11.3 Mechanics of Animal Swimming
359
sharks, whales and dolphins, are characterized by a distinctive, high aspect
ratio and lunate candal fin. Undulations of the body are confined to the candal
peduncle and fin. They have attracted a great deal of attention from biologists
and hydrodynamicists because of the high speeds they attain.
Ostraciiform mode is used by species which are unstreamlined. They are
not propelled by undulations of the body and candal fin, but they employ the
action of their median or paired fins for most of their swimming behaviour.
11.3.3 Kinematics, Speed and Size
The swimming speed of fish is related to the body size of the fish. Large
fish swim faster than small fish. There is rather extensive literature on various
aspects of fish swimming (see, for example, the books by Childress, 1981; Blake,
1983; Schmidt-Nielsen, 1989; Videler, 1993; Vogel, 1994, and many papers in
various professional journals). Therefore, in this section we will consider only
some specific problems, closely related to fluid mechanics. First, let us examine
the relationship between animal speed, U, and its length, L.
For marine ecologists dealing with systems that span an enormous size range,
the Reynolds number Re = U L / v is one of the basic scaling parameters commonly used for categorizing the flow induced by these various systems. To
illustrate this, in Table 11.1 the range of Reynolds numbers associated with
swimming of various marine organisms is shown.
As the Reynolds number is linearly proportional to the product of size and
speed, it becomes very high for large organisms moving fast and very low for
small organisms moving very slowly. Therefore, the Reynolds number varies
over thirteen orders of magnitude, while the length of organisms vary only over
seven orders of magnitude. Although whale and bacteria swim in the same
water, they live in different environments. The first lives in an environment
dominated by inertial phenomena, while the second is totally dominated by
viscous phenomena.
Using the data from Table 11.1, the approximate relationship between velocity, U, length, L, and Reynolds number, Re, can be established, i.e.:
(11.7)
(11.8 )
in which length, L, is in metres and velocity, U, is in metres per second. Equation (11.7) can be rewritten as:
( u L )0.49
U = 1.94 X 10- 3 x Re°.49 = 1.94 x 10- 3 --;;,
or:
(11.9)
U = 4.83 X 10- 6 x LO. 96 X v-0 96 ,
(11.10)
359
sharks, whales and dolphins, are characterized by a distinctive, high aspect
ratio and lunate candal fin. Undulations of the body are confined to the candal
peduncle and fin. They have attracted a great deal of attention from biologists
and hydrodynamicists because of the high speeds they attain.
Ostraciiform mode is used by species which are unstreamlined. They are
not propelled by undulations of the body and candal fin, but they employ the
action of their median or paired fins for most of their swimming behaviour.
11.3.3 Kinematics, Speed and Size
The swimming speed of fish is related to the body size of the fish. Large
fish swim faster than small fish. There is rather extensive literature on various
aspects of fish swimming (see, for example, the books by Childress, 1981; Blake,
1983; Schmidt-Nielsen, 1989; Videler, 1993; Vogel, 1994, and many papers in
various professional journals). Therefore, in this section we will consider only
some specific problems, closely related to fluid mechanics. First, let us examine
the relationship between animal speed, U, and its length, L.
For marine ecologists dealing with systems that span an enormous size range,
the Reynolds number Re = U L / v is one of the basic scaling parameters commonly used for categorizing the flow induced by these various systems. To
illustrate this, in Table 11.1 the range of Reynolds numbers associated with
swimming of various marine organisms is shown.
As the Reynolds number is linearly proportional to the product of size and
speed, it becomes very high for large organisms moving fast and very low for
small organisms moving very slowly. Therefore, the Reynolds number varies
over thirteen orders of magnitude, while the length of organisms vary only over
seven orders of magnitude. Although whale and bacteria swim in the same
water, they live in different environments. The first lives in an environment
dominated by inertial phenomena, while the second is totally dominated by
viscous phenomena.
Using the data from Table 11.1, the approximate relationship between velocity, U, length, L, and Reynolds number, Re, can be established, i.e.:
(11.7)
(11.8 )
in which length, L, is in metres and velocity, U, is in metres per second. Equation (11.7) can be rewritten as:
( u L )0.49
U = 1.94 X 10- 3 x Re°.49 = 1.94 x 10- 3 --;;,
or:
(11.9)
U = 4.83 X 10- 6 x LO. 96 X v-0 96 ,
(11.10)