Normal Mode Spectra of Idealized Baroclinic Waves
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Date
2020-02-01
Authors
Ambacher, Matthew R.
Waite, Michael L
Journal Title
Journal ISSN
Volume Title
Publisher
AMS
Abstract
Normal modes are used to investigate the contributions of geostrophic vortices and inertia–gravity waves to
the energy spectrum of an idealized baroclinic wave simulation. The geostrophic and ageostrophic modal
spectra (GE and AE, respectively) are compared to the rotational and divergent kinetic energy (RKE and
DKE, respectively), which are often employed as proxies for vortex and wave energy. In our idealized f-plane
framework, the horizontal modes are Fourier, and the vertical modes are found by solving an appropriate
eigenvalue problem. For low vertical mode number n, both the GE and AE spectra are steep; however, for
higher n, while both spectra are shallow, the AE is shallower than the GE and the spectra cross. The AE
spectra are peaked at the Rossby deformation wavenumber kR
n , which increases with n. Analysis of the
horizontal mode equations suggests that, for large wavenumbers k kR
n , the GE is approximated by the
RKE, while the AE is approximated by the sum of the DKE and potential energy. These approximations are
supported by the simulations. The vertically averaged RKE and DKE spectra are compared to the sum of
the GE and AE spectra over all vertical modes; the spectral slopes of the GE and AE are close to those of
the RKE and DKE, supporting the use of the Helmholtz decomposition to estimate vortices and waves
in the midlatitudes. However, the AE is consistently larger than the DKE because of the contribution from
the potential energy. Care must be taken when diagnosing the mesoscale transition from the intersection
of the vortex and wave spectra; GE and AE will intersect at a different scale than RKE and DKE, despite their
similar slopes.
Description
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Keywords
Baroclinic flows, Gravity waves, Turbulence, Fourier analysis, Mesoscale models, Spectral analysis/models/distribution