The work suggests a simple qualitative model of the wind wave 'horse-s
hoe' patterns often seen on the sea surface. The model is aimed at exp
laining the persistent character of the patterns and their specific as
ymmetric shape. It is based on the idea that the dominant physical pro
cesses are quintet resonant interactions, input due to wind and dissip
ation, which balance each other. These processes are described at the
lowest order in nonlinearity. The consideration is confined to the mos
t essential modes: the central (basic) harmonic and two symmetric obli
que satellites, the most rapidly growing ones due to the class II inst
ability. The chosen harmonics are phase locked, i.e. all the waves hav
e equal phase velocities in the direction of the basic wave, This fact
along with the symmetry of the satellites ensures the quasi-stationar
y character of the resulting patterns. Mathematically the model is a s
et of three coupled ordinary differential equations for the wave ampli
tudes. It is derived starting with the integro-differential formulatio
n of water wave equations (Zakharov's equation) modified by taking int
o account small (of order of quartic nonlinearity) non-conservative ef
fects. In the derivation the symmetry properties of the unperturbed Ha
miltonian system were used by taking special canonical transformations
, which allow one exactly to reduce the Zakharov equation to the model
. The study of system dynamics is focused on its qualitative aspects.
It is shown that if the non-conservative effects are neglected one can
not obtain solutions describing persistent asymmetric patterns, but th
e presence of small non-conservative effects changes drastically the s
ystem dynamics at large times. The main new feature is attractive equi
libria, which are essentially distinct from the conservative ones. For
the existence of the attractors a balance between nonlinearity and no
n-conservative effects is necessary. A wide class of initial configura
tions evolves to the attractors of the system, providing a likely scen
ario for the emergence of the long-lived three-dimensional wind wave p
atterns. The resulting structures reproduce all the main features of t
he experimentally observed horse-shoe patterns. In particular, the mod
el provides the characteristic 'crescent' shape of the wave fronts ori
ented forward and the front-back asymmetry of the wave profiles.