Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Initialization and the quasi-geostrophic slow manifold   Atmospheric dynamics span a range of time-scales. The projection of measured
data to a slow manifold, ${\cal M}$, removes fast gravity waves from the
initial state for numerical simulations of the atmosphere. We explore further
the slow manifold for a simple atmospheric model introduced by Lorenz and
anticipate that our results will relevant to the vastly more detailed dynamics
of atmospheres and oceans. Within the dynamics of the Lorenz model, we make
clear the relation between a slow manifold $\cal M$ and the ``slowest invariant
manifold'' ({\SIM}), which was constructed by Lorenz in order to avoid the
divergence of approximation schemes for $\cal M$. These manifolds are shown to
be identical to within exponentially small terms, and so the {\SIM} in fact
shares the asymptotic nature of $\cal M$. We also investigate the issue of
balancing initial data in order to remove gravity waves. This is a question of
how to compute an ``initialized'' point on $\cal M$ whose subsequent evolution
matches that from the measured initial data that in general lie off $\cal M$.
We propose a choice based on the intuitive idea that the initialization
procedure should not significantly alter the forecast. Numerical results
demonstrate the utility of our initialization scheme. The normal form for
Lorenz' atmospheric model shows clearly how to separate the dynamics of the
different atmospheric waves. However, its construction demonstrates that {\em
any} initialization procedure must eventually alter the forecast--the
time-scale of the divergence between the initialized and the uninitialized
solutions is inevitable and is inversely proportional to the square of initial
level of gravity-wave activity.

3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an
25
The categories of this paper are: patt-sol
27
The categories of this paper are: comp-gas
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ
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The categories of this paper are: astro-ph
14
The categories of this paper are: math-ph
13
The categories of this paper are: quant-ph
23
The categories of this paper are: solv-int
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The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys
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The categories of this paper are: math
34
The categories of this paper are: chem-ph
15
The categories of this paper are: nucl-ex