It has been observed for a long time that under certain conditions
a vortex or even
a group of vortices forms in bays which have a narrow opening to the sea.
What
leads to the formation of such vortices confined in a quiet, almost closed
bay? Why
does their number vary? Can such vortices form in any specific bay with
known
hydrological conditions, coastal configuration and bottom topography? The
answers
to these questions are essential in practice because, if several vortices
form in a bay,
a sort of a ‘vortex cork’ is created which prevents the
outflow of pollution from the
bay. This pollution will be locked in the bay practically permanently.
The formation
of vortices can also very strongly modify the topology of the background
flow and
lead to the formation of structures which intensify such processes as beach
drifting,
silting, and coastal erosion.
This article considers the topology of the vortex regimes generated
in harbour-like
basins by the external potential longshore current at large Reynolds numbers.
The
theory discusses the issues of what solution compatible with the
Prandtl–Batchelor
theorem for inviscid fluids, and under what conditions, may be realized
as an
asymptotic state of the open hydrodynamical system. The analysis is
developed based on the
variational principle, the most appropriate fundamental method of modern
physics
in this case, modified for the open degenerated hydrodynamical system.
It is shown
that the steady state corresponds to the circulational regime in
which the system has
minimal energy and enstrophy. This state is fixed by the Reynolds number.
The
relation between the Reynolds number, the geometry factor and
the topological number, characterizing the number of vortex cells, is found.