Download Drag Reduction and the Effects of Internal Waves on Bottle

Drag Reduction and the Effects of Internal Waves on Bottle-Nosed Dolphins
Senior Thesis Proposal By: Patrick Eddy
Advisor: Daniel Valentine
4-18-03
Introduction:
The goal of this thesis is to develop a model of a bottle-nosed dolphin swimming. The
model will include the effects of a boundary layer on that swimming. Its purpose is to further our
understanding of the fluid mechanical effects around the dolphin.
Dolphins are mammals of the order of Cetacea. They are lunate-tailed and use a vertical
tail flapping motion to swim. Traditional fluid mechanics suggests that dolphins must possess
incredibly powerful muscles in order to swim as well as they do, muscles several times the
strength of land based mammals of similar size. This is shown not to be the case biologically.
This suggests that the dolphins have an unusual means of reducing their drag.
The motivations behind studying the swimming motions of dolphins are many. The
flapping tail of dolphins and fishes may be the basis for a new propulsion device. The dolphin's
methods of drag reduction may be useful by ships, submarines, or even for swimmers.
Understanding how dolphins swim would be very useful for biologists. The US Navy has done
studies on using dolphins for various purposes, and getting a better understanding of dolphin
swimming could be invaluable.
The ocean has a density stratification. The lower depths of the ocean have a slightly
higher density than the upper levels, and there is a thin boundary layer with a continuous
variation in density between the upper and lower levels. This boundary layer is known as the
pycnocline. The pycnocline is known to support internal waves and even influence ship motions.
This investigation is intended to examine the effect of the pycnocline on the swimming of
dolphins and the effects of internal wave resistance on a dolphin swimming in the pycnocline.
Background:
The bottle-nosed dolphin has a characteristic, crescent-shaped, lunate tail. The lunate tail
improves the efficiency of the tail by increasing the effective tail length. The space between the
tips of the crescent-shaped tail does work just as well as the rest of the tail. The effect of the tail
on propulsion can be modeled by the properties of a vortex sheet (Lighthill, 1975). Lighthill
states that the vertical movements of the dolphin's tail are the same as the carangifonn motion of
lunate finned fish tails. Dolphins use their forward fins for control and as negative lift when they
are overly buoyant. Lighthill also indicates a need for further three-dimensional analysis, because
three-dimensional analysis is needed to analyze the vortical structures created by the dolphin's tail
and fins (1975).
Dolphin’s skin contains quasi-periodic vertical cutaneous ridges. These ridges seem to
exist in region of the dolphins body where there would be steady turbulent flow. These ridges
seem to become more pronounced at higher speeds. These ridges may be a way developed by the
dolphin to control the turbulent flow around parts of his body (Lisi, 1999). This may be one of
the methods the dolphin uses to reduce drag.
Proposed Tasks:
The first step of this project will be to assemble all of the previous research and get
information about what research has already been done on this subject, or related subjects. There
is a large volume of related literature in both the biological and the engineering aspects of this
project.
The next step in the project will be to develop a two-dimensional model of a flapping
hydrofoil model, which roughly mimics the dolphin caudal fins. This will be followed by doing a
two-dimensional analysis of the drag reduction mechanism and a two-dimensional analysis of the
internal-wave resistance of a body of revolution of cetacean size. FLUENT, FEMLAB, or
ETUDE programs will be used to model the two- dimensional problems.
After looking at the two-dimensional problems, three-dimensional models of the
unsteady flows will be made using either FEMLAB or FLUENT. The NASA panel- method code
PMARC may also be used to model the three-dimensional flow around the caudal fins, which are
lifting bodies.
References:
Childress, S. (1981): Mechanics of Swimming and Flying. Cambridge University Press, New
York.
Lighthill, M.J. (1975): Mathematical Biofluidynamics. Society for Industrial Applied
Mathematics, Philadelphia.
Wu, T. Y. (2001): On Theoretical Modeling of Aquatic and Aerial Animal Locomotion, Advances
in Applied Mechanics 38, 291-363.
Lisi, A. G. (1999) : Drag Reduction over Dolphin Skin via the Pondermotive Forcing of Vortex
Filaments, arXiv:physics/9907041 v1, 23 July.
(URL: http://www.lanl.gov/PScache/physics/pdf/9907 /9907041.pdf )