JDIAMOND@BAT.BATES.EDU (01/13/90)
Hello fractalers and modelers,
A short while ago, I made a request about models of sand transport
phenomena. Unfortunately, we had a major hardware failure here that
resulted in a shut down of our mail system; all mail received at our
site since 89 DEC 13 was etherized. Mail was revived 90 JAN 9. I hate to
clog mailboxes (especially after this annoying loop business), but I am
really stuck for info, so I am repeating (in edited form) my original
message. Sorry for the inconvenience.
------------------- PARTIAL TRANSCRIPT OF ORIGINAL REQUEST -------------
I am a physical chemist who has become interested in periodic
and chaotic phenomena over the last couple of years. I'd like some
assistance on modeling some beach erosion problems.
Two particular patterns interested me the most. The first are a
series of small asymmetric waves of sand with crests approximately
perpendicular to the direction of flow; the wavelengths are about 2-4
cm, with maxima and minima of about 2-3 mm. Trains of a hundred
oscillations are not unusual, by my observations. I believe these are
called `current ripples'. The wave pattern is apparently formed by some
velocity-coupled mechanism, in which the rate of sand transport is
proportional to some high power of the water velocity (greater than of
equal to 6). [I base these comments on my only source of technical
information, Willard Bascom's "Waves and Beaches", which was delightful
as well as provoking, but leaned far away from quantitative models.] The
velocity of the outgoing water depends on the slope of the surface
(among other vairables). I observed an entirely different mode of sand
transport on slightly steeper slopes of apparently identical
composition, a few yards away from one site of current rippling. This
mode is characterized by a sequence of nearly overlapping diamonds,
about 15 cm in length, with diagonal trenches perhaps 5 mm deep, at an
angle of about 60 degrees on each side of the direction of flow. I think
this is called 'backwash'. As I said, the only difference between the
two sites which I (with an untrained eye) observed was the slope of the
beach; in addition, the water flowing over the current ripples seemed to
carry far less suspended material than the water over the backwash. It
seemed to me then that this sort of abrupt transition in behavior should
be susceptible to a mathematical treatment, although the underlying
dynamics are probably quite complicated.
I am interested in modelling these phenomena, but I am stuck on where
to turn, for a handle on the relevant dynamical equations. I would be
most appreciative of any advice or comments.
------------------- END OF PARTIAL TRANSCRIPT -----------------------------
Fractally Yours,
Jim Diamond
JDIAMOND@BAT.BATES.EDU
Chemistry Department
Bates College
Lewiston, Maine USA
P.S. I will be happy to pass along the information sent to me. Please make
replies and requests to me personally. Adios!