Title: The nonlinear dynamics of large-scale atmospheric flows.
course will first introduce the basic laws that govern atmospheric
on the planetary scale, i.e., the motions of a
fluid in the presence of rotation and stratification. Next,
evidence will be described for persistent and recurrent
departures from the climatological mean of these motions
and multiple regimes of atmospheric flows will be modeled.
oscillatory behavior of such flows - on the time scale
of weeks-to-months - will be described and analyzed. The dynamical
approach to the study of low-frequency variability of the
atmosphere will be used throughout to analyze the models
and their solutions. The course will conclude with a
of perspectives for extended-range predictability of
atmospheric motions in mid-latitudes.
Title: Transport, stirring and mixing in atmospheric chemistry
lectures will introduce fundamental ideas on transport, stirring
and mixing, including
relevant mathematical models. The extent
to which transport and mixing in the atmosphere is captured
the `large-scale flow' paradigm (chaotic advection and
Batchelor turbulence) will be discussed. Potential vorticity
introduced as a dynamical tracer, allowing description of
the dynamics of the atmosphere in terms of transport and
mixing. The structure
of transport barriers and mixing regions in kinematic
and dynamically consistent flows and theories for tracer
in two- dimensional and `layerwise two-dimensional' flows
will be described.
These ideas will then be used to describe different aspects
of the observed structure of the atmosphere,
including transport and mixing of chemical
species in troposphere and stratosphere and a dynamical
theory for the structure of the extratropical troposphere
ocean is a highly inhomogeneous medium, characterized by
spatial and temporal contrasts in temperature
and salinity, as well as in chemical composition
and in the distribution of biological agents.
The inhomogeneity of the ocean, however,
is not static, but follows from a dynamical equilibrium,
contrasts are permanently being created and attenuated.
Local processes that generate contrasts include evaporation
freezing and melting of sea--ice, river inflows, and
volcanic activity. Attenuation is mainly due to mixing processes,
such as turbulent diffusion, breaking waves, and
by surface winds, ocean currents, and planetary tides
interacting with the ocean's bottom and lateral morphology.
equilibrium emerging from the balance of these
processes is a determining factor to the Earth's climate:
changes in the properties of the upper layers of the
ocean, in particular, can lead to significant variations
of its ice--coverage,
of local patterns of convection and rain and, ultimately,
to dramatic changes in the global patterns of surface temperature,
humidity and prevailing winds.
Yet the quantification, and even the identification of some of
the critical processes involved in this dynamical balance, remain to a large degree incomplete. The mixing side of the
balance is particularly elusive, due to its vast distribution
over whole basins, to the difficulties inherent
to its observation and measurement, to its highly anisotropic
nature, and to the incompletely understood physics of
its underlying processes, such as turbulent diffusion, shear
and convective instabilities, and wave overturning.
State-of-the-art computational ocean circulation models
typically parameterize these processes, introducing empirical
closures designed to fit as well as possible the [sparse]
available experimental and observational data.
Such an approach, driven by necessity,
may yield large errors in the prediction
of climatic changes, since the adjustment
of parameters to match features of today's climate may
fail to capture those of tomorrow's.
This course will describe
various approaches to the mathematical modeling
of ocean mixing. These include models of nonlinear turbulent
diffusion, mixing by internal breaking waves, and descriptions
of mixing based on statistical physics.