Geoscience Reference
In-Depth Information
12
Large-Amplitude Coastal Shelf Waves
Andrew L. Stewart
1
,PaulJ.Dellar
2
, and Edward R. Johnson
3
12.1. SHELF WAVES AND COASTAL CURRENTS
IN THE LABORATORY
The sharp increase in depth at the continental shelf
break exerts a strong constraint on the flow via
conservation of potential vorticity (PV) [see
Pedlosky
,
1987;
Vallis
, 2006]. This motivates a description of the
flow in terms of topographic Rossby waves.
Longuet-
Higgins
[1968] first showed that a continental shelf
acts as a waveguide, approximating the bathymetry as
a discontinuity in depth. Shelf wave theory was subse-
quently adapted to a wide range of bathymetric config-
urations and applied to regions of the real ocean [
Mysak
,
1980a,1980b]. For example,
Mysak et al.
[1979] applied
linear wave theory applied to double-exponential approx-
imations of coastal depth profiles in the Pacific Ocean,
while
Gill and Schumann
[1979] attempted to predict the
path of Agulhas using an idealized representation of con-
tinental slope and deep ocean in a two-layer model. Linear
shelf wave theory has since been extended to describe
more realistic configurations such as continental shelves
with along-shore depth variations [
Johnson
, 1985;
Johnson
and Davey
, 1990], curved coastlines [
Kaoullas and Johnson
,
2010;
Johnson et al.
, 2012], and arbitrary isobath varia-
tions [
Rodney and Johnson
, 2012;
Kaoullas and Johnson
,
2012].
Coastal currents complicate this Rossby wave descrip-
tion of shelf dynamics, particularly when they flow over
along-shore variations in the bathymetry and when they
are driven by a time-dependent inflow or wind stress
[
Allen
, 1980;
Brink
, 1991]. The development of numerical
ocean models, particularly those adapted to large vari-
ations in bathymetry [e.g.,
Haidvogel et al.
, 2008], has
advanced our understanding of such situations consider-
ably in recent decades. Yet laboratory studies of coastal
dynamics have tended to focus either on topographic
Rossby wave propagation or on coastal current evolution,
so in this section we review separate selections of previ-
ous studies along each line of investigation. Both provide
context for the experiments that serve as the focus of this
Coastal currents flowing along continental shelves are a
complex dynamical feature of the global ocean. Such cur-
rents separate the coastal waters from the open ocean and
so control the transport of both dynamical and passive
tracers across and along the continental slope [
Nittrouer
and Wright
, 1994]. Some of the most climatically impor-
tant currents in the world ocean flow partly or entirely as
shelf currents, so understanding their behavior represents
an important oceanographic and dynamical problem. For
example, the Antarctic Slope Front (ASF) [
Thompson and
Heywood
, 2008] mediates transport of continental deep
water onto the Antarctic continental shelf. This is respon-
sible for preserving biological primary production around
the Antarctic margins [
Prézelin et al.
, 2004] and con-
trols the melting rate of ice shelves [
Martinson et al.
, 2008].
The Agulhas current, which flows over the continental
shelf in the Mozambique Channel [
Bryden et al.
, 2005;
Beal et al.
, 2006, 2011], facilitates mass and heat exchange
between the Indian and Atlantic oceans via thermocline
water transported in Agulhas eddies [
Gordon
, 1985, 1986].
The Gulf Stream flows along the coastal shelf of North
America until it separates at Cape Hatteras [
Stommel
,
1972;
Johns andWatts
, 1986;
Pickart
, 1995]. This current is
associated with large meridional heat transport and closes
the upper branch of the Atlantic Meridional Overturning
Circulation [
Minobe et al.
, 2008].
1
Department of Atmospheric and Oceanic Sciences,
University of California, Los Angeles, Los Angeles, California,
United States of America.
2
Oxford Centre for Industrial and Applied Mathematics,
University of Oxford, Oxford, United Kingdom.
3
Department of Mathematics, University College London,
London, United Kingdom.
