Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Interaction of Tollmien-Schlichting Waves in the Air with the Sea
  Surface   Linear stability of fully developed flows of air over water is carried out in
order to study non-linear effects in the generation of solitons by wind. A
linear stability analysis of the basic flow is made and the conditions at which
solitons first begin to grow is determined. Then, following [10], the
non-linear stability of the flow is examined and the quintic non-linear
Schr\"{o}dinger equation is derived for the amplitude of disturbances. The
coefficients of the non-linear Schr\"odinger equation are calculated from the
eigenvalue problem which determines the stability of air-water interface. An
asymptotic and a numerical stability analysis is carried out to determine the
neutrally stable flow conditions for air-sea interface. Four different profiles
are considered for the airflow blowing over the surface of the sea, namely,
plane Couette flow (pCf), plane Poiseuille flow (pPf), laminar and turbulent
boundary layer (L,TBL) profiles. For each of the above cases the shear flow
counterpart in the water is assumed to be a pPf. It is shown that the above
amplitude equation produces `snake' solitons [9] for pCf, pPf and LBL profiles,
with striking similarities. On the other hand, for TBL we observe a very
violent surface motion. For cases of pCf and LBL remarkable similarity is
observed with observations made at sea. We conclude that the effect of
nonlinearity in the airflow over the sea surface is much larger than nonlinear
interactions in the water, and hence it is not possible to decouple the motion
in the air and the water for finite amplitude wind-wave interactions,
particularly in the case of wind-generated solitons in shallow waters.

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The categories of this paper are: chao-dyn
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The categories of this paper are: chem-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: acc-phys
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The categories of this paper are: gr-qc
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The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
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The categories of this paper are: solv-int
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The categories of this paper are: cond-mat
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The categories of this paper are: astro-ph
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The categories of this paper are: patt-sol
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-th
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The categories of this paper are: econ
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The categories of this paper are: adap-org
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The categories of this paper are: dg-ga