468 research outputs found
Eigenoscillations of the Differentially Rotating Sun: I. 22-year, 4000-year, and quasi-biennial modes
Retrograde waves with frequencies much lower than the rotation frequency
become trapped in the solar radiative interior. The eigenfunctions of the
compressible, nonadiabatic, Rossby-like modes (-mechanism and
radiative losses taken into account) are obtained by an asymptotic method
assuming a very small latitudinal gradient of rotation, without an arbitrary
choice of other free parameters. An integral dispersion relation for the
complex eigenfrequencies is derived as a solution of the boundary value
problem. The discovered resonant cavity modes (called R-modes) are
fundamentally different from the known r-modes: their frequencies are functions
of the solar interior structure, and the reason for their existence is not
related to geometrical effects. The most unstable R-modes are those with
periods of 1--3 yr, 18--30 yr, and 1500--20000 yrs; these three separate period
ranges are known from solar and geophysical data. The growing times of those
modes which are unstable with respect to the -mechanism are and years, respectively. The amplitudes of the R-modes are
growing towards the center of the Sun. We discuss some prospects to develop the
theory of R-modes as a driver of the dynamics in the convective zone which
could explain, e.g., observed short-term fluctuations of rotation, a control of
the solar magnetic cycle, and abrupt changes of terrestrial climate in the
past.Comment: 17 pages, 6 figures, To appear in Astronomy and Astrophysic
Generation of internal gravity waves by penetrative convection
The rich harvest of seismic observations over the past decade provides
evidence of angular momentum redistribution in stellar interiors that is not
reproduced by current evolution codes. In this context, transport by internal
gravity waves can play a role and could explain discrepancies between theory
and observations. The efficiency of the transport of angular momentum by waves
depends on their driving mechanism. While excitation by turbulence throughout
the convective zone has already been investigated, we know that penetrative
convection into the stably stratified radiative zone can also generate internal
gravity waves. Therefore, we aim at developing a semianalytical model to
estimate the generation of IGW by penetrative plumes below an upper convective
envelope. We derive the wave amplitude considering the pressure exerted by an
ensemble of plumes on the interface between the radiative and convective zones
as source term in the equation of momentum. We consider the effect of a thermal
transition from a convective gradient to a radiative one on the transmission of
the wave into the radiative zone. The plume-induced wave energy flux at the top
of the radiative zone is computed for a solar model and is compared to the
turbulence-induced one. We show that, for the solar case, penetrative
convection generates waves more efficiently than turbulence and that
plume-induced waves can modify the internal rotation rate on shorter time
scales. We also show that a smooth thermal transition significatively enhances
the wave transmission compared to the case of a steep transition. We conclude
that driving by penetrative convection must be taken into account as much as
turbulence-induced waves for the transport of internal angular momentum.Comment: Accepted for publication in A&A, 21 page
Mixing in thermally stratified nonlinear spin-up with sources and sinks
Stratified spin-up experiments in enclosed cylinders have reported the
presence of small pockets of well-mixed fluids but quantitative measurements of
the mixedness of the fluid has been lacking. Previous numerical simulations
have not addressed these measurements. Here we present numerical simulations
that address how the combined effect of spin-up and thermal boundary conditions
enhances or hinders mixing of a fluid in a cylinder. Measurements of efficiency
of mixing are based on the variance of temperature and explained in terms of
the potential energy available. The numerical simulations of the Navier--Stokes
equations for the problem with different sets of thermal boundary conditions at
the horizontal walls helped shed some light on the physical mechanisms of
mixing, for which a clear explanation was lacking.Comment: Submitted to Physics of Fluids, 9 figure
An applied mathematical view of meteorological modeling
The earthâs atmosphere is of overwhelming complexity due to a rich interplay between
a large number of phenomena interacting on very diverse length and time
scales. There are mathematical equation systems which, in principle, provide a
comprehensive description of this system. Yet, exact or accurate approximate solutions
to these equations covering the full range of complexities they allow for are not
available. As a consequence, one of the central themes of theoretical meteorology
is the development of simplified model equations that are amenable to analysis and
computational approximate solution, while still faithfully representing an important
subset of the observed phenomena
On the emergence of helicity in rotating stratified turbulence
We perform numerical simulations of decaying rotating stratified turbulence
and show, in the Boussinesq framework, that helicity (velocity-vorticity
correlation), as observed in super-cell storms and hurricanes, is spontaneously
created due to an interplay between buoyancy and rotation common to large-scale
atmospheric and oceanic flows. Helicity emerges from the joint action of eddies
and of inertia-gravity waves (with inertia and gravity with respective
associated frequencies and ), and it occurs when the waves are
sufficiently strong. For the amount of helicity produced is correctly
predicted by a quasi-linear balance equation. Outside this regime, and up to
the highest Reynolds number obtained in this study, namely ,
helicity production is found to be persistent for as large as , and for and respectively as large as and
.Comment: 10 pages, 5 figure
Ribbon Turbulence
We investigate the non-linear equilibration of a two-layer quasi-geostrophic
flow in a channel forced by an imposed unstable zonal mean flow, paying
particular attention to the role of bottom friction. In the limit of low bottom
friction, classical theory of geostrophic turbulence predicts an inverse
cascade of kinetic energy in the horizontal with condensation at the domain
scale and barotropization on the vertical. By contrast, in the limit of large
bottom friction, the flow is dominated by ribbons of high kinetic energy in the
upper layer. These ribbons correspond to meandering jets separating regions of
homogenized potential vorticity. We interpret these result by taking advantage
of the peculiar conservation laws satisfied by this system: the dynamics can be
recast in such a way that the imposed mean flow appears as an initial source of
potential vorticity levels in the upper layer. The initial baroclinic
instability leads to a turbulent flow that stirs this potential vorticity field
while conserving the global distribution of potential vorticity levels.
Statistical mechanical theory of the 1-1/2 layer quasi-geostrophic model
predict the formation of two regions of homogenized potential vorticity
separated by a minimal interface. We show that the dynamics of the ribbons
results from a competition between a tendency to reach this equilibrium state,
and baroclinic instability that induces meanders of the interface. These
meanders intermittently break and induce potential vorticity mixing, but the
interface remains sharp throughout the flow evolution. We show that for some
parameter regimes, the ribbons act as a mixing barrier which prevent relaxation
toward equilibrium, favouring the emergence of multiple zonal jets
Mathematical Theory and Modelling in Atmosphere-Ocean Science
Mathematical theory and modelling in atmosphere-ocean science combines a broad range of advanced mathematical and numerical techniques and research directions. This includes the asymptotic analysis of multiscale systems, the deterministic and stochastic modelling of sub-grid-scale processes, and the numerical analysis of nonlinear PDEs over a broad range of spatial and temporal scales. This workshop brought together applied mathematicians and experts in the disciplinary fields of meteorology and oceanography for a wide-ranging exchange of ideas and results in this area with the aim of fostering fundamental interdisciplinary work in this important science area
The stability of a canonical front
The stability of a geostrophic frontal current of constant slope over a stratified ocean is investigated using asymptotic techniques for large horizontal wavenumber and a small Burger number. The front is called canonical because it should approximate the edges of eddies or boundary currents. Results show that the front is unstable for an along the front wavenumber greater than f/V0 where V0 is the current velocity. But the instability is confined to a region near the vertex of the front of horizontal extent 0(V0/f). The flow becomes more unstable for increasing wavenumber and it is speculated that this region near the vertex will be strongly mixed, rounding off the sharp vertex of the steady state flow. There will be strong internal wave propagation from the interface of this region into the ocean when the frequency is greater than f
Notes on the 1965 Summer Study Program in Geophysical Fluid Dynamics at the Woods Hole Oceanographic Institution
Originally issued as Reference No. 65-51, series later renamed WHOI-.National Science Foundatio
Dynamics of the outer planets : 1992 Summer Study Program in Geophysical Fluid Dynamics
The topic this summer was "The Dynamics of the Outer Planets." Andrew Ingersoll gave an excellent review of the current
understanding of the strcture of the atmospheres of Jupiter, Neptune, Saturn, and Uranus. He presented the flow structures inferred
from the information gathered by the Voyager probes and other observations. The models of the circulations of the interior and of
the weather layer - the jets and vortices that we see in the images - were discussed. Jun-Ichi Yano gave further discussions on
vortex dynamics in the lab, analytical, and numerical models as applied to the outer planets. Finally, Andy returned with a
discussion of thin atmospheres (some so thin that they disappear at night) and new approaches to the dynamics of the interiors.
These lectures provided a thorough background in both the data and the theory.
As usual, we had talks (or what are sometimes called interactive seminars!) from many visitors during the summer, some
directly related to the main topic and others covering other new research in geophysical fluid dynamics. From these, the fellows
and staff found new aras for collaborative research and new ideas which they may explore after the summer.
Finally, the summer was completed with talks from the fellows on their individual research during the summer. These reports
reflect the thought and energy that went into learning new topics and formulating new problems. We look forward to seeing fuller
versions of these in journal articles.
We gratefully acknowledge the support of the National Science Foundation and the Office of Naval Research. The assistance of
Jake Peirson and Barbara Ewing-DeRemer, made the summer, once again, pleasant and easy for all.Funding was provided by the National Science Foundation
under Grant No. OCE8901012
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