Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Exact instantaneous optimals in the non-geostrophic Eady problem and the
  detrimental effects of discretization   We derive exact analytical expressions for flow configurations that optimize
the instantaneous growth rate of energy in the linear Eady problem, along with
the associated growth rates. These optimal perturbations are relevant linear
stability analysis, but, more importantly, they are relevant for understanding
the energetics of fully nonlinear baroclinic turbulence. The optimal
perturbations and their growth rates are independent of the Richardson number.
The growth rates of the optimal perturbations grow linearly as the horizontal
wavelength of the perturbation decreases. Perturbation energy growth at large
scales is driven by extraction of potential energy from the mean flow, while at
small scales it is driven by extraction of kinetic energy from the mean shear.
We also analyze the effect of spatial discretization on the optimal
perturbations and their growth rates. A second order energy-conserving
discretization on the Arakawa B grid generally has too-weak growth rates at
small scales and is less accurate than two second order discretizations on the
Arakawa C grid. The two C grid discretizations, one that conserves energy and
another that conserves both energy and enstrophy, yield very similar optimal
perturbation growth rates that are significantly more accurate than the B grid
discretization at small scales.

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The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
1
The categories of this paper are: cs
26
The categories of this paper are: bayes-an
31
The categories of this paper are: ao-sci
13
The categories of this paper are: quant-ph
33
The categories of this paper are: plasm-ph
21
The categories of this paper are: adap-org
32
The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
5
The categories of this paper are: gr-qc
25
The categories of this paper are: patt-sol
24
The categories of this paper are: dg-ga
27
The categories of this paper are: comp-gas
19
The categories of this paper are: eess