627 research outputs found
Interaction Between Convection and Pulsation
This article reviews our current understanding of modelling convection
dynamics in stars. Several semi-analytical time-dependent convection models
have been proposed for pulsating one-dimensional stellar structures with
different formulations for how the convective turbulent velocity field couples
with the global stellar oscillations. In this review we put emphasis on two,
widely used, time-dependent convection formulations for estimating pulsation
properties in one-dimensional stellar models. Applications to pulsating stars
are presented with results for oscillation properties, such as the effects of
convection dynamics on the oscillation frequencies, or the stability of
pulsation modes, in classical pulsators and in stars supporting solar-type
oscillations.Comment: Invited review article for Living Reviews in Solar Physics. 88 pages,
14 figure
Nonlinear diffusion equations for anisotropic MHD turbulence with cross-helicity
Nonlinear diffusion equations of spectral transfer are systematically derived
for anisotropic magnetohydrodynamics in the regime of wave turbulence. The
background of the analysis is the asymptotic Alfv\'en wave turbulence equations
from which a differential limit is taken. The result is a universal
diffusion-type equation in -space which describes in a simple way and
without free parameter the energy transport perpendicular to the external
magnetic field for transverse and parallel fluctuations. These
equations are compatible with both the thermodynamic equilibrium and the finite
flux spectra derived by Galtier et al. (2000); it improves therefore the model
built heuristically by Litwick \& Goldreich (2003) for which only the second
solution was recovered. This new system offers a powerful description of a wide
class of astrophysical plasmas with non-zero cross-helicity.Comment: 20 pages, 3 figure
Fast Macroscopic Forcing Method
The macroscopic forcing method (MFM) of Mani and Park and similar methods for
obtaining turbulence closure operators, such as the Green's function-based
approach of Hamba, recover reduced solution operators from repeated direct
numerical simulations (DNS). MFM has been used to quantify RANS-like operators
for homogeneous isotropic turbulence and turbulent channel flows. Standard
algorithms for MFM force each coarse-scale degree of freedom (i.e., degree of
freedom in the RANS space) and conduct a corresponding fine-scale simulation
(i.e., DNS), which is expensive. We combine this method with an approach
recently proposed by Sch\"afer and Owhadi (2023) to recover elliptic integral
operators from a polylogarithmic number of matrix-vector products. The
resulting Fast MFM introduced in this work applies sparse reconstruction to
expose local features in the closure operator and reconstructs this
coarse-grained differential operator in only a few matrix-vector products and
correspondingly, a few MFM simulations. For flows with significant nonlocality,
the algorithm first "peels" long-range effects with dense matrix-vector
products to expose a local operator. We demonstrate the algorithm's performance
for scalar transport in a laminar channel flow and momentum transport in a
turbulent one. For these, we recover eddy diffusivity operators at 1% of the
cost of computing the exact operator via a brute-force approach for the laminar
channel flow problem and 13% for the turbulent one. We observe that we can
reconstruct these operators with an increase in accuracy by about a factor of
100 over randomized low-rank methods. We glean that for problems in which the
RANS space is reducible to one dimension, eddy diffusivity and eddy viscosity
operators can be reconstructed with reasonable accuracy using only a few
simulations, regardless of simulation resolution or degrees of freedom.Comment: 16 pages, 10 figures. S. H. Bryngelson and F. Sch\"afer contributed
equally to this wor
Phase mixing vs. nonlinear advection in drift-kinetic plasma turbulence
A scaling theory of long-wavelength electrostatic turbulence in a magnetised,
weakly collisional plasma (e.g., ITG turbulence) is proposed, with account
taken both of the nonlinear advection of the perturbed particle distribution by
fluctuating ExB flows and of its phase mixing, which is caused by the streaming
of the particles along the mean magnetic field and, in a linear problem, would
lead to Landau damping. It is found that it is possible to construct a
consistent theory in which very little free energy leaks into high velocity
moments of the distribution function, rendering the turbulent cascade in the
energetically relevant part of the wave-number space essentially fluid-like.
The velocity-space spectra of free energy expressed in terms of Hermite-moment
orders are steep power laws and so the free-energy content of the phase space
does not diverge at infinitesimal collisionality (while it does for a linear
problem); collisional heating due to long-wavelength perturbations vanishes in
this limit (also in contrast with the linear problem, in which it occurs at the
finite rate equal to the Landau-damping rate). The ability of the free energy
to stay in the low velocity moments of the distribution function is facilitated
by the "anti-phase-mixing" effect, whose presence in the nonlinear system is
due to the stochastic version of the plasma echo (the advecting velocity
couples the phase-mixing and anti-phase-mixing perturbations). The partitioning
of the wave-number space between the (energetically dominant) region where this
is the case and the region where linear phase mixing wins its competition with
nonlinear advection is governed by the "critical balance" between linear and
nonlinear timescales (which for high Hermite moments splits into two
thresholds, one demarcating the wave-number region where phase mixing
predominates, the other where plasma echo does).Comment: 45 pages (single-column), 3 figures, replaced with version published
in JP
Cumulant expansions for atmospheric flows
The equations governing atmospheric flows are nonlinear. Consequently, the
hierarchy of cumulant equations is not closed. But because atmospheric flows
are inhomogeneous and anisotropic, the nonlinearity may manifest itself only
weakly through interactions of mean fields with disturbances such as thermals
or eddies. In such situations, truncations of the hierarchy of cumulant
equations hold promise as a closure strategy.
We review how truncations at second order can be used to model and elucidate
the dynamics of atmospheric flows. Two examples are considered. First, we study
the growth of a dry convective boundary layer, which is heated from below,
leading to turbulent upward energy transport and growth of the boundary layer.
We demonstrate that a quasilinear truncation of the equations of motion, in
which interactions of disturbances among each other are neglected but
interactions with mean fields are taken into account, can capture the growth of
the convective boundary layer even if it does not capture important turbulent
transport terms. Second, we study the evolution of two-dimensional large-scale
waves representing waves in Earth's upper atmosphere. We demonstrate that a
cumulant expansion truncated at second order (CE2) can capture the evolution of
such waves and their nonlinear interaction with the mean flow in some
circumstances, for example, when the wave amplitude is small enough or the
planetary rotation rate is large enough. However, CE2 fails to capture the flow
evolution when nonlinear eddy--eddy interactions in surf zones become
important. Higher-order closures can capture these missing interactions.
The results point to new ways in which the dynamics of turbulent boundary
layers may be represented in climate models, and they illustrate different
classes of nonlinear processes that can control wave dissipation and momentum
fluxes in the troposphere.Comment: 43 pages, 10 figures, accepted for publication in the New Journal of
Physic
Stochastic Models for the Kinematics of Moisture Transport and Condensation in Homogeneous Turbulent Flows
The transport of a condensing passive scalar is studied as a prototype model for the kinematics of moisture transport on isentropic surfaces. Condensation occurs whenever the scalar concentration exceeds a specified local saturation value. Since condensation rates are strongly nonlinear functions of moisture content, the mean moisture flux is generally not diffusive. To relate the mean moisture content, mean condensation rate, and mean moisture flux to statistics of the advecting velocity field, a one-dimensional stochastic model is developed in which the Lagrangian velocities of air parcels are independent Ornstein–Uhlenbeck (Gaussian colored noise) processes. The mean moisture evolution equation for the stochastic model is derived in the Brownian and ballistic limits of small and large Lagrangian velocity correlation time. The evolution equation involves expressions for the mean moisture flux and mean condensation rate that are nonlocal but remarkably simple. In a series of simulations of homogeneous two-dimensional turbulence, the dependence of mean moisture flux and mean condensation rate on mean saturation deficit is shown to be reproducible by the one-dimensional stochastic model, provided eddy length and time scales are taken as given. For nonzero Lagrangian velocity correlation times, condensation reduces the mean moisture flux for a given mean moisture gradient compared with the mean flux of a noncondensing scalar
Doctor of Philosophy
dissertationAccording to a UN report, more than 50% of the total world's population resides in urban areas and this fraction is increasing. Urbanization has a wide range of potential environmental impacts, including those related to the dispersion of potentially dangerous substances emitted from activities such as combustion, industrial processing or from deliberate harmful releases. This research is primarily focused on the investigation of various factors which contribute to the dispersion of certain classes of materials in a complex urban environment and improving both of the fundamental components of a fast response dispersion modeling system - wind modeling and dispersion modeling. Specifically, new empirical parameterizations have been suggested for an existing fast response wind model for street canyon flow fields. These new parameterizations are shown to produce more favorable results when compared with the experimental data. It is also demonstrated that the use of Graphics Processing Unit (GPU) technology can enhance the efficiency of an urban Lagrangian dispersion model and can achieve near real-time particle advection. The GPU also enables real-time visualizations which can be used for creating virtual urban environments to aid emergency responders. The dispersion model based on the GPU architecture relies on the so-called "simplified Langevin equations (SLEs)" for particle advection. The full or generalized form of the Langevin equations (GLEs) is known for its stiffness which tends to generate unstable modes in particle trajectory, where a particle may travel significant distances in a small time step
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