhardt. 2004
165 citations recorded by the source corpus.
We analyse a low-dimensional model for turbulent shear flows. The model is based on Fourier modes and describes sinusoidal shear flow, in which the fluid between two free-slip walls experiences a sinusoidal body force. The model contains a total of nine modes, including modes describing the basic mean velocity profile and its modification, downstream vortices, streaks, and instabilities of streaks, with other modes being a consequence of the non-linear interactions. The transition to turbulence for the model is subcritical and intermittent, and the distributions of turbulent lifetimes are exponential, in agreement with observations in many shear flows.
Subfields: Computational Mechanics, Global and Planetary Change
View Paper: https://www.semanticscholar.org/paper/3be198ac276d525b8b9de3924dbb200c0b8cd806
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In Computational Mechanics
- John H. Wise
- Matthew J. Turk
- Luca Brandt
- Jonathan J. Halcrow
- J. Gibson
- Predrag Cvitanović
- Tobias M. Schneider
- Bruno Eckhardt
In Global and Planetary Change
- Luca Brandt
- Jonathan J. Halcrow
- J. Gibson
- Predrag Cvitanović
- John H. Wise
- Tobias M. Schneider
- Bruno Eckhardt
- Tom Abel
Citations in the corpus
- Turbulence transition in pipe flow (2007, background): “Low-dimensional systems provide examples with algebraic (Kaneda 1990), exponential (Moehlis et al. 2004), and even superexponential increases (Crutchfield & Kaneko 1988).”
- The lift-up effect : The linear mechanism behind transition and turbulence in shear flows (2014, methodology): “More complicated models, based on Galerkin projection, also always need a linear amplification mechanism for transition and sustained turbulence, the lift-up effect (e.g. Moehlis et al., 2004).”
- Visualizing the geometry of state space in plane Couette flow (2007, methodology): “The energy, the dissipation rate, and mean and RMS velocity profiles of the Nagata (1990) upper-branch equilibrium and the Kawahara & Kida (2001) periodic orbit are all numerically close to the long-term turbulent averages.”
- An introductory essay on subcritical instabilities and the transition to turbulence in visco-elastic parallel shear flows (2007, background): “[58] yield explicit predictions for the spectra and various average quantities measured in the weak turbulence.”
- Resolving the Formation of Protogalaxies. II. Central Gravitational Collapse (2007, background): “However, there are many modes of instability if the Rayleigh criterion is not met, and even gas with a low Reynolds number will eventually become fully turbulent on a timescale that is chaotic, depending on the initial perturbation and Reynolds number (Shu 1992; Moehlis et al. 2004).”