A type of eddy-damped quasinormal Markovian (EDQNM) closure is shown to be potentially nonrealizable in the presence linear wave phenomena. This statistical results from application a fluctuation–dissipation (FD) ansatz direct-interaction approximation (DIA); unlike phenomenological formulations EDQNM, both frequency and damping rate are renormalized. violation realizability can have serious physical consequences, including prediction negative or even divergent energies. new approximation,...

We study quasisteady inverse cascades in unbounded and bounded two-dimensional turbulence driven by time-independent injection dissipated molecular viscosity. It is shown that an cascade carries only a fraction r of the energy input to largest scales requires enstrophy-range spectrum be steeper than k(-5) (ruling out direct cascade) unless 1-r<<1. A presence virtually all (1-r<<1). These facts underlie robustness Kolmogorov-Kraichnan k(-5/3) cascade, which readily observable numerical...

The test-field model is shown to be potentially nonrealizable in the presence of linear waves such as those frequently encountered models plasma and geophysical turbulence. A new statistical closure, realizable (RTFM), proposed a remedy. Both damping rate frequency are renormalized account for nonlinear shifts. Like Markovian closure (RMC), RTFM based on modified fluctuation-dissipation ansatz. Numerical solutions RTFM, RMC, direct-interaction approximation Hasegawa–Mima equation presented;...

Resistive drift-wave turbulence in a slab geometry is studied by statistical closure methods and direct numerical simulations. The two-field Hasegawa–Wakatani (HW) fluid model, which evolves the electrostatic potential plasma density self-consistently, paradigm for understanding generic nonlinear behavior of multiple-field turbulence. A gyrokinetic derivation HW model sketched. recently developed Realizable Markovian Closure (RMC) applied to model; spectral properties, energy transfers,...

Inertial-range scaling laws for two- and three-dimensional turbulence are re-examined within a unified framework. A new correction to Kolmogorov's $k^{-5/3}$ is derived the energy inertial range. related modification found Kraichnan's logarithmically corrected two-dimensional enstrophy-range law that removes its unexpected divergence at injection wavenumber. The significance of these corrections illustrated with steady-state spectra from recent high-resolution closure computations....

Classically, the net action of nonlinear turbulent processes is interpreted as either a direct or inverse cascade. However, in nonuniform/shear flows dominant process redistribution over wave number angle perturbation spatial Fourier harmonics. We call this transverse (NTR). This phenomenon demonstrated for simple two-dimensional constant shear (non-normal) flow by numerically simulating dynamics coherent and stochastic vortical perturbations flow. NTR general feature that should manifest...

Algorithms are developed for calculating dealiased linear convolution sums without the expense of conventional zero-padding or phase-shift techniques. For one-dimensional in-place convolutions, memory requirements identical with technique, important distinction that additional work need not be contiguous input data. This decoupling data and arrays dramatically reduces computation time required to evaluate higher-dimensional convolutions. The technique also allows one dealias higher-order...

Traditional explicit numerical discretizations of conservative systems generically predict artificial secular drifts any nonlinear invariants. In this work we present a general approach for developing nontraditional algorithms that conserve such invariants exactly. We illustrate the method by applying it to three-wave truncation Euler equations, Lotka--Volterra predator-prey model, and Kepler problem. The ideas are discussed in context symplectic (phase--space-conserving) integration methods...

.Efficient algorithms based on the fast Fourier transform are developed for computing linear convolutions. A hybrid approach is described that combines conventional practice of explicit dealiasing (explicitly padding input data with zeros) and implicit (mathematically accounting these zero values). The new generalizes to arbitrary ratios includes as a special case. Unlike existing implementations dealiasing, tailors its subtransform sizes convolution geometry. Multidimensional convolutions...

Abstract In addition to conserving energy and enstrophy, the nonlinear terms of two-dimensional incompressible Navier–Stokes equation are well known conserve global integral any continuously differentiable function scalar vorticity field. However, phenomenological role these additional inviscid invariants, including issue as whether they cascade large or small scales, is an open question. this work, well-resolved implicitly dealiased pseudospectral simulations suggest that fourth power...

A method is described for predicting statistical properties of turbulence. Collections Fourier amplitudes are represented by nonuniformly spaced modes with enhanced coupling coefficients. The statistics the full dynamics can be recovered from time-averaged predictions reduced model. Liouville theorem leads to inviscid equipartition solutions. Excellent agreement obtained two-dimensional forced-dissipative pseudospectral simulations. For enstrophy cascade, logarithmic corrections high-order...

Explaining anomalous plasma transport in magnetic confinement devices requires a deeper understanding of the underlying turbulent processes than presently exists. In this work, Markovian closures are built by imposing constraints realizability, conservation quadratic invariants, and covariance to arbitrary linear transformations. One such closure is solved numerically. The results compare favorably data available from numerical simulations.

Models presented in several recent papers [1–3] dealing with particle transport by, and deposition from, bottom gravity currents produced by the sudden release of dilute, well‐mixed fixed‐volume suspensions have been relatively successful duplicating experimentally observed long‐time, distal, areal density deposit on a rigid horizontal bottom. These models, however, fail their ability to capture proximal pattern its pronounced dip region initially occupied suspension equally local maximum at...

We study energy transfer in unbounded Charney-Hasegawa-Mima and surface quasigeostrophic turbulence. The possible inverse-cascading quantities these systems are, respectively, I identical with integral ( infinity )(0)k(-2)E(k) dk J )(0)k(-1)E(k) dk, where E(k) is the kinetic spectrum. supposed direct-cascading for both Navier-Stokes turbulence are shown to be bounded. derive a constraint on system.