Kolmogorov flow: Linear Stability and Energy Transfers in a minimal low-dimensional model
arXiv:2007.06513 · doi:10.1063/5.0002751
Abstract
In this paper, we derive a four-mode model for the Kolmogorov flow by employing Galerkin truncation and Craya-Herring basis for the decomposition of velocity field. After this, we perform a bifurcation analysis of the model. Though our low-dimensional model has fewer modes than the past models, it captures the essential features of the primary bifurcation of the Kolmogorov flow. For example, it reproduces the critical Reynolds number for the supercritical pitchfork bifurcation and the flow structures of the past works. We also demonstrate energy transfers from intermediate scales to large scales. We perform direct numerical simulations of the Kolmogorov flow and show that our model predictions match with the numerical simulations very well.
arXiv comment9 pages, 5 figures
References in corpus (9)
- Statistical Theory of Magnetohydrodynamic Turbulence: Recent Results
- Energy transfer in two-dimensional magnetohydrodynamic turbulence: formalism and numerical results
- Spatiotemporal dynamics in 2D Kolmogorov flow over large domains
- Energy and enstrophy spectra and fluxes for the inertial-dissipation range of two-dimensional turbulence
- Dynamo Transition in Low-dimensional Models
- Velocity Profile in a Two-Layer Kolmogorov-Like Flow
- Dynamics of reversals and condensates in 2D Kolmogorov flows
- Nonlocal interactions versus viscosity in turbulence
- Order and chaos in two-dimensional Rayleigh-Bénard convection