Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Effects of Phase Difference between Instability Modes on Boundary Layer
  Transition   Phase effect on the modal interaction of flow instabilities is investigated
for laminar-to-turbulent transition in a flat-plate boundary layer flow.
Primary and secondary instabilities are numerically studied with 2D
Tollmien-Schlichting wave and subharmonic 3D oblique waves at various initial
phase differences between these two instability modes. Three numerical methods
are used for a systematic approach for the entire transition process, i.e.,
before the onset of transition well into fully turbulent flow. The Floquet
analysis predicts the subharmonic resonance where a subharmonic mode locally
resonates for a given basic flow composed of the steady laminar flow and the
fundamental mode. Because the Floquet analysis is limited to the resonating
subharmonic mode, nonlinear parabolized stability equations (PSE) simulation is
conducted with various phase shifts of the subharmonic mode with respect to the
given fundamental mode. PSE offers insights on the modal interaction affected
by the phase difference up to the weakly nonlinear stage of transition.
Large-eddy simulation (LES) is conducted for a complete transition to turbulent
boundary layer because PSE becomes prohibitively expensive in the late
nonlinear stage of transition. The modulation of the subharmonic resonance with
the initial phase difference leads to a significant delay in the transition
location up to $\Delta Re_{x, tr} \simeq 4\times 10^5$ as predicted by the
current LES. Effects of the initial phase difference on the spatial evolution
of the modal shape of the subharmonic mode are further investigated. The
mechanism of the phase evolution is discussed, based on current numerical
results and relevant literature data.

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The categories of this paper are: hep-ph
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The categories of this paper are: q-bio
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The categories of this paper are: q-alg
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The categories of this paper are: comp-gas
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The categories of this paper are: cs
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The categories of this paper are: nucl-th
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The categories of this paper are: gr-qc
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-th
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The categories of this paper are: cond-mat
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The categories of this paper are: nlin
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The categories of this paper are: stat
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The categories of this paper are: math
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The categories of this paper are: nucl-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: atom-ph