arXiv subjects
Publications and source records attributed to Florin Spineanu.
This paper is focused on the coherent effects that appear in tracer statistics in two-dimensional incompressible turbulence in the presence of an average velocity. We show that this determines strong modifications of the transport and trajectory statistics, which are essentially caused by hidden coherent components of the motion.
We discuss a possible perspective on the process of transition from the layer of sheared poloidal rotation in the H-mode to a set of discrete filaments that concentrate vorticity and current density. They may be precursors of the Edge Localized Modes.
A process specific to the dynamics of the heavy impurities in turbulent tokamak plasmas is found and analysed. We show that the parallel stochastic acceleration is strongly coupled to the perpendicular transport and generates a radial pinch velocity. The interaction is produced with the hidden drifts, a quasi-coherent component of the motion that consists of a pair of average radial velocities in opposite directions. The parallel acceleration breaks this symmetry and yields a radial average velocity that can be in the inward or outward direction. The transport of the tungsten ions in three-dimensional turbulence is analysed in the frame of a test particle model using numerical simulations. The results show that the acceleration induced pinch can be important for W impurity transport in present days tokamaks and in ITER.
The paper defines and discusses the concept of hidden drifts in two-dimensional turbulence. These are ordered components of the trajectories that average to zero and do not produce direct transport. Their effects appear in the evolution of the turbulence as a special type of fluxes, which consist of average motion of positive and negative fluctuations in opposite directions. We show that these fluxes have important nonlinear effects in turbulent fluids and in confined plasmas. In the first case, they determine the increase of the large scale vorticity and velocity at the expense of the small scale fluctuations by a process of separation of the vorticity fluctuations according to their sign. In the second case, they provide a mechanism for zonal flow generation and a vorticity flux that influences the sheared rotation of the plasma.
Fundamental Lagrangian, frozen-in and topological invariants can be useful to explain systematic connections between plasma parameters. At high plasma temperature the dissipation is small and the robust invariances are manifested. We invoke a frozen-in invariant which is an extension of the Ertel's theorem and connects the vorticity of the large scale motions with the profile of the safety factor and of particle density. Assuming ergodicity of the small scale turbulence we consider the approximative preservation of the invariant for changes of the vorticity in an annular region of finite radial extension (i.e. poloidal rotation). We find that the ionization-induced rotation triggered by a pellet requires a reversed-$q$ profile in an off-axis region of the core. In the $H$-mode, the invariance requires the accumulation of the current density in the rotation layer at the edge. Then this becomes a vorticity-current sheet which may explain experimental observations related to the penetration of the Resonant Magnetic Perturbation and the filamentation during the Edge Localized Modes.
The effects of the resonant magnetic perturbations (RMPs) on the turbulent transport are analyzed in the framework of the test particle approach using a semi-analytical method. The normalized RMP amplitude $P_{b}$ extends on a large range, from the present experiments to ITER conditions. The results are in agreement with the experiments at small $P_{b}.$ The predictions for ITER strongly depend on the type of turbulent transport. A very strong increase of the turbulent transport is obtained in the nonlinear regime, while the effects of the RMPs are much weaker for the quasilinear transport.
At incident powers much higher than the threshold for filamentation a pulse from a high-power laser generates in the transversal plane a complex structure. It consists of randomly meandering stripes defining connected regions where the field intensity is high; and, the complementary regions dominated by diffusive plasma with defocusing property. The pattern is similar to an ensemble of clusters of various extensions. We provide evidence that there is a correlation between this filamentation and the {\it labyrinth} instability in reaction-diffusion systems. Besides the similarity of the spatial organization in the two cases, we show that the differential equations that describe these two dynamical processes lead to effects that can be mutually mapped. For the laser beam at high power the Non-linear Schrodinger Equation in a regime of strong self-focusing and ionization of the air leads to multiple filamentation and the structure of clusters. Under the effect of the {\it labyrinth} instability a model of activator-inhibitor leads to a similar pattern. The origin of this connection must be found in the fact that both optical turbulence and the activator-inhibitor dynamics have the nature of competition between two phases of the same system.
The ideal incompressible fluid in two dimensions (Euler fluid) evolves at relaxation from turbulent states to highly coherent states of flow. For the case of double spatial periodicity and zero total vorticity it is known that the streamfunction verifies the \emph{sinh}-Poisson equation. These exceptional states can only be identified in a description based on the extremum of an action functional. Starting from the discrete model of interacting point-like vortices it was possible to write a Lagrangian in terms of a matter function and a gauge potential. They provide a dual representation of the same physical object, the vorticity. This classical field theory identifies the stationary, coherent, states of the $2D$ Euler fluid as derived from the self-duality. We first provide a more detailed analysis of this model, including a comparison with the approach based on the statistical physics of point-like vortices. The second main objective is the study of the dynamics in close proximity of the stationary self-dual state, \emph{i.e.} before the system has reached the absolute extremum of the action functional. Finally, limitations and possible extensions of this field theoretical model for the $2D$ fluids model are discussed and some possible applications are mentioned.
The large scale atmospheric vortices (tropical cyclones, tornadoes) are complex physical systems combining thermodynamics and fluid-mechanical processes. The well known tendency of vorticity to self-organization, an universal property of the two-dimensional fluids, is part of the full dynamics, but its description requires particular methods. The general framework for the thermodynamical and mechanical processes is based on conservation laws while the vorticity self-organization needs a variational approach. It is difficult to estimate to what extent the vorticity self-organization (a purely kinematic process) have influenced the characteristics of the tropical cyclone at stationarity. If this influence is substantial it is expected that the stationary state of the tropical cyclone has the same nature as the vortices of many other systems in nature: ideal (Euler) fluids, superconductors, Bose - Einstein condensate, cosmic strings, etc. In previous works we have formulated a description of the $2D$ vorticity self-organization in terms of a classical field theory. The field theoretical (FT) formulation finds that the quasi-coherent form of the atmospheric vortex (tropical cyclone) at stationarity is an expression of the Self-Duality. In the present work we examine a strong property of the tropical cyclone, which arises in the FT formulation in a natural way: the equality of the masses of the particles associated to the matter field and respectively to the gauge field in the FT model is translated into the equality between the maximum radial extension of the tropical cyclone and the Rossby radius. For the cases where the FT model is a good approximation we calculate characteristic quantities of the tropical cyclone and find good comparison with observational data.
The connection between the poloidal and the toroidal rotation of plasma in tokamak is important for the high confinement regimes, in particular in reactor regime. The sudden onset of closed convection structures in the poloidal section, due to the baroclinic production of vorticity, will sustain a fast increase of the poloidal velocity and a substantial effect on the toroidal rotation. However this is limited to the short time of the onset transition. In real plasma however there is random generation and suppression of convection cells and the sequence of these transient events can prove able to sustain the effect on the toroidal rotation. We formulate a simplified model which consists of a laminar sheared, regular, flow situated at the boundary of a region of drift-wave turbulence. Vortical structures, randomly generated in this turbulent region are spontaneously advected toward the flow and are absorbed there, sustaining with their vortical content, the sheared flow. We examine this dynamics in the wavenumber $\mathbf{k}$ space, using reasonable approximations. We derive a system of equations (which is a class of Davey-Stewartson system) and find that indeed, the vortices advected and absorbed into the layer can preserve its regular, poloidal, flow.
The transition from toroidal counter- to co- rotation in the core plasma has been observed at L to H transition in several tokamaks. Spontaneous reversal has also been observed in TCV beyond a threshold in the density. We develop a model based on the following phenomenology: (1) the increase of the gradient of the pressure triggers formation on a fast time scale of cells of convection (similar to Rayleigh-Benard (RB), but with a single sign of vorticity); (2) poloidal rotation is induced by the envelope of the peripheric velocity of the convection cells; via the baroclinic term the gradients of temperature and density sustain the poloidal rotation against the decay due to the parallel viscosity; (3) the fast increase of poloidal flow induces a high time derivative of the radial electric field; (4) the neoclassical polarization creates a series of parallel accelerations (kiks on each bounce) of the trapped ions, leading to an increase of the toroidal precession or to its reversal; the source of energy is the work done by the radial electric field. (5) the diffusion transfers on resistive scale the toroidal momentum from the trapped ions to the untrapped ones. The correlated interactions are examined and the estimated time scales are found to be compatible with the observations.
Evolving from turbulent states the 2D fluids and the plasmas reach states characterized by a high degree of order, consisting of few vortices. These asymptotic states represent a small subset in the space of functions and are characterised by properties that are difficult to identify in a direct approach. The field theoretical approach to the dynamics and to the asymptotic states of fluids and plasmas in 2D provides a considerable extension of the usual perspective. The present works discusses a series of consequences of the field theoretical approach, when it is applied to particular problems. The discussion is developed around known physical problems: the current density profiles in cylindrical plasma, the density pinch in tokamak and the concentration of vorticity.
The two-dimensional ideal (Euler) fluids can be described by the classical fields of streamfunction, velocity and vorticity and, in an equivalent manner, by a model of discrete point-like vortices interacting in plane by a self-generated long-range potential. This latter model can be formalized, in the continuum limit, as a field theory of scalar matter in interaction with a gauge field, in the $su(2) $ algebra. This description has already offered the analytical derivation of the \emph{sinh}-Poisson equation, which was known to govern the stationary coherent structures reached by the Euler fluid at relaxation. In order this formalism to become a familiar theoretical instrument it is necessary to have a better understanding of the physical meaning of the variables and of the operations used by the field theory. Several problems will be investigated below in this respect.
Strong electrostatic turbulence in magnetically confined plasmas is characterized by trapping or eddying of particle trajectories produced by the $E\times B$ stochastic drift. Trapping is shown to produce strong effects on test particles and on test modes. It determines non-standard statistics of trajectories: non-Gaussian distribution, memory effects and coherence. Trapped trajectories form quasi-coherent structure. Trajectory trapping has strong nonlinear effects on the test modes on turbulent plasmas. We determine the growth rate of drift modes as function of the statistical characteristics of the background turbulence. We show that trapping provides the physical mechanism for the inverse cascade observed in drift turbulence and for the zonal flow generation.
In a two-dimensional model of the planetary atmosphere the compressible convective flow of vorticity represents a strong nonlinearity able to drive the fluid toward a quasi-coherent vortical pattern. This is similar to the highly organised motion generated at relaxation in ideal Euler fluids. The problem of the atmosphere is however fundamentally different since now there is an intrinsic length, the Rossby radius. Within the Charney Hasegawa Mima model it has been derived a differential equation governing the stationary, two-dimensional, highly organised vortical flows in the planetary atmosphere. We present results of a numerical study of this differential equation. The most characteristic solution shows a strong similarity with the morphology of a tropical cyclone. Quantitative comparisons are also favorable and several relationships can be derived connecting the characteristic physical parameters of the tropical cyclone: the radius of the eye-wall, the maximum azimuthal velocity and the radial extension of the vortex.
The special problem of transport in 2-dimensional divergence-free stochastic velocity fields is studied by developing a statistical approach, the nested subensemble method. The nonlinear process of trapping determined by such fields generates trajectory structures whose statistical characteristics are determined. These structures strongly influence the transport.