Oceanography
THE OFFICIAL MAGAZINE OF THE OCEANOGRAPHY SOCIETY
VOL.31, NO.3, SEPTEMBER 2018
SPECIAL ISSUE ON
Mathematical Aspects of
Physical Oceanography
VOL. 31, NO. 3, September 2018
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Oceanography | September 2018
contents
VOL. 31, NO. 3, September 2018
SPECIAL ISSUE ON MATHEMATICAL ASPECTS
OF PHYSICAL OCEANOGRAPHY
12
FROM THE GUEST EDITORS: Introduction to the Special Issue on
Mathematical Aspects of Physical Oceanography
By A. Constantin and G. Haller
14
The Value of Asymptotic Theories in Physical Oceanography
By R.S. Johnson
22
Nonlinear Features of Equatorial Ocean Flows
By D. Henry
28
On the Vorticity of Mesoscale Ocean Currents
By C.I. Martin
36
Simplified Models for Equatorial Waves with Vertical Structure
By M.H. Wheeler
42
Steady Large-Scale Ocean Flows in Spherical Coordinates
By A. Constantin and R.S. Johnson
51
On a Three-Dimensional Nonlinear Model of Pacific Equatorial Ocean
Dynamics: Velocities and Flow Paths
By B. Basu
59
Short-Term Predictions of Oceanic Drift
By K.H. Christensen, Ø. Breivik, K.-F. Dagestad, J. Röhrs, and B. Ward
68
Applying the Stereographic Projection to Modeling of the Flow of the
Antarctic Circumpolar Current
By S.V. Haziot and K. Marynets
REGULAR ISSUE FEATURES
76
A Multidisciplinary Approach for Generating Globally Consistent Data on
Mesophotic, Deep-Pelagic, and Bathyal Biological Communities
By L.C. Woodall, D.A. Andradi-Brown, A.S. Brierley, M.R. Clark, D. Connelly, R.A. Hall,
K.L. Howell, V.A.I. Huvenne, K. Linse, R.E. Ross, P. Snelgrove, P.V. Stefanoudis,
T.T. Sutton, M. Taylor, T.F. Thornton, and A.D. Rogers
90
Functioning of Coastal River-Dominated Ecosystems and Implications for
Oil Spill Response: From Observations to Mechanisms and Models
By A.T. Greer, A.M. Shiller, E.E. Hofmann, J.D. Wiggert, S.J. Warner, S.M. Parra,
C. Pan, J.W. Book, D. Joung, S. Dykstra, J.W. Krause, B. Dzwonkowski, I.M. Soto,
M.K. Cambazoglu, A.L. Deary, C. Briseño-Avena, A.D. Boyette, J.A. Kastler, V. Sanial,
L. Hode, U. Nwankwo, L.M. Chiaverano, S.J. O’Brien, P.J. Fitzpatrick, Y.H. Lau,
M.S. Dinniman, K.M. Martin, P. Ho, A.K. Mojzis, S.D. Howden, F.J. Hernandez,
I. Church, T.N. Miles, S. Sponaugle, J.N. Moum, R.A. Arnone, R.K. Cowen, G.A. Jacobs,
O. Schofield, and W.M. Graham
90
42
51
76
Oceanography | September 2018
Oceanography | Vol.31, No.3
CONTACT US
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SPECIAL ISSUE GUEST EDITORS
• ADRIAN CONSTANTIN, University of Vienna
• GEORGE HALLER, ETH Zürich
06
DEPARTMENTS
03
QUARTERDECK. Let’s Try Some Math for a Change
By E.S. Kappel
05
FROM THE PRESIDENT. Policies for a Member-Run Organization
By A.C. Mix
06
RIPPLE MARKS. Over the Hump: Beleaguered in Whaling Days,
Humpback Whales Chart a New Course in the Gulf of Maine
By C.L. Dybas
104 THE OCEANOGRAPHY CLASSROOM. You Say Color, I Say Colour,
She Says Colugo
By S. Boxall
106 CAREER PROFILES. Anna J. Malek Mercer, Executive Director,
Commercial Fisheries Research Foundation • Orens de Fommervault,
Research Scientist, Alseamar
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Oceanography
THE OFFICIAL MAGAZINE OF THE OCEANOGRAPHY SOCIETY
VOL.31, NO.3, SEPTEMBER 2018
SPECIAL ISSUE ON
the Mathematical Aspects of
Physical Oceanography
ON THE COVER
This SeaWiFS image, constructed using data collected on June 13,
2002, highlights the presence of biological activity in the ocean
west of British Columbia’s Queen Charlotte Islands and Alaska’s
Alexander Archipelago. The bright red, green, and turquoise
patches, which indicate high concentrations of chlorophyll, also
make visible a number of eddies in the Pacific Ocean. Image
credit: SeaWiFS Project, NASA/Goddard Space Flight Center,
and ORBIMAGE
Oceanography | September 2018
QUARTERDECK
Let’s Try Some Math
for a Change
Since publication of the first issue of Oceanography in 1988, by far the
majority of articles in the magazine have been descriptive, in keeping
with our mission of “cross-disciplinary communication.” This format
also reflects that our bread and butter is disseminating information on
seagoing programs—observational oceanography.
This issue is a clear departure, where several theoretical ocean-
ographers describe the mathematical aspects of the discipline, phys-
ical oceanography in particular. These writers set aside the modern
emphasis on numerical techniques and focus instead on the fruits of
old-fashioned, pencil-and-paper equation-solving. Observations and
theory are the yin and yang of scientific progress, and our hope is that
these articles will stimulate further discussions, new insights, and
adventurous collaborations.
Ellen S. Kappel, Editor
December 2018
Gulf of San Jorge, Patagonia,
Argentina
March 2019
Scientific Ocean Drilling:
Looking to the Future
June 2019
Salinity Processes in the Upper
ocean Regional Study (SPURS) – 2
September 2019
Partnership for Interdisciplinary
Studies of Coastal Oceans (PISCO)
December 2019
Flow Encountering Abrupt
Topography (FLEAT)
https://tos.org/oceanography
Do you have an idea for a special
issue of Oceanography? Please send
your suggestions to Editor Ellen Kappel
at ekappel@geo-prose.com.
Oceanography
SPECIAL ISSUES
UPCOMING
CALL FOR IDEAS!
Be sure to drop by
TOS Booth #518
at the
AGU 2018 Fall Meeting
December 10–14
Washington, DC
Oceanography | Vol.31, No.3
EDITOR
Ellen S. Kappel
Geosciences Professional Services Inc.
5610 Gloster Road
Bethesda, MD 20816 USA
t: (1) 301-229-2709
ekappel@geo-prose.com
ASSISTANT EDITOR
Vicky Cullen
PO Box 687
West Falmouth, MA 02574 USA
t: (1) 508-548-1027
vcullen@whoi.edu
CONTRIBUTING WRITER
Cheryl Lyn Dybas
cheryl.lyn.dybas@gmail.com
DESIGN/PRODUCTION
Johanna Adams
johanna-adams@cox.net
Oceanography
https://tos.org/oceanography
Oceanography contains peer-reviewed articles that chronicle all aspects of
ocean science and its applications. The journal presents significant research,
noteworthy achievements, exciting new technology, and articles that address
public policy and education and how they are affected by science and technol-
ogy. The overall goal of Oceanography is cross-disciplinary communication in
the ocean sciences.
Oceanography (ISSN 1042-8275) is published by The Oceanography
Society, 1 Research Court, Suite 450, Rockville, MD 20850 USA. ©2018 The
Oceanography Society Inc. All rights reserved. Permission is granted for indi-
viduals to copy articles from this magazine for personal use in teaching and
research, and to use figures, tables, and short quotes from the magazine for
republication in scientific books and journals. There is no charge for any of
these uses, but the material must be cited appropriately.
Republication, systemic reproduction, or collective redistribution of any mate-
rial in Oceanography is permitted only with the approval of The Oceanography
Society. Please contact Jennifer Ramarui at info@tos.org.
ASSOCIATE EDITORS
Claudia Benitez-Nelson
University of South Carolina
cbnelson@geol.sc.edu
Ian Brosnan
NASA Ames Research Center
ian.g.brosnan@nasa.gov
Grace Chang
Integral Consulting Inc.
gchang@integral-corp.com
Margaret L. (Peggy) Delaney
University of California, Santa Cruz
delaney@ucsc.edu
Philip N. Froelich
Duke University
froelich@magnet.fsu.edu
Charles H. Greene
Cornell University
chg2@cornell.edu
William Smyth
Oregon State University
smyth@coas.oregonstate.edu
Kiyoshi Suyehiro
Yokohama Institute for Earth
Sciences, JAMSTEC
suyehiro@jamstec.go.jp
Peter Wadhams
University of Cambridge
p.wadhams@damtp.cam.ac.uk
The Oceanography Society was founded in 1988
to advance oceanographic research, technology,
and education, and to disseminate knowledge of
oceanography and its application through research
and education. TOS promotes the broad under-
standing of oceanography, facilitates consensus
building across all the disciplines of the field, and
informs the public about ocean research, innova-
tive technology, and educational opportunities
throughout the spectrum of oceanographic inquiry.
OFFICERS
PRESIDENT: Alan Mix
PRESIDENT-ELECT: Martin Visbeck
PAST-PRESIDENT: Susan Lozier
SECRETARY: Susan Cook
TREASURER: Susan Banahan
COUNCILLORS
AT-LARGE: Dennis McGillicuddy
APPLIED TECHNOLOGY: James Girton
BIOLOGICAL OCEANOGRAPHY: Charles H. Greene
CHEMICAL OCEANOGRAPHY: Peter Sedwick
EDUCATION: Carolyn Scheurle
GEOLOGY AND GEOPHYSICS: Richard Murray
PHYSICAL OCEANOGRAPHY: Magdalena Andres
STUDENT REPRESENTATIVE: Stefanie Mack
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Jennifer Ramarui
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Oceanography | Vol.31, No.3
Oceanography | September 2018
FROM THE PRESIDENT
Over the past year, The Oceanography Society Council (https://tos.org/governance)
has been addressing several organizational policy issues. Some of our policies and pro-
cedures needed updating because the Society has grown and matured, and government
agency policies have changed. What was appropriate for a small organization when it was
founded 30 years ago may not be a good fit for today’s larger and growing organization that
is much more diverse.
One particular policy issue that has become very public over the past year relates to pro-
fessional ethics, including issues of sexual harassment. This issue has been in the news fre-
quently, touching many organizations. The Oceanography Society has always been a wel-
coming community that emphasizes open expression and exchange of ideas with equal
opportunity and fair treatment of all, free from all forms of discrimination or harassment.
This policy has long been posted on our website (https://tos.org/about). Fortunately, the
TOS Council is not aware of any problems in this area related to TOS activities; however, it
still is imperative that our written policies express our implicit expectations.
To that end, the TOS Council has developed a much more detailed and stronger policy
that provides clear reporting and enforcement mechanisms for claims of harassment while
participating in TOS-supported professional activities. (Note that the new policies also
address publication ethics.) It is important that participants know that TOS has taken
actions to ensure that its activities are as safe and as welcoming as possible. I would like to
thank the Seattle office of the Fisher Phillips law firm, a group with particular expertise in
workplace law, and Jennifer Freyd of the University of Oregon, a psychologist who special-
izes in the study of harassment, sexual violence, and impacts on individuals and institu-
tions, for providing reviews of this TOS policy at no cost.
This policy review and update has also served as a good reminder that TOS is a member-
run organization in which input is always welcome. Our operations and policies are trans-
parent and responsive to the needs and wishes of our members. Your feedback makes TOS
a stronger organization. Thank you!
Alan C. Mix, TOS President
Policies for a
Member-Run Organization
Oceanography | Vol.31, No.3
RIPPLE MARKS: THE STORY BEHIND THE STORY
OVER THE HUMP Beleaguered in Whaling Days,
Humpback Whales Chart a New Course in the Gulf of Maine
BY CHERYL LYN DYBAS
It’s the longest day of the year, summer solstice, in Stellwagen Bank National Marine
Sanctuary 32 km off Provincetown, Massachusetts. The sea is a promenade of hump-
back, finback, and minke whales.
Humpback fins and tails break the ocean’s surface on all sides of the 15 m research
vessel Auk. Aboard ship, an audience with front row seats watches more than
30 humpback whales perform a ballet. A calf born this year peacefully swims along-
side its mother. Suddenly, it twirls up and out of the sea, pirouettes in a full breach,
and sprays sparkling water droplets in all compass directions before slipping beneath
the waves. Other humpbacks lob-tail, lifting their tail fins, or flukes, free of the water
and curving them down in smacks on the surface.
Humpbacks (Megaptera novaeangliae) are baleen whales that filter-feed with
“strainers” made of keratin inside their huge mouths. Adults range from 12 m to
16 m long and weigh about 36,000 kg. Humpbacks have distinctive body shapes,
with long pectoral fins and knobby heads. Males “sing” complex songs lasting 10 to
20 minutes, which they repeat, sometimes for hours. The whale music may have a
role in mating.
Found around the world, humpback whales migrate up to 25,000 km each year.
Humpbacks feed in summer when they’re in northern waters, then migrate to tropical
or subtropical waters to breed and give birth in winter, when they live on fat reserves.
Humpback whales often work in groups to cor-
ral elusive sand lance. Here, six whales emerge
from a jointly created bubble net. Image credit:
Ilya Raskin; NMFS Permit #782-1719.
NET OF WHALE BUBBLES
What are humpbacks eating—and how do
they get enough of it—to tide them over
until the following summer? In the Gulf of
Maine, the answer lies in a cloud of bub-
bles and a tiny fish.
The whales engage in bubble-netting, a
recently discovered means of feeding on
small fish such as sand lance, also called
sand eels. One or more whales sound, or
dive, then exhale together underwater.
When their bubbles reach the surface, they
form a large ring with seafoam in the cen-
ter. The bubble ring becomes a net, trap-
ping countless sand lance. Seconds later,
one—then several—whales surface in the
ring’s center, huge baleen-lined mouths
open, straining the water, or dragging, as
marine biologists call it, for sand lance.
“Humpbacks have large flukes relative
to their size, providing thrust for quick
maneuvers,” says David Wiley, a ceta-
cean biologist and research coordinator
at the Stellwagen Bank National Marine
Oceanography | Vol.31, No.3
Oceanography | September 2018
Sanctuary. “Other baleen whales feed by
rapidly swimming forward, but humpbacks
are adapted for fine-scale movements that
allow them to create bubble nets.”
Humpbacks release the bubbles while
swimming in upward spirals, often during
a behavior called double loops. Double
loops starts with an ascending spiral to
corral fish, then the smack of a fluke on
the ocean surface and a second upward
lunge to capture the corralled prey. The
whales work in teams of two to 10 or more,
emerging at the ocean surface in a boiling
cauldron of open mouths. “The sequence
is as complex as the tool use of apes in
the forest,” says Wiley. He and colleagues
reported bubble netting and double loops
in 2011 in the journal Behaviour.
Further research has uncovered other
new-to-science whale feeding behaviors
such as bottom side-rolls and repetitive
scooping. The findings are detailed in a
2014 paper in Marine Mammal Science
coauthored by Wiley and others. In bottom
side-rolls and repetitive scooping, hump-
backs repeatedly dive to the seafloor,
roll onto their sides, tilt their heads down,
open their mouths, and expand their throat
pleats. They then swim along the bottom,
funneling in sand lance as they go.
Bottom side-rolls are common on
Stellwagen Bank and in the Great South
Channel, a deepwater passage between
Nantucket, Massachusetts, and Georges
Bank to the southeast.
Scientists wondered whether the whales
were bottom side-roll feeding when
they saw scars on the humpbacks’ jaws.
Indeed, humpbacks bottom side-roll for
extended periods wherever sand lance
are common. Research conducted this
summer is revealing new information on
humpbacks’ bottom-feeding techniques.
IT ALL COMES DOWN TO SAND LANCE
What’s driving all the bubble netting and
bottom feeding? Stellwagen Bank, with
its sandy bottom and relatively shallow
waters, is prime habitat for sand lance.
The bank’s abundant sand lance, which
travel in huge schools reaching the tens of
thousands, offer the whales high- calorie
meals. In one day, a whale might eat a ton
of the fish.
At night, sand lance burrow into sandy
sediments or form schools close to the
seafloor. During the day, the fish often
swim in dense mats along the seabed. The
humpbacks’ recently discovered feeding
techniques, especially side-rolling, result
in efficient fish-catching when the whales
Humpback whales blow bubbles to form “fishing nets” that capture sand lance. Image credit: NOAA/
NEFSC/Allison Henry; MMPA research permit #17355
Oceanography | September 2018
Oceanography | Vol.31, No.3
SIDEBAR | Sand Lance: Newcomers to Fishery Management Plans
To explore the role of a tiny fish in the North Atlantic Ocean ecosystem, 55 sci-
entists, natural resource managers, and conservationists attended a sand lance
workshop in May 2017 at the Parker River National Wildlife Refuge in Newburyport,
Massachusetts.
The participants concluded that research is needed into how climate change
may influence the fish, and what effect possible offshore energy development or
sand and gravel mining may have on sand lance.
“We have an opportunity to proactively manage a fish that’s not currently tar-
geted for commercial harvest in the US,” says biologist Lynda Welch of the Maine
Coastal Islands National Wildlife Refuge. She, Wiley, and Michelle Staudinger, sci-
ence coordinator of the Northeast Climate Science Center at the University of
Massachusetts Amherst, were co-organizers of the workshop.
“There’s no active talk—yet—of a sand lance fishery,” says Wiley, “but there’s also
no protection for sand lance or the ‘ecosystem services’ they provide.”
For insights into what a fishery management plan for sand lance might look
like, the scientists are reviewing harvest levels for species with similar ecosystem
roles, such as herring and menhaden in the Northeast and Mid-Atlantic regions.
“Management plans for these ‘forage fish’ must balance the needs of the fish with
those of commercial endeavors,” says Staudinger. “We’d like to see the same
approach for sand lance.”
The researchers say that US fisheries managers can learn from overharvesting
of sand lance in the UK. Uncontrolled fishing for sand lance there led to crashes
of seabirds such as black-legged kittiwakes, which depend on sand lance. To
avoid a repeat, the UK sand lance fishery is now managed as several smaller sub-
populations rather than one overall population. That allows biologists to change
harvest levels based on the presence of seabirds, whales, and other sand lance-
eating species.
The future for North Atlantic humpback whales, says Wiley, depends on a fish so
small it’s a mere glint in the sunlight.
are near the seafloor. One humpback the
researchers studied side-rolled every 6 m.
The maneuver netted 10 to 17 scoops of
fish per dive.
Where sand lance are found in the Gulf
of Maine, so, too, humpbacks. Although
last summer’s research cruise was sched-
uled to depart from Provincetown, the sand
lance—and the whales—took up residence
off a different Cape Cod port, Chatham. To
keep up with the shifting scene, the sci-
entists moved R/V Auk from its berth in
Provincetown to a dock in Chatham. “We
may be all about whales,” says Wiley, “but
they’re all about sand lance. So we look at
where sand lance are concentrated.”
Adds Mike Thompson, a spatial ecol-
ogist at the Stellwagen Bank National
Marine Sanctuary, “Whales, seabirds like
shearwaters, and pretty much anything
looking for a meal here is feeding on
these fish. We’re starting to understand
that on Stellwagen Bank, it all depends on
sand lance.”
To track the fish, Wiley, Thompson, and
crew use the SEABed Observation and
Sampling System, or SEABOSS. This boxy
eye-in-the-sea allows researchers to col-
lect sediment samples and obtain videos
of sand lance seafloor hangouts. Sand
lance surveys are conducted at 44 sta-
tions on or near Stellwagen Bank at vari-
ous times of year, including about a month
before the whale cruise in June.
TO TAG A WHALE
R/V Auk serves as the mother ship of two
smaller boats, the rigid-hulled inflatable
boats (RHIBs) Balena and Luna. Balena
ferries biologists to the center of a whale
pod. There, in an attempt to place a track-
ing tag on a humpback, the researchers
nose up to a whale whose flank, where
the tag will be placed, is exposed.
The digital tag, or DTAG, is attached with
a suction cup. This acoustic recording
tag provides data on the whale’s orienta-
tion (pitch, roll, and heading) and depth—
50 times per second. The DTAG also
records all sounds made and heard by the
tagged whale, says Wiley. Visualization
software
called
TrackPlot
provides
(right) A Cory’s shearwater with a
sand lance in its bill. The slender body
shape of sand lance makes the fish an
ideal prey item for seabirds. Image:
NOAA/SBNMS
(below) Feeding humpback whales
concentrate sand lance at the surface,
where the fish are also eaten by sea-
birds. Image: NOAA/SBNMS; NMFS
permit #782-1719
Oceanography | Vol.31, No.3