Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Reynolds stresses in Holmboe instabilities: from linear growth to
  saturation   The Reynolds stress in Holmboe instabilities at moderate Reynolds numbers is
investigated using single wavelength simulations (SWS), multiple wavelength
simulations (MWS), and laboratory experiments. The rightward and leftward
propagating instabilities are separated with the two-dimensional discrete
Fourier transform, enabling a direct comparison of the perturbation fields
between the numerical simulations and linear stability analysis. The
decomposition and superposition of the perturbation fields provide a new
insight into the origin of Reynolds stresses. Conventionally, only the
statistics of horizontal and vertical velocity perturbation pairs, ($u',w'$),
are presented to show the degree of anisotropy in turbulent fields. Here, we
present these ($u',w'$)-pairs using both theory-based and statistical
approaches to reveal the mechanism of the anisotropy of perturbation field. For
an individual Holmboe mode, both the simulations and linear theory show that
($u',w'$)-pairs tilt towards the 2nd and 4th quadrants ($u'w'<0$) within upper
and lower vorticity interfaces, indicating an anisotropic perturbation field.
As a result, a negative correlation between the horizontal and vertical
velocity perturbation is produced, $i.e.$ negative Reynolds stresses on
average. Combining the leftward and rightward Holmboe modes, ($u',w'$)-pairs
are also ellipses whose orientation and aspect ratio are phase dependent. The
joint probability density functions of ($u',w'$) in the linear theory and SWS
show `steering wheel' structures, while in MWS and laboratory experiments the
presence of waves of varying wavelength smears out the `steering wheel'
structure leaving an elliptical cloud with similar orientation to the
corresponding linear prediction. The vertical structure of the Reynolds
stresses in the simulations and the laboratory experiment agree with the linear
stability predictions.

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The categories of this paper are: stat
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The categories of this paper are: funct-an
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The categories of this paper are: eess
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The categories of this paper are: dg-ga
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The categories of this paper are: alg-geom
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The categories of this paper are: math-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: comp-gas
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The categories of this paper are: nlin
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The categories of this paper are: chem-ph
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The categories of this paper are: cs
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The categories of this paper are: q-fin
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The categories of this paper are: cond-mat
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The categories of this paper are: patt-sol