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Steady Boussinesq flow in a weakly curved channel driven by a horizontal temperature gradient is considered. Linear variation in the transverse direction is assumed so that the problem reduces to a system of ordinary differential equations. A series expansion in
$G$
, a parameter proportional to the Grashof number and the square root of the curvature, reveals a real singularity and anticipates hysteresis. Numerical solutions are found using path continuation and the bifurcation diagrams for different parameter values are obtained. Multivalued solutions are observed as
$G$
and the Prandtl number vary. Often fields with the imposed structure that satisfy all the governing equations are insensitive to the boundary conditions and can be regarded as perturbations of the homogeneous (or ‘unforced’) problem. Four such unforced solutions are found. In two of these the velocity remains coupled with temperature which, formally, scales as
$1/G$
as
$G\rightarrow 0$
. The other two are purely hydrodynamic. The existence of such solutions is due to the unbounded nature of the domain. It is shown that these occur not only for the Dean equations, but constitute previously unreported solutions of the full Navier–Stokes equations in an annulus of arbitrary curvature. Two additional unforced solutions are found for large curvature.
The eastern English Channel, the narrow channel of water separating northern
France and southeast England is an area of intense human use of the array of
resources concentrated into its relative small area. The vulnerability of
living resources and their habitats brought together French and British
maritime experts within a common project (called CHARM): to create an atlas
of marine resource habitats in the eastern English Channel so as to provide
planners and decision-makers with the necessary information to help managing
the use of its living and non-living resources. This multidisciplinary and
richly illustrated atlas provides abundant information on the legal
framework and physical environment; benthic invertebrates, fish and their
habitats; fishing activities; and a first attempt at developing a trophic
network model (using ECOPATH software) and a marine conservation planning
exercise (using MARXAN software, at a spatial resolution of 25 km
$^{2})$
.
Although most of the data used were collected elsewhere, some were collected
especially for the project. Similarly, most of the analyses performed on the
data where entirely original for this geographical area. The CHARM atlas has
significantly improved the knowledge about the eastern Channel while
contributing to the recognition that such holistic or multidisciplinary
approaches to exploited marine systems are necessary to efficiently and
durably manage their resources use.
