Swimming in the Stream
Captain Tim Johnson, PE
Associate Professor
Wentworth Institute of Technology
Boston, Massachusetts
Open Water Swimming Dimensions
Who generally benefits
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Swimmers
Small boat owners (kayaks)
Aquatic lovers
Adventurers/opportunists
and more…
Who generally contributes
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Mathematicians
Oceanographers
Navigators
Boat owners
And others…
Applied Open Water Swimming
• A swimmer is a self-contained marine vessel
that is human powered with a top speed of
approximately 3 mph with low visibility. In flat
water conditions the swimmer can see his
immediate surroundings but relies on a
herding strategy if swimming in a group
and/or their coach if accompanied by an
escort boat/kayak.
Basics I
• Water is constantly moving. The source of
movement is gravitational pull from the moon
and sun combined with the rotation of the earth.
• Every 12 ½ hours the tides rise and fall and in the
majority of locations there are 2 high and 2 low
tides. These tides are called semi-diurnal.
• Tide height varies from one tide to the next.
• The times for the high/low tides change daily by
approximately 1 hour later each day.
Basics II
• The change of height the water rises is called the
tide.
• The flow of the water is called the current.
• Swimmers are most affected by the current.
• Current varies in a sinusoidal manner.
• Open ocean current rotate 360° around a point.
• A river that empties out into the ocean allows the
river to flow in two directions.
• Surface current is different from current at depth
in speed and direction.
Basic III
• Windblown waves creates a current to
the right of direction the wind is
blowing in the northern hemisphere
through the water column due to the
Coriolis effect. (see slide 24)
• The maximum velocity of the current
can be found from Current Tables for
locations around the globe.
• The velocity of the current at any time
can be calculated from the maximum
velocity, Vmax, and the time since the
current switched direction in minutes
with the mode for the sine wave in
degrees.
Vmax sin( x / 2)
Wind-blown snow showing the
twist caused by the Coriolis
effect and friction between
the air/land interface
Current flow
• Current flow in a river is laminar or turbulent.
• Laminar flow is orderly, consistent throughout
and fastest in the center.
• Turbulent flow is variable in speed and
direction and create shear walls separating
different domains.
• Fluid dynamic formulas and principles can
represent a river as an open-channel flow.
Tidal diagrams
DATUMS (Add’l nomenclature)
Monthly variations
• The tides(currents) vary between fast and
slow over a two week duration.
• When the sun and the moon align, the tides
are higher and currents are faster: Spring tides
• When the sun and the moon are out of phase
by 90° the tides(currents) moderate: Neap
tides.
• Use of the terms spring and neap are useful
when swimming in the English Channel.
From the NOAA website http://oceanservice.noaa.gov/education/kits/tides/media/supp_tide06b.html
Spring and Neap
Sun in
stationary
position
When the sun, moon, and the
earth line up they are on a syzygy,
a straight line configuration of 3
celestial bodies. These positions
create max. tides and currents.
The actual tides
can be delayed
as much as two
days after the
astronomical
occurrence.
Lunar rotation about the earth is counterclockwise in this representation.
Theoretical tide
Angular momentum creates a “balancing tide” that compensates
for the water attracted by the gravitation pull of the moon thus
creating two tides. The earth is a self-correcting gyroscope!
On a perfect geoid with no land masses and the earth rotated in step with the moon…
The tidal pull of the moon would create a tide of 21 inches
The tidal pull of the sun would create a tide of ≈ ±10 inches
And the elliptical orbit of the earth→sun and moon→earth ≈ ±5 inches
The extremes range would vary between 6 inches to 36 inches
The highest tides are on perigean tides when the sun and moon are closest to the earth
The tides repeat every 18.6 years which is the Metonic cycle.
A tide wave is created as the earth moves under these bulges.
The Tide Wave
In this illustration the delay of the tidal bulge caused by the lunar gravitational pull
A is drawn showing the frictional force F that the rotation of the earth creates as it
turns under the water with enough energy to move all that water eastward in a
wave front B moving at approximately 400 miles per hour. Think of a wave in a
sport stadium…people only stand up and sit down, not moving very far but the
wave can sweep around a stadium quite fast. On the opposite side of the earth is
the balancing wave caused by the centrifugal force creating a diurnal tide(twice
daily).
Global view of the tides
The redder the color the larger the range of the tide.
The larger the range, the faster the flow of the current.
White lines are dividing tidal section by one hour.
Black arrow showing a six hour group and direction of increase.
Rotary Tides
• Tides within a basin where the natural period of
the basin approximates the tidal wave period
move around the edge of the basin in a circle
with one point known as an amphidromic point.
• The tides at this central point are minimal and
points further away are higher.
• Locations off Cape Cod are well known and
documented in Current Charts by NOAA.
• The tide rotates counterclockwise in a basin while
the currents flow clockwise.
Deep Water Ocean Waves
Waves generated by the wind are different than the tide wave. Probably
everyone whose ever floated or treaded water just outside of the breakers has
had occasion to experience the rotary movement of the water particles as a wave
passes by. If these waves occur in water deeper than ½ the length of the wave
(trough to trough or crest to crest) then it’s a deep water wave. The speed of the
wave front is approximately equal to the length of the wave divided by the period
(time between peaks), C=L/T.
Wave Energy
• A wave form represents a flow of energy.
• The wave height is potential energy.
• Kinetic energy is the motion of the water
particles.
• Waves lose energy by transferring the wave form
to the undisturbed water.
• Most waves seen at sea are generated by the
wind. Once a wave has been created it’s period
will not change. Long period waves known as
swells can travel thousands of miles.
Shallow Water Waves
• Shallow waves such as seen on the beach are created
when the length of the wave divided by 20 is greater
than the depth.
• Notice how the water molecules orbits are compressed.
• So if the depth of the water is less than 1/20th of the
length the orbits of the molecules compress are longer
causing increased friction slowing the base of the wave.
Breaking Waves
• Wave steepness is ratio of the height to the length of the wave,
H/L. When the ratio approaches 1:7 the angle between front
and the back of the wave approaches 120°.
• The wave will become unstable and break. This instability is
caused as the wave approaches the shore and the compacted
wave orbit seen in the last slide cause more friction.
• Based on the formula for the wave C=L/T, since the wave’s
period T can’t change, as the speed C drops the wave length L
decreases. All the water in the wave compacts raising the wave
height and changing the ratio of the wave steepness, H/L.
• Eventually, the orbits at the top of the wave exceed the speed at
the bottom of the wave as the wave molecule orbits flatten.
• Waves crests always fall forward because the top of the wave is
moving faster than the bottom of the wave.
Refraction-changing wave direction
Refraction occurs when we can’t see
the obstruction causing the bending.
Waves approaching shore slow when depth approaches
L/2 causing the wave to bend (refracted) as part of the
wave is in shallow water and the rest in deeper water.
The part of the wave in deeper water rushes straight
ahead filling in behind turning the slower part.
Diffraction-changing wave direction
• When we can see the obstacle to a wave that is bent, it’s
called diffraction. The wave fills in around the obstruction
lessening the wave energy causing the wave height
distribute. This energy dissipation cause the wave to slow
down and bend. These obstacle are often man-made to
protect shore line developments like harbors and marinas.
Standing wave oscillations
Single node, ½ wave length
Double node, full wave length
Standing waves occur when the wave
length matches an entrapment such
as a bay. A node is the part of the
wave that doesn’t change height
(much) and the antinode is where
the wave rises and falls.
Single node, ¼ wave length
Elkman Spiral
• Wind generated currents at the surface are moving at 45⁰ to the
right (in the Northern Hemisphere) of the wind. This directional
movement doesn’t translate to lower depth exactly because of
the low friction between water molecules. The direction as the
movement is passed down rotates clockwise (in the northern
hemisphere). The total water transport is 90⁰ to the winds
direction. The reason for the initial 45⁰ difference is the even
lower friction at the wind/water interface.
• The bad news…the current generated is 1/100 of the wind speed,
so to get a 1 knot boost from the wind it has to blow 100 knots.
Sea Breezes
An onshore sea breezes is
when the wind direction
brings a cooling wind from
the ocean toward land. It
occurs during the day.
At night the breeze reverses
after a lull. When the
offshore breeze begins you
have to tack back to port.
But a night cruise is very
comfortable.
Open Channel Flow
• River current flows in rivers can be modeled using
open channel flow principles from fluid dynamics.
• Major features of river behavior can be expressed
in a few variables (inertia, gravity, and viscosity)
and using generalized constants some simple
equations are all that are needed.
• For instance, a river on a constant slope will reach
a constant velocity where the gravitational force
is equal to the resistance to flow.
Open Channel Flow characteristics
• Rule of thumb is that the average velocity is .8
the surface velocity.
• Flows are long compared to their crosssections so a single velocity can express the
situation at any point in the cross-section.
• Flow depths and dimensions are larger than
the thickness of the boundary layer so river
flow is considered turbulent.
• The velocity at the boundary is zero.
Other characteristics
• When you consider the energy of the flowing water, there is a critical
depth equal to 2/3 the depth divided by the energy when plotted where if
the depth is greater than the critical depth the flow is slower (upper stage)
and if the depth is less than the critical depth the flow is faster (lower
stage).
Open channel flow conclusions
• To determine if the flow is slower or faster than
the flow at the critical depth, toss a stone into the
water. If the flow is slower the waves from the
disturbance will propagate upstream as well as
down stream.
• These observations assume some constants like
holding the energy and discharge constant so
tidal flow would introduce a dynamic aspect to
open channel flow. For example none of the
open channel formulas allow for a river’s flow to
stop and reverse.
Eddy current considerations
• The next part of the lecture is the toughest
because we’re going to talk about something that
is nearly impossible to detect. Here are some
visual clues:
– If you see debris collected and floating near shore,
you’re looking at the center of a gyre or circular water
rotation.
– Or you see flat water surrounded by choppy water.
– Think Sargasso Sea…dead water.
• Give these waters a wide berth.
What does an eddy look like?
• Turbulence is described by a Reynolds number that characterize the
intensity of the velocity gradient between still water and the faster
water. This gradient is like a curtain that separates two different
regimes that touch each other and is very thin. Water molecules are
being pushed and dragged much like how the wind pushes and ripples
down a flag causing the flag to lift up. The gradient is a shear wall.
• The Reynolds number indicates the relative significance of the viscous
effect compared to the inertia effect. The Reynolds number is
proportional to inertial force divided by viscous* force. The flow is:
– laminar when Re < 2300
– transient when 2300 < Re < 4000
– turbulent when 4000 < Re
• Here is a video of the creation of an eddy.
• The formula for the Reynolds number of a river: Re = 2667*R*V where
R is the hydraulic radius (width + 2* depth)/depth and V is the speed of
the flow. All units in meters.
*viscous means resistance to flow
River/harbor entrances
• Think of a funnel—wide at the top and narrow at the bottom.
Assume the funnel is filled with water and you are looking down on
the funnel. The water level drops slowly at first then picks up speed
reaching its maximum speed at the narrowest part.
• This is a model for how the current behaves when the water is
flooding into an entrance that is controlled by tidal flow.
Slow then it picks up speed at the narrowest part.
• When the current is ebbing and you are swimming out the
entrance, the speed goes from fast to slow.
• When the bottom contour is equal, there is no one place faster
than another. This is rare because of sand bars and natural/manmade channels often found at entrances.
Changes in river width
• The funnel representation is useful to describe current flow
when a river changes width.
• When you are entering a narrowing with the current, you’ll
get a nice speed boost.
• When you exit the funnel into a wider section of the river, you
have eddies to content with followed by slower waters.
• An eddy is a circular rotation of water. They are created by an
increased boundary layer of slower water; they cause water to
shear off from the main flow and spin. They are speed killers.
• Sometimes you have to be careful to check the bottom
contour as there could be an under water shelf creating
eddies.
• Here is a video of a creation of an eddy along shore.
Bends in rivers
• When a river turns either to the right or the left, the
inside shore usually will have a shallower depth due to
the slower water dropping particles that were being
carried along in the faster moving water.
• The water as it enter the bend will want to keep going
straight and as the inner bank bends away, an eddy
develops.
• Depending on the amount of the bend, some eddies can
occupy from ¼ to ½ the width of the river.
• This forces even more water into a narrower part along
the outside shore creating a fast channel.
Solving the river bend problem
• The course through the bend depends on the
speed of the current entering, the severity of
the turn, the depth of the river, and the width
of the river.
• The idea is to avoid the eddy along the inside
shore. Of the four variables, 3 are constant so
a good answer on one current may be the
wrong answer on a faster current.
• My suggestion is to stay with the faster
current for as long as possible but avoid going
to the outside shore. On slow currents, turn
when 1/3 past the start of the bend but wait
no more than 2/3 on fast currents.
• In the graphic, red is shallow water, yellow is
the nominal depth, with green to blue
increasing graduated depth showing the
channel cut by the fast water.
Bottom contour of a bend is show in a channel,
flow begins with nominal depth in yellow then
either its shallower, reddish or green/blue deeper.
Shallow is slower water, deep is faster water.
Littoral drift current
Wave action creates an onshore current that lifts sand from sand bars to deposit on the
beach and along shore transport. Littoral is Latin for along shore.
Swimming across Monterey Bay? Here’s a fabulous simulation of the currents for a
24-hour time period of 6/1/2003 that show a large eddy and a littoral drift current
that is off-shore. What is significant is none of these currents are predictable.
Difference between swims & events
• Swimming in an organized event is different from
swimming individually on your own.
• Events require planning, preparation, and organization.
Usually these are manned by volunteers who have devoted
time year after year because of their love for the water.
• Good organizations improve over the years and a body of
knowledge about the swim is built up that is imparted to
the following year’s group of swimmer in the hopes of
making the event better.
• So they have rules to help the swimmers observe
regulations that make the swim safe, fair to all users of the
waterways, and competitive.
• Information you learn about swims thru a study of currents
you may not be able to act upon in an organized event but
you could design your own swim that would demonstrate
your skill at swimming with currents.
Planning a Swim
• Get a chart.
– The larger the scale of the chart the better
• Large scale charts cover small areas so you can see
details.
• Small scale chart cover large areas and are useful for
getting the large picture.
• You may need several charts.
• Study the tide and current information
• Research the history of the swim.
Planning a Swim II
• Plot your presumed course to take advantage
of the fastest current.
– Measure the distance.
– Assuming swimmer speed is 2 knots calculate the
time for the swim.
– 1st plot, assume speed is swimmer alone. Mark
hourly progress off on charts.
– 2nd plot, add estimated current to swimmer
Planning a swim III
• How to estimate current flow over 6 hours.
– Assume you are starting in the morning so a long
swim can be in daylight.
– Based on the direction of the swim, find a current
going that direction whose slack water occurs in
the morning.
– This gives you the date of the swim and the start
time.
– Record the maximum current flow
Planning a Swim IV
– Use the hourly cofactor from the chart below multiplied by
the maximum current to estimate the current speed which
is added to the swimmer’s speed for your 2nd plot.
Hourly cofactors of max current over time
1
1.00
0.87
0.87
0.75
0.5
0.50
0.50
0.25
0
0
0.00
1
2
3
4
5
6
0.00
7
0.00
8
9
10
11
12
-0.25
-0.5
-0.50
-0.50
-0.75
-0.87
-1
-1.25
-0.87
-1.00
Cofactor
Planning a Swim V
• As you plot the locations on the chart, check to see if
you are entering another current (time-difference)
location to verify maximum current at the new
location. The entire Hudson river is measured against
the current at the Verrazano-Narrows Bridge with a
time difference and another cofactor.
• If you go past the 6 ½ hour mark and you haven’t
reach your destination the current will turn and the
current speed is subtracted from the swimmer’s
speed.
• In these cases you have two choices: swim over the
current (you’ll need a slow current) or swim on a
faster current on another day.
Planning a Swim VI
– Get a sanction for your swim.
– Get Coast Guard permits for the swim.
– Get a support boat that can comfortably hold your
support crew and any well wishers.
– Get a knowledgeable marine navigator whose sole job
is to coordinate your swim course while you are in the
water—not your swim coach nor your kayak paddler.
Not every boat owner is a good pilot.
– Take a course in seamanship from the Power squadron
or Auxiliary Coast Guard—they are usually free.
Distance estimations
A swimmer starting at slack water swimming with the tidal current
over one 6 hour period could possibly swim…
Estimated No
distance
Current
Max.
Current
1 knots
Max.
Current
2 knots
Max.
Current
3 knots
Swimmer
1 .5 knot
9 nm
13 nm
17 nm
21 nm
Swimmer
2 knots
12 nm
16 nm
20 nm
24 nm
Swimmer
2.5 knots
15 nm
19 nm
23 nm
27 nm
This estimation assumes the tidal current maximum speed is the
same over the entire distance. The only known place this
happens is in the Gulf Stream where the hourly cofactor is one for
each hour.
Solving a problem swim
• This is a video of a 3rd attempt to swim from the Farallon Islands to
San Francisco on April 14th, 2011. A successful attempt was made
May 20, 2011 taking 14:45:08 hours going the other direction.
Distance is 27 statute miles (43 kilometers).
• First problem is lack of nautical familiarity. The boat is tied to the
dock and the cameraman who is the narrator suggest they “hoist
the anchor” to cast off.
• At 7:55 minutes into the video, the harbor entrance buoy is
identified as “Large Navigational Buoy”. Later the swim stalls 10
miles or so outside the harbor due to the flood current. Flood
current usually flow into a harbor…even in San Francisco.
• Finally, the last scene show the skipper explaining what he thinks
went wrong with the swim which you can’t hear because the video
editor turned the music up. You learn from your mistakes…
Reference tidal info @ http://wolfweb.unr.edu/homepage/edc/tides.html
References
• History of Open-Water Marathon Swimming, Timothy M. Johnson,
2004, available at Amazon.com with much more information.
• An Introduction to the World’s Oceans, Duxbury, 3rd Ed., Wm. Brown
Publishers, 1991. http://en.wikipedia.org/wiki/Tide
• Open Channel Flow by J. B. Calver, 2003, from website:
http://mysite.du.edu/~etuttle/tech/opench.htm
• The Engineering Toolbox website:
http://www.engineeringtoolbox.com/reynolds-number-d_237.html
• Large eddy simulation of river flows, Wolfgang Rodi, 2010, Institute
of Hydromechanics, Karlsruhe institute of Technology, Karlsruhe,
Germany. (slide 35)
http://www.iahrmedialibrary.net/db/iii1/slides/large_eddy_simulati
on_river_flows.pdf
• A Global Ocean Tide Model from TOPEX/POSEIDON altimetry:
GOT99.2, Richard Ray, NASA, Goddard Space Flight Center, 1999.
(slide 15)