Condensates in thin-layer turbulence

Abstract

We examine the steady state of turbulent flows in thin layers using direct numerical simulations. It is shown that when the layer thickness is smaller than a critical height, an inverse cascade arises which leads to the formation of a steady state condensate where most of the energy is concentrated in the largest scale of the system. For layers of thickness smaller than a second critical height, the flow at steady state becomes exactly two-dimensional. The amplitude of the condensate is studied as a function of layer thickness and Reynolds number. Bi-stability and intermittent bursts are found close to the two critical points. The results are interpreted based on a mean field three-scale model that reproduces some of the basic features of the numerical results.

References in corpus (11)

• Cascades and transitions in turbulent flows
• Growing condensate in two-dimensional turbulence
• Random changes of flow topology in two dimensional and geophysical turbulence
• Inverse cascade and symmetry breaking in rapidly-rotating Boussinesq convection
• Large-scale vortices in rapidly rotating Rayleigh-Bénard convection
• Turbulence-condensate interaction in two dimensions
• Rotating Taylor-Green Flow
• On the edge of an inverse cascade
• Split energy cascade in turbulent thin fluid layers
• Dimensional transition of energy cascades in stably stratified thin fluid layers
• The effect of helicity on the correlation time of large scale turbulent flows

Cited by in corpus (22)

• Subcritical turbulent condensate in rapidly rotating Rayleigh-Bénard convection
• Critical transition in fast-rotating turbulence within highly elongated domains
• Condensate formation and multiscale dynamics in two-dimensional active suspensions
• Abrupt transition between three and two-dimensional quantum turbulence
• Inverse cascades of kinetic energy and thermal variance in three-dimensional horizontally extended turbulent convection
• Discontinuous Transitions Towards Vortex Condensates in Buoyancy-Driven Rotating Turbulence
• Rare transitions to thin-layer turbulent condensates
• Bistability of the large-scale dynamics in quasi-two-dimensional turbulence
• Onset of three-dimensionality in rapidly rotating turbulent flows
• Energy cascades in rapidly rotating and stratified turbulence within elongated domains
• Geometric microcanonical theory of two-dimensional Truncated Euler flows
• Role of the forcing dimensionality in thin-layer turbulent energy cascades
• Nonuniversal transition to condensate formation in two-dimensional turbulence
• Lévy on-off intermittency
• Phase Transition From Turbulence To Zonal Flows In The Hasegawa-Wakatani System
• Intermittency of three-dimensional perturbations in a point-vortex model
• Chaotic measure of the transition between two and three dimensional turbulence
• Effective transport by 2D turbulence: Vortex-gas theory vs. scale-invariant inverse cascade
• Inverse cascade suppression and shear layer formation in MHD turbulence subject to a guide field and misaligned rotation
• $\lambda$-Navier-Stokes turbulence
• Spontaneous suppression of inverse energy cascade in instability-driven 2D turbulence
• Transition to inverse cascade in turbulent rotating convection in absence of the large-scale vortex