Related papers: Zonal Flow as Pattern Formation
We demonstrate that the space-time statistics of the birth of turbulent spots in boundary layers can be reconstructed qualitatively from the average behavior of macroscopic measures in the transition zone. The conclusion in \cite{vg04} that…
Planetary and magnetohydrodynamic drift-wave turbulence is observed to self-organize into large scale structures such as zonal jets and coherent vortices. In this Letter we present a non-equilibrium statistical theory, the Stochastic…
A new, frequency modulation mechanism for zonal flow pattern formation is presented. The model predicts the probability distribution function of the flow strength as well as the evolution of the characteristic spatial scale. Magnetic…
Planetary turbulent flows are observed to self-organize into large scale structures such as zonal jets and coherent vortices. One of the simplest models of planetary turbulence is obtained by considering a barotropic flow on a beta-plane…
The toroidal geometry of tokamaks and stellarators is known to play a crucial role in the linear physics of zonal flows, leading to e.g. the Rosenbluth-Hinton residual and geodesic acoustic modes. However, descriptions of the nonlinear…
A dynamical systems approach to turbulence envisions the flow as a trajectory through a high-dimensional state space transiently visiting the neighbourhoods of unstable simple invariant solutions (E. Hopf, Commun. Appl. Maths 1, 303, 1948).…
The consequences of discrete particle noise for a system possessing a possibly unstable collective mode are discussed. It is argued that a zonostrophic instability (of homogeneous turbulence to the formation of zonal flows) occurs just…
Non-linear dynamics of zonal flows is investigated in the context of the gyrofluid modified Hasegawa-Wakatani model. Merging of zonal flows and the chaotic developement of the initial zonal flow pattern is explored. Conservation equations…
Pattern formation from homogeneity is well-studied, but less is known concerning symmetry-breaking instabilities in heterogeneous media. It is nontrivial to separate observed spatial patterning due to inherent spatial heterogeneity from…
We study statistical properties of turbulent inverse cascades in a class of nonlinear models describing a scalar field transported by a two-dimensional incompressible flow. The class is characterized by a linear relation between the…
Statistical mechanics provides an elegant explanation to the appearance of coherent structures in two-dimensional inviscid turbulence: while the fine-grained vorticity field, described by the Euler equation, becomes more and more filamented…
Zonal flows are mean flows in the east-west direction, which are ubiquitous on planets, and can be formed through 'zonostrophic instability': within turbulence or random waves, a weak large-scale zonal flow can grow exponentially to become…
The formation of zonal flows from inhomogeneous drift-wave (DW) turbulence is often described using statistical theories derived within the quasilinear approximation. However, this approximation neglects wave--wave collisions. Hence, some…
This paper is concerned with the processes of spatial propagation and penetration of turbulence from the regions where it is locally excited into initially laminar regions. The phenomenon has come to be known as "turbulence spreading" and…
The transitional regime of plane channel flow is investigated {above} the transitional point below which turbulence is not sustained, using direct numerical simulation in large domains. Statistics of laminar-turbulent spatio-temporal…
We present a theory of the nonlinear growth of zonal flows in magnetized plasma turbulence, by the mechanism of secondary instability. The theory is derived for general magnetic geometry, and is thus applicable to both tokamaks and…
Understanding inhomogeneous and anisotropic fluid flows require mathematical and computational tools that are tailored to such flows and distinct from methods used to understand the canonical problem of homogeneous and isotropic turbulence.…
The theory of mesoscopic fluctuations is applied to inhomogeneous solids consisting of chaotically distributed regions with different crystalline structure. This approach makes it possible to describe statistical properties of such mixture…
Solitary zonal structures have recently been identified in gyrokinetic simulations of subcritical drift-wave (DW) turbulence with background shear flows. However, the nature of these structures has not been fully understood yet. Here, we…
Planetary turbulence is observed to self-organize into large-scale structures such as zonal jets and coherent vortices. One of the simplest models that retains the relevant dynamics of turbulent self-organization is a barotropic flow in a…