Self-sustaining turbulence in a restricted nonlinear model of plane Couette flow
arXiv:1402.5059 · doi:10.1063/1.4898159
Abstract
This paper demonstrates the maintenance of self-sustaining turbulence in a restricted nonlinear (RNL) model of plane Couette flow. The RNL system is derived directly from the Navier Stokes equations and permits computationally tractable studies of the dynamical system obtained using stochastic structural stability theory (S3T), which is a second order approximation of the statistical state dynamics of the flow. The RNL model shares the dynamical restrictions of the S3T model but can be easily implemented through reducing a DNS code to the equations governing the RNL system. Comparisons of turbulence arising from DNS and RNL simulations demonstrate that the RNL system supports self-sustaining turbulence with a mean flow as well as structural and dynamical features that are consistent with DNS. These results demonstrate that the simplified RNL/S3T system captures fundamental aspects of fully developed turbulence in wall-bounded shear flows and motivates use of the RNL/S3T system for further study of wall turbulence.
arXiv comment19 Pages, 7 Figures, 14 subfigures
References in corpus (11)
- A critical layer model for turbulent pipe flow
- The Significance of Simple Invariant Solutions in Turbulent Flows
- Visualizing the geometry of state space in plane Couette flow
- Equilibrium and traveling-wave solutions of plane Couette flow
- Stochastic Structural Stability Theory applied to roll/streak formation in boundary layer shear flow
- Model-based design of transverse wall oscillations for turbulent drag reduction
- Statistics of an Unstable Barotropic Jet from a Cumulant Expansion
- Astrophysical Fluid Dynamics via Direct Statistical Simulation
- A Streamwise Constant Model of Turbulence in Plane Couette Flow
- Turbulence in the highly restricted dynamics of a closure at second order: comparison with DNS
- Amplification and Nonlinear Mechanisms in Plane Couette Flow
Cited by in corpus (29)
- Color of turbulence
- From bypass transition to flow control and data-driven turbulence modeling: An input-output viewpoint
- Bispectral mode decomposition of nonlinear flows
- A statistical state dynamics-based study of the structure and mechanism of large-scale motions in plane Poiseuille flow
- A minimal model of self-sustaining turbulence
- Standard logarithmic mean velocity distribution in a band-limited restricted nonlinear model of turbulent flow in a half-channel
- Recent Developments in Theories of Inhomogeneous and Anisotropic Turbulence
- Three-Dimensional Rotating Couette Flow Via The Generalised Quasilinear Approximation
- Dynamics of homogeneous shear turbulence: A key role of the nonlinear transverse cascade in the bypass concept
- A statistical state dynamics approach to wall-turbulence
- Statistical state dynamics of jet/wave coexistence in barotropic beta-plane turbulence
- Statistical State Dynamics: a new perspective on turbulence in shear flow
- Generalised quasilinear approximations of turbulent channel flow: Part 1. Streamwise nonlinear energy transfer
- Instability of the roll/streak structure induced by free-stream turbulence in pre-transitional Couette flow
- Generalised quasilinear approximations of turbulent channel flow: Part 2. Spanwise scale interactions
- Model-based spectral coherence analysis
- Synchronization of Low Reynolds Number Plane Couette Turbulence
- Frequency prediction from exact or self-consistent meanflows
- Multiple scales analysis of slow--fast quasilinear systems
- Statistical state dynamics-based analysis of the physical mechanisms sustaining and regulating turbulence in Couette flow
- Statistical state dynamics of weak jets in barotropic beta-plane turbulence
- Three-dimensional coherent structures in a curved pipe flow
- Minimal model of quasi-cyclic behaviour in turbulence driven by Taylor--Green forcing
- Eigenvalue bounds for compressible stratified magneto-shear flows varying in two transverse directions
- Transient growth and nonlinear breakdown of wavelet-based resolvent modes in turbulent channel flow
- Turbulence-Resolving Integral Simulations for Wall-Bounded Flows
- The mechanism by which nonlinearity sustains turbulence in plane Couette flow
- Model for transitional turbulence in a planar shear flow
- -based sparsification of energy interactions in two-dimensional turbulent flows