Dear toto_fl,
The location you specify as the release point of the ashes is just off
the Atlantic coast of Florida, near Fort Lauderdale. The prevailing
current here is indeed the Gulf Stream, which would carry the ashes
in a northeasterly direction. At the Grand Banks, off the coast of
Newfoundland, a good part of the ashes would then be caught up by the
North Atlantic Current, which continues northeast into polar waters. Some
portion of the ashes would finally enter the North Atlantic Drift Current,
which swirls north and east toward the British Isles.
The following map shows the general direction of the Gulf Stream and of
the North Atlantic Drift Current, which form the first and last legs of
the ashes' journey. The middle leg takes place along the North Atlantic
Current, roughly where the blue arrow of the Labrador Current is pointing
on the map.
British Geomorphological Research Group: Gulf Stream Map
http://www.bgrg.org/pages/education/alevel/coldenvirons/Gulf%20Stream%20Map%201.gif
As a reasonable approximation of where the ashes would first reach the
English coast, we can use the town of Penzance, which is nearly at the
southwestern tip of England. This is a convenient point because we know
that Penzance is located at latitude 50'07" and longitude 05'33"W.
MapQuest: 50° 07 Min. 0 Sec., -05° 33 Min. 0 Sec.
http://www.mapquest.com/maps/map.adp?searchtype=address&formtype=latlong&latlongtype=degrees&latdeg=50&latmin=07&latsec=0&longdeg=-05&longmin=33&longsec=0
A web-based distance calculator will show that the distance between
these two points is about 6750 kilometers as the crow flies.
Bali & Indonesia on the Net: Distance Calculator
http://www.indo.com/cgi-bin/dist?place1=fort+lauderdale%2C+florida&place2=50%3A07%3A00N+05%3A33%3A00W
A more visual way to determine this is to use a model globe. My own
globe has a scale of 880 miles to the inch, or 1000 kilometers per 1.8
centimeters. I marked off a strip of paper accordingly and laid it on
the linear path from Fort Lauderdale to Penzance. A photograph of this
span on the globe demonstrates that the distance is about 6750 kilometers.
personal photo: linear distance from Ft. Lauderdale to Penzance
http://plg.uwaterloo.ca/~mlaszlo/answers/florida2england.jpg
Now we are faced with the matter of determining how far and how fast
the ashes would travel in each of the three currents that make up the
journey. The following web pages provide information on the typical
transport velocities in the Gulf Stream, the North Atlantic Current,
and the North Atlantic Drift Current, respectively.
The core of the Gulf Stream current is about 90 km wide and has
peak velocities of greater than 2 m/s (5 knots).
University of Miami: Ocean Currents: The Gulf Stream
http://oceancurrents.rsmas.miami.edu/atlantic/gulf-stream.html
A more typical maximum velocity for the North Atlantic Current
is the 100 cm s-1 reported by Krausse et al. (1987).
University of Miami: Ocean Currents: The North Atlantic Current
http://oceancurrents.rsmas.miami.edu/atlantic/north-atlantic.html
The NADC is generally a slow-moving body of water [...] Its
northward speed averages about 3 cm s-1 (Otto & van Aken, 1996)
along the western edge of the Rockall Plateau.
University of Miami: Ocean Currents: The North Atlantic Drift Current
http://oceancurrents.rsmas.miami.edu/atlantic/north-atlantic-drift.html
These web pages also link to illustrations of the vector fields of water
transport in each of the three currents. By comparing these illustrations
with an overall map of the Atlantic, we can estimate that the first
leg of the ashes' journey, in the Gulf Stream, would cover about 4500
kilometers; the middle leg, in the North Atlantic current, would take
about 2000 kilometers; and the final leg, in the North Atlantic Drift
Current, would take about 1000 kilometers.
Note that the total length of the journey is about 7500 kilometers,
which exceeds the linear distance from Fort Lauderdale to Penzance due
to the curving path of the currents. See the illustrations below.
University of Miami: Gulf Stream transport velocities, Apr-May-Jun
http://oceancurrents.rsmas.miami.edu/atlantic/img_mgsva/gulf-stream-AMJ.gif
University of Miami: Gulf Stream transport velocities, Apr-May-Jun
http://oceancurrents.rsmas.miami.edu/atlantic/img_mgsva/north-atlantic-AMJ.gif
University of Miami: Gulf Stream transport velocities, Apr-May-Jun
http://oceancurrents.rsmas.miami.edu/atlantic/img_mgsva/north-atlantic-drift-AMJ.gif
According to the information quoted above, the fastest-moving ash
particles would travel at 2 meters per second on the first leg, 1 meter
per second on the middle leg, and only 0.03 meters per second on the
final leg. Knowing these velocities along with the length of each leg,
we can calculate the total time of travel as follows.
Gulf Stream:
4,500,000 m / 2.00 m/s = 2,250,000 s
North Atlantic Current:
2,000,000 m / 1.00 m/s = 2,000,000 s
North Atlantic Drift Current:
1,000,000 m / 0.03 m/s = 33,333,333 s
total:
2,250,000 s + 2,000,000 s + 33,333,333 s = 37,583,333 s
Note that the great majority of the travel time would be spent in the
sluggish waters of the North Atlantic Drift Current. To arrive at a more
comprehensible result, we consider that there are 86,400 seconds in a day.
37,583,333 / 86,400 = 435
Thus, the first few ashes from the scattering would arrive on the coast
of England in 435 days, which amounts to one year and ten weeks. By
consulting next year's calendar, we determine that this day would fall
on Monday, August 21, 2006.
It has been an interesting challenge to address this question on your
behalf. If you find that any part of my answer requires elaboration or
correction, do let me know through a Clarification Request so that I
have the opportunity to fully meet your needs before you assign a rating.
Regards,
leapinglizard |
Clarification of Answer by
leapinglizard-ga
on
30 Jun 2005 18:17 PDT
1) I did not explicitly take the Florida Stream into account, but the
seasonal vector fields show a strong current in early summer heading
north along the Atlantic coast of Florida. Judging from the magnitude
of the vectors, we can safely assume that the ashes will be carried
into the Gulf Stream at velocities close to those of the Gulf Stream
itself.
2) You are right to point out that there are seasonal variations in
all three currents. Indeed, the vector fields to which I link above
are from the late spring and early summer, whereas the ashes would
pass through all four seasons along their year-round journey. However,
if you look closely at the seasonal vector fields, you will note that
the strongest part of each current, containing the transport vectors
of greatest magnitude, is essentially constant from season to season.
Because we are interested in computing the arrival date of the
earliest ashes from the scattering, the seasonal variation in
transport velocities along the periphery of each current does not
affect us.
3) The swirling and eddying characteristics at the fringes of each
stream are, again, of no consequence in considering those ashes
traveling in the core of the ocean current. Ashes diverging from the
vanguard, by the way, will end up dispersed in entirely unpredictable
ways. Those ashes that escape deposition on the ocean floor or
shoreline will end up distributed uniformly throughout the seas of the
world, and will gradually reach the shore of England in infinitesimal
quantities for decades to come.
I should point out that the number I arrived at above, namely 435
days, is expressed too precisely. Given the approximate nature of the
intermediate calculations, I should restrict myself to one significant
digit. I shall therefore say that I estimate the travel time of the
fastest-moving ashes to be 400 days, or approximately one year. I
would expect variance of plus or minus 100 days, which is to say about
three months in either direction.
leapinglizard
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