130 research outputs found
Generalized Action Invariants for Drift Waves-Zonal Flow Systems
Generalized action invariants are identified for various models of drift wave turbulence in the presence of the mean shear flow. It is shown that the wave kinetic equation describing the interaction of the small scale turbulence and large scale shear flow can be naturally written in terms of these invariants. Unlike the wave energy, which is conserved as a sum of small- and large- scale components, the generalized action invariant is shown to correspond to a quantity which is conserved for the small scale component alone. This invariant can be used to construct canonical variables leading to a different definition of the wave action (as compared to the case without shear flow). It is suggested that these new canonical action variables form a natural basis for the description of the drift wave turbulence with a mean shear flow
The effective equation method
In this chapter we present a general method of constructing the effective
equation which describes the behaviour of small-amplitude solutions for a
nonlinear PDE in finite volume, provided that the linear part of the equation
is a hamiltonian system with a pure imaginary discrete spectrum. The effective
equation is obtained by retaining only the resonant terms of the nonlinearity
(which may be hamiltonian, or may be not); the assertion that it describes the
limiting behaviour of small-amplitude solutions is a rigorous mathematical
theorem. In particular, the method applies to the three-- and four--wave
systems. We demonstrate that different possible types of energy transport are
covered by this method, depending on whether the set of resonances splits into
finite clusters (this happens, e.g. in case of the Charney-Hasegawa-Mima
equation), or is connected (this happens, e.g. in the case of the NLS equation
if the space-dimension is at least two). For equations of the first type the
energy transition to high frequencies does not hold, while for equations of the
second type it may take place. In the case of the NLS equation we use next some
heuristic approximation from the arsenal of wave turbulence to show that under
the iterated limit "the volume goes to infinity", taken after the limit "the
amplitude of oscillations goes to zero", the energy spectrum of solutions for
the effective equation is described by a Zakharov-type kinetic equation.
Evoking the Zakharov ansatz we show that stationary in time and homogeneous in
space solutions for the latter equation have a power law form. Our method
applies to various weakly nonlinear wave systems, appearing in plasma,
meteorology and oceanology
A scaling theory of 3D spinodal turbulence
A new scaling theory for spinodal decomposition in the inertial hydrodynamic
regime is presented. The scaling involves three relevant length scales, the
domain size, the Taylor microscale and the Kolmogorov dissipation scale. This
allows for the presence of an inertial "energy cascade", familiar from theories
of turbulence, and improves on earlier scaling treatments based on a single
length: these, it is shown, cannot be reconciled with energy conservation. The
new theory reconciles the t^{2/3} scaling of the domain size, predicted by
simple scaling, with the physical expectation of a saturating Reynolds number
at late times.Comment: 5 pages, no figures, revised version submitted to Phys Rev E Rapp
Comm. Minor changes and clarification
Extending the Langevin model to variable-density pressure-gradient-driven turbulence
We extend the generalized Langevin model, originally developed for the
Lagrangian fluid particle velocity in constant-density shear-driven turbulence,
to variable-density (VD) pressure-gradient-driven flows. VD effects due to
non-uniform mass concentrations (e.g. mixing of different species) are
considered. In the extended model large density fluctuations leading to large
differential fluid accelerations are accounted for. This is an essential
ingredient to represent the strong coupling between the density and velocity
fields in VD hydrodynamics driven by active scalar mixing. The small scale
anisotropy, a fundamentally "non-Kolmogorovian" feature of
pressure-gradient-driven flows, is captured by a tensorial stochastic diffusion
term. The extension is so constructed that it reduces to the original Langevin
model in the limit of constant density. We show that coupling a Lagrangian
mass-density particle model to the proposed extended velocity equation results
in a statistical representation of VD turbulence that has important benefits.
Namely, the effects of the mass flux and the specific volume, both essential in
the prediction of VD flows, are retained in closed form and require no explicit
closure assumptions. The paper seeks to describe a theoretical framework
necessary for subsequent applications. We derive the rigorous mathematical
consequences of assuming a particular functional form of the stochastic
momentum equation coupled to the stochastic density field in VD flows. A
previous article discussed VD mixing and developed a stochastic Lagrangian
model equation for the mass-density. Second in the series, this article
develops the momentum equation for VD hydrodynamics. A third, forthcoming paper
will combine these ideas on mixing and hydrodynamics into a comprehensive
framework: it will specify a model for the coupled problem and validate it by
computing a Rayleigh-Taylor flow.Comment: Accepted in Journal of Turbulence, Jan 7, 201
Exact Resummations in the Theory of Hydrodynamic Turbulence: I The Ball of Locality and Normal Scaling
This paper is the first in a series of three papers that aim at understanding
the scaling behaviour of hydrodynamic turbulence. We present in this paper a
perturbative theory for the structure functions and the response functions of
the hydrodynamic velocity field in real space and time. Starting from the
Navier-Stokes equations (at high Reynolds number Re) we show that the standard
perturbative expansions that suffer from infra-red divergences can be exactly
resummed using the Belinicher-L'vov transformation. After this exact (partial)
resummation it is proven that the resulting perturbation theory is free of
divergences, both in large and in small spatial separations. The hydrodynamic
response and the correlations have contributions that arise from mediated
interactions which take place at some space- time coordinates. It is shown that
the main contribution arises when these coordinates lie within a shell of a
"ball of locality" that is defined and discussed. We argue that the real
space-time formalism developed here offers a clear and intuitive understanding
of every diagram in the theory, and of every element in the diagrams. One major
consequence of this theory is that none of the familiar perturbative mechanisms
may ruin the classical Kolmogorov (K41) scaling solution for the structure
functions. Accordingly, corrections to the K41 solutions should be sought in
nonperturbative effects. These effects are the subjects of papers II and III in
this series, that will propose a mechanism for anomalous scaling in turbulence,
which in particular allows multiscaling of the structure functions.Comment: PRE in press, 18 pages + 6 figures, REVTeX. The Eps files of figures
will be FTPed by request to [email protected]
Anomalous Scaling of Structure Functions and Dynamic Constraints on Turbulence Simulations
The connection between anomalous scaling of structure functions
(intermittency) and numerical methods for turbulence simulations is discussed.
It is argued that the computational work for direct numerical simulations (DNS)
of fully developed turbulence increases as , and not as
expected from Kolmogorov's theory, where is a large-scale Reynolds number.
Various relations for the moments of acceleration and velocity derivatives are
derived. An infinite set of exact constraints on dynamically consistent subgrid
models for Large Eddy Simulations (LES) is derived from the Navier-Stokes
equations, and some problems of principle associated with existing LES models
are highlighted.Comment: 18 page
Dispersion and collapse in stochastic velocity fields on a cylinder
The dynamics of fluid particles on cylindrical manifolds is investigated. The
velocity field is obtained by generalizing the isotropic Kraichnan ensemble,
and is therefore Gaussian and decorrelated in time. The degree of
compressibility is such that when the radius of the cylinder tends to infinity
the fluid particles separate in an explosive way. Nevertheless, when the radius
is finite the transition probability of the two-particle separation converges
to an invariant measure. This behavior is due to the large-scale
compressibility generated by the compactification of one dimension of the
space
Gemini Observations of Disks and Jets in Young Stellar Objects and in Active Galaxies
We present first results from the Near-infrared Integral Field Spectrograph
(NIFS) located at Gemini North. For the active galaxies Cygnus A and Perseus A
we observe rotationally-supported accretion disks and adduce the existence of
massive central black holes and estimate their masses. In Cygnus A we also see
remarkable high-excitation ionization cones dominated by photoionization from
the central engine. In the T-Tauri stars HV Tau C and DG Tau we see
highly-collimated bipolar outflows in the [Fe II] 1.644 micron line, surrounded
by a slower molecular bipolar outflow seen in the H_2 lines, in accordance with
the model advocated by Pyo et al. (2002).Comment: Invited paper presented at the 5th Stromlo Symposium. 9 pages, 7
figures. Accepted for publication in Astrophysics & Space Scienc
Anomalous scaling of a passive scalar in the presence of strong anisotropy
Field theoretic renormalization group and the operator product expansion are
applied to a model of a passive scalar field, advected by the Gaussian strongly
anisotropic velocity field. Inertial-range anomalous scaling behavior is
established, and explicit asymptotic expressions for the n-th order structure
functions of scalar field are obtained; they are represented by superpositions
of power laws with nonuniversal (dependent on the anisotropy parameters)
anomalous exponents. In the limit of vanishing anisotropy, the exponents are
associated with tensor composite operators built of the scalar gradients, and
exhibit a kind of hierarchy related to the degree of anisotropy: the less is
the rank, the less is the dimension and, consequently, the more important is
the contribution to the inertial-range behavior. The leading terms of the even
(odd) structure functions are given by the scalar (vector) operators. For the
finite anisotropy, the exponents cannot be associated with individual operators
(which are essentially ``mixed'' in renormalization), but the aforementioned
hierarchy survives for all the cases studied. The second-order structure
function is studied in more detail using the renormalization group and
zero-mode techniques.Comment: REVTEX file with EPS figure
Revisiting the Local Scaling Hypothesis in Stably Stratified Atmospheric Boundary Layer Turbulence: an Integration of Field and Laboratory Measurements with Large-eddy Simulations
The `local scaling' hypothesis, first introduced by Nieuwstadt two decades
ago, describes the turbulence structure of stable boundary layers in a very
succinct way and is an integral part of numerous local closure-based numerical
weather prediction models. However, the validity of this hypothesis under very
stable conditions is a subject of on-going debate. In this work, we attempt to
address this controversial issue by performing extensive analyses of turbulence
data from several field campaigns, wind-tunnel experiments and large-eddy
simulations. Wide range of stabilities, diverse field conditions and a
comprehensive set of turbulence statistics make this study distinct
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