Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dynamic triad interactions and evolving turbulence spectra   We investigate the effect of a four-dimensional Fourier transform on the
formulation of Navier-Stokes equation in Fourier space and the way the energy
is transferred between Fourier components (modal interactions, commonly
referred to as triad interactions in the classical 3-dimensional analysis). We
specifically consider the effect of a spatially and temporally finite,
digitally sampled velocity record on the modal interactions and find that
Fourier components may interact within a broadened frequency window as compared
to the usual integrals over infinite ranges. We also see how these finite
velocity records have a significant effect on the efficiency of the different
modal interactions and thereby on the shape and development of velocity power
spectra. The observation that mismatches in the wavevector triadic interactions
may be compensated by a corresponding mismatch in the frequencies supports the
empirically deduced delayed interactions reported in [Josserand \textit{et
al.}, \textit{J. Stat. Phys.} (2017)]. Collectively, these results explain the
occurrence and time development of the so-called Richardson cascade and also
why deviations from the classical Richardson cascade may occur. Finally, we
quote results from companion papers that deal with measurements and computer
simulations of the time development of velocity power spectra in a turbulent
jet flow into which a single Fourier mode (narrow band oscillation) is
injected.

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The categories of this paper are: alg-geom
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The categories of this paper are: quant-ph
11
The categories of this paper are: hep-lat
21
The categories of this paper are: adap-org
12
The categories of this paper are: nucl-th
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The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
9
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: eess
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-th
25
The categories of this paper are: patt-sol
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The categories of this paper are: acc-phys