Scale Separation In Space Research Articles

Controlling excitable wave behaviors through the tuning of three parameters.

Excitable systems are a class of dynamical systems that can generate self-sustaining waves of activity. These waves are known to manifest differently under diverse conditions, whereas some travel as planar or radial waves, and others evolve into rotating spirals. Excitable systems can also form stationary stable patterns through standing waves. Under certain conditions, these waves are also known to be reflected at no-flux boundaries. Here, we review the basic characteristics of these four entities: traveling, rotating, standing and reflected waves. By studying their mechanisms of formation, we show how through manipulation of three critical parameters: time-scale separation, space-scale separation and threshold, we can interchangeably control the formation of all the aforementioned wave types.

Towards Adaptive Grids for Atmospheric Boundary-Layer Simulations

We present a proof-of-concept for the adaptive mesh refinement method applied to atmospheric boundary-layer simulations. Such a method may form an attractive alternative to static grids for studies on atmospheric flows that have a high degree of scale separation in space and/or time. Examples include the diurnal cycle and a convective boundary layer capped by a strong inversion. For such cases, large-eddy simulations using regular grids often have to rely on a subgrid-scale closure for the most challenging regions in the spatial and/or temporal domain. Here we analyze a flow configuration that describes the growth and subsequent decay of a convective boundary layer using direct numerical simulation (DNS). We validate the obtained results and benchmark the performance of the adaptive solver against two runs using fixed regular grids. It appears that the adaptive-mesh algorithm is able to coarsen and refine the grid dynamically whilst maintaining an accurate solution. In particular, during the initial growth of the convective boundary layer a high resolution is required compared to the subsequent stage of decaying turbulence. More specifically, the number of grid cells varies by two orders of magnitude over the course of the simulation. For this specific DNS case, the adaptive solver was not yet more efficient than the more traditional solver that is dedicated to these types of flows. However, the overall analysis shows that the method has a clear potential for numerical investigations of the most challenging atmospheric cases.

Quantum-Phase-Field Concept of Matter: Emergent Gravity in the Dynamic Universe

Abstract A monistic framework is set up where energy is the only fundamental substance. Different states of energy are ordered by a set of scalar fields. The dual elements of matter, mass and space, are described as volume- and gradient-energy contributions of the set of fields, respectively. Time and space are formulated as background-independent dynamic variables. The evolution equations of the body of the universe are derived from the first principles of thermodynamics. Gravitational interaction emerges from quantum fluctuations in finite space. Application to a large number of fields predicts scale separation in space and repulsive action of masses distant beyond a marginal distance. The predicted marginal distance is compared to the size of the voids in the observable universe.

Modeling spatio‐temporal nonlocality in mean‐field dynamos

AbstractWhen scale separation in space or time is poor, the mean‐field α effect and turbulent diffusivity have to be replaced by integral kernels by which the dependence of the mean electromotive force on the mean magnetic field becomes nonlocal. Earlier work in computing these kernels using the test‐field method is now generalized to the case in which both spatial and temporal scale separations are poor. The approximate form of the kernel for isotropic stationary turbulence is such that it can be treated in a straightforward manner by solving a partial differential equation for the mean electromotive force. The resulting mean‐field equations are solved for oscillatory α –shear dynamos as well as α2 dynamos with α linearly depending on position, which makes this dynamo oscillatory, too. In both cases, the critical values of the dynamo number is lowered due to spatio‐temporal nonlocality.When scale separation in space or time is poor, the mean‐field α effect and turbulent diffusivity have to be replaced by integral kernels by which the dependence of the mean electromotive force on the mean magnetic field becomes nonlocal. Earlier work in computing these kernels using the test‐field method is now generalized to the case in which both spatial and temporal scale separations are poor. The approximate form of the kernel for isotropic stationary turbulence is such that it can be treated in a straightforward manner by solving a partial differential equation for the mean electromotive force. The resulting mean‐field equations are solved for oscillatory α –shear dynamos as well as α2 dynamos

Direct multiscale coupling of a transport code to gyrokinetic turbulence codes

Direct coupling between a transport solver and local, nonlinear gyrokinetic calculations using the multiscale gyrokinetic code TRINITY [M. Barnes, “TRINITY: A unified treatment of turbulence, transport, and heating in magnetized plasmas,” Ph.D. thesis, University of Maryland, 2008 (eprint arXiv:0901.2868)] is described. The coupling of the microscopic and macroscopic physics is done within the framework of multiscale gyrokinetic theory, of which we present the assumptions and key results. An assumption of scale separation in space and time allows for the simulation of turbulence in small regions of the space-time grid, which are embedded in a coarse grid on which the transport equations are implicitly evolved. This leads to a reduction in computational expense of several orders of magnitude, making first-principles simulations of the full fusion device volume over the confinement time feasible on current computing resources. Numerical results from TRINITY simulations are presented and compared with experimental data from JET [M. Keilhacker, Plasma Phys. Controlled Fusion 41, B1 (1999)] and ASDEX Upgrade [O. Gruber, Nucl. Fusion 47, S622 (2007)] plasmas.

Time Integration and Steady-State Continuation for 2d Lubrication Equations

Lubrication equations allow to describe many structurin processes of thin liquid films. We develop and apply numerical tools suitable for their analysis employing a dynamical systems approach. In particular, we present a time integration algorithm based on exponential propagation and an algorithm for steady-state continuation. In both algorithms a Cayley transform is employed to overcome numerical problems resulting from scale separation in space and time. An adaptive time-step allows to study the dynamics close to hetero- or homoclinic connections. The developed framework is employed on the one hand to analyse different phases of the dewetting of a liquid film on a horizontal homogeneous substrate. On the other hand, we consider the depinning of drops pinned by a wettability defect. Time-stepping and path-following are used in both cases to analyse steady-state solutions and their bifurcations as well as dynamic processes on short and long time-scales. Both examples are treated for two- and three-dimensional physical settings and prove that the developed algorithms are reliable and efficient for 1d and 2d lubrication equations, respectively.

Finite ion Larmour radius effects in the problem of zonal flow generation by kinetic drift-Alfvén turbulence

A theory of spontaneous generation of zonal flows by kinetic drift-Alfvén turbulence in the finite-pressure plasma (β > me/mi) is generalized to include the ion diamagnetic effects and the finite ion Larmour radius effects. In the framework of the corresponding set of generalized two-fluid magnetohydrodynamic equations and on the assumption of a distinct time- and space-scale separation between the turbulent oscillations and the zonal flow, a set of coupled equations is derived to describe the interaction between the turbulence and the flow, consisting of the evolution equation for the spectral function of turbulence and the mean-field equations for zonal flow. The possibility of spontaneous zonal flow generation by the kinetic drift-Alfvén turbulence is investigated in details in several cases. In the case of kinetic drift-Alfvén turbulence with the space scale of the order of the ion Larmour radius or below, the instability caused by the resonant interaction of the wave packet with the slow modulations of zonal flow has been analysed, and the criterion for the onset of the zonal flow instability has been derived. In the case of short-wavelength turbulence, two regimes are considered. It is shown, that, when the frequency of short-wavelength oscillations is close to the electron-drift frequency and the zonal perturbation of plasma density can be described by the Boltzmann Law, the instability criterion is a generalization of the previously obtained result to the case of non-equal temperatures of the ions and electrons. The new regime is found, in which the zonal perturbation of plasma density is negligible. The condition for the onset of resonant instability is obtained.

Diapycnal Mixing in the Ocean: Equations for Large-Scale Budgets

Abstract The Osborn–Cox model is the basis for the most direct estimates of the diapycnal diffusivity Kv for tracers. When used to interpret temperature variance dissipation measurements, it leads to Kv of O (10−5 m2 s−1) or less in the main thermocline. Large-scale diagnostic models typically match observations best using Kv of O (10−4 m2 s−1). The framework for describing diapycnal fluxes of tracers like temperature or density from large-scale property distributions is reexamined in an attempt to discover possible causes for this disagreement. Starting from basic thermodynamics principles, suitable tracer conservation equations are developed and the simplifications leading to conventional mean-field and variance balances are examined. It is argued that separation of mean and eddy fields is best based on long but finite time averages rather than the usual space-scale separation. Because this separation leads to a more vigorous eddy field than the usual procedure it is necessary to reexamine all conventio...