A.M. ZOOLOGIST, 2:143-149(1962).
BODY FORM AND SWIMMING PERFORMANCE
IN THE SGOMBROID FISHES
VLADIMIR WALTERS
Department
of Zoology, University of California, Los Angeles
If the Reynolds Number and the nature of
surface friction are known, the surface drag
The perciform suborder Scombroidei concoefficient can be determined from pubtains six families of fast-swimming oceanic
lished tables. The power output for profishes: Scombridae (mackerels), Cybiidae
pulsion varies with the drag coefficient (sur(Spanish mackerels), Thunnidae (tunas),
face drag coefficient plus form drag coeffiKatsuwonidae (skipjacks), Istiophoridae
cient—discussed later). Such a table indi(sailfish, marlins) and Xiphiidae (swordcates that when R is between 2 and 3 X '0r>
fish). The diversity in body size, body shape,
the drag coefficient for turbulent skin fricand surface structure in these fishes (Table
tion is about twice that for Jaminar skin
1) reflects the evolutionary end-products of
friction. With increasing R, the turbulent
the interaction between organisms and their
surface drag coefficient becomes progressiveimmediate environments. The immediate
ly greater than the laminar; transitional
environment of a swimming fish is afilmof
flow is indicated by intermediate values.
water adjacent to its body, the boundary
Laminar flow has not been observed above
layer. The behavior of the boundary layer
R = 2 X 1°6 a n d all flow is believed to be
governs the swimming performance of the
either transitional or fully turbulent befish, and it is from the viewpoint of boundyond this point. Thus, as the Reynolds
ary layer control to yield an efficient swimNumber increases, the fish is gradually reming performance that we shall interpret
stricted to a family of shapes and structural
the structural diversity of this suborder. A
devices which can maintain low surface
discussion of boundary layer mechanics
drag coefficients over the greatest possible
may be found in the introductory work by
length of its body.
Shapiro (1961) and the detailed monograph by Schlichting (1960).
SCOMBROID REYNOLDS NUMBERS
INTRODUCTION
In order to estimate R, the total length
and velocity of the fish as well as the kinematic viscosity of the water must be known.
The shape and structure of a fish, as well
The scombroid environment is arbitrarily
as how it moves its body, influences the flow
assumed to be 15° C with a kinematic visof water past the body surface. This flow
cosity of 1.21 X 10"° m2/sec, although most
can be fully turbulent, transitional, or comspecies live at higher temperatures and conpletely laminar (streamlined), and the nasequently lower kinematic viscosities. Nursture of the flow determines the surface fricall (this issue) questions the validity of the
tion or drag which is developed. The Reyreported swimming speeds of 80 and 90
nolds Number expresses the ratio of inertial
km/hr for tuna, 130 km/hr for marlin and
forces to viscous forces acting on a body as
swordfish and of 120 km/hr for sailfish. Adit moves through a fluid medium, as folditional estimates of scombroid swimming
lows:
speeds follow: bluefin tuna, 44 mph (Lane,
1941); skipjack, 25 mph (Kishinouye, 1923:
R = length X velocity X density of
455);
swordfish, 90 km/hr (Shuleykin, 1949)
medium/viscosity of medium = length
and
130
km/hr (Golenchenko, 1960). If
X velocity/kinematic viscosity.
REYNOLDS NUMBER AND THE SURFACE DRAG
COEFFICIENT
144
VLADIMIR WALTERS
TABLE 1. Summary of the Scombroid Families
Family
Size
Range
(m)
Reynolds
Number
3.7 X 105 Joukovsky
to
1.3 X 10«
22-25%
absent
present 5
Scombridae
0.3-0.6
"normal", absent
cycloid
present
present 5-9
corselet
absent
0.3-2
3.7 X 10s Laminar
to
1.6 X 10-
16-27%
Cybiidae
present
present 7-11
corselet
present
0.8-4
2.2 X 10' Joukovsky
mainly
to
7.3 X 10'
3.7 X 10" Joukovsky
mainly
to
4.1 X 10"
24-29%
Thunnidae
27-30%
present
present 7-9
corselet
present
quills,
oil-filled
canals,
pores
Katsuwonidae 0.3-1
Istiophoridae
Xiphiidae
Profile
Type
Head Peduncular Caudal Finlets Integument Cutaneous
System
Length
Keel
Keels
•2-4
1.6 X 10'
Laminar
to
7.3 X 10'
24-33%
absent
present
1
4
7.3 X 10' Laminar
43%
present
absent
1
these velocities are considered in respect to
the average size of the species involved, all
travel in excess of 10 lengths/sec. A velocity of 10 lengths/sec is a fair estimate of the
speed of smaller species belonging to other
systematic groups (Gray, 1957; Bainbridge,
1958, 1960), but Bainbridge (1961) is unwilling to accept this value for fish much
larger than the trout. In the absence of
contradictory (lower) measurements, the
recorded estimates for scombroids cannot
be set aside; perhaps they really do swim
this fast. A velocity of 10 lengths/sec is
therefore used to approximate the swimming speeds of various members of the suborder. The Reynolds Numbers have been
calculated for individuals of two-thirds
maximum size. The values (Table 1) range
from 3.7 X 10<s t o 7.S X 1<>T. These are felt
to be conservative estimates.
SCOMBROIDS AS HYDROFOILS
The plan view (frontal aspect) of a fish
which swims by means of carangiform
movements (Breder, 1926) resembles a hydrofoil profile. According to Harris' (19S6)
designations, yawing movements pivot the
longitudinal axis of the fish horizontally
and pitching movements pivot the longitudinal axis vertically. Since the hydrofoil
absent
naked;
canals and absent
pores?
develops lift and drag in the pitching plane,
while propulsive movements of the fish take
place in the yawing plane, the yawing plane
of the fish and the pitching plane of the hydrofoil may be regarded as equivalent.
There is scarcely any validity in comparing the entire fish with a simple hydrofoil,
since the fish undulates whereas the hydrofoil does not. We shall interpret scombroids
not as simple hydrofoils but as complex hydrofoils having movable high-lift (drag reduction) devices, each continually changing
its angle of attack with respect to the axis
of progression of the hydrofoil as a whole.
Information on hydrofoil performance is
from Abbott and von Doenhoff (1959),
Jones and Cohen (1960), and Schlichting
(1960).
First of all, the scombroid head can be
compared with a leading-edge slat. These
fishes do not make independent respiratory
movements with their mouths and gill covers1. They have synchronized their swim'This is a widely-stated fact. The author has
verified, for his own satisfaction, that members of
the following families indeed do not open and close
their mouths, nor do they move their gill covers to
breathe: Scorabridae, Cybiidae, Thunnidae, Katsuwonidae. The author has not been able to verify
this statement for the Istiophoridae and Xiphiidae.
SWIMMING IN SCOMBROID FISHES
ming with their respiration, so that when
the body bends, the gill cover on the convex side lifts free of the trunk while the
gill cover on the concave surface moves
against the trunk. The exhaled jet issuing
from beneath the gill cover thus varies directly with the curvature of the anterior
part of the trunk. Such synchronization has
not been observed for fishes which utilize a
branchial pump2. The importance of such
synchrony in scombroid swimming performance becomes apparent when the head
of the fish is compared with the alula of a
bird wing or with a hydrofoil having a
leading-edge slat. In hydrofoil and wing
the slot behind the slat directs high-energy
fluid into the low-energy boundary layer of
the upper surface, blowing off the old and
thick layer and replacing it with a young
and thin boundary layer; this delays boundary layer separation and also leads to a decrease in surface drag. In losing the branchial pump, scombroids have acquired a
compensating slat to vary the amount of
high-energy water injected into the aging
boundary layer behind the gill covers, and
hence may possess the ability to control the
point of separation in accordance with the
inherent thickness of the boundary layer.
Secondly, the finlets of scombroids can be
compared with wing-tip slats and slots. In
scombroids the posterior rays of the dorsal
and anal fins become detached during ontogeny and form 1 to 11 separate, non-depressible, sail-like finlets with their booms
well clear of the body surface. The anterior
portions of the dorsal and anal fins fold
down into grooves while the fish swims, and
only the posterior portions of the fins and
2
Employing photoviscosity methods to make the
flow visible about a swimming fish, the author has
studied the movements of a variety of species of
small freshwater fishes (families Anguillidae, Characidae, Cobitidae, Cyprinidae, Gasterosteidae, Gobiidae, Gymnotidae, Hemirhamphidae, Pimelodelidae, and Siluridae). The method involves the use
of a bentonite emulsion and polarized light, and a
paper describing this is in preparation. None of the
forms studied shows any synchronization between
respiratory and locomotor movements, and the exhaled jet is often a source of turbulence leading to
separation of the boundary layer.
145
their finlets project from the dorsal and
ventral profiles. (In the swordfish the dorsal fin does not fold into a groove.) The finlets' small size indicates they serve no important propulsive role. They may contribute to stability by preventing roll, one
of the principal functions of vertical fins in
other fishes (Harris, 1936), but their small
size and their numbers indicate an additional and more important function as a
drag control system.
In most scombroids the body is transformed from vertically elliptical in crosssection behind the head, to circular near
the base of the tail, to horizontally elliptical with knife-like edges at the caudal
peduncle (scombrids and istiophorids have
a circular or vertically elliptical peduncle);
body height diminishes caudad to a minimum at the peduncle. The change in body
shape and body depth, together with the increasing amplitude of the backward-travelling undulations, indicates that a potential
cross-flow exists in the boundary layer along
the rear of the trunk and the tail. This results from the increasing gradient in dynamic pressure between right and left sides
as the body travels laterally during an undulation. If permitted to occur, cross-flow
will cause separation of the boundary layer
with a drastic increase in drag. The avian
wing controls cross-flow through the use of
multiple wing-tip slots. Scombroids may
have solved their cross-flow problem by developing finlets which function as movable
slats, the angle of attack varying with the
pressure gradient between right and left
sides, and their presence serving to transform the flow from a transverse to a longitudinal direction. Their clearance above
and below the body profile may correspond
to that thickness of the boundary layer
which moves too slowly to offer a separation
problem.
If the finlets act as movable slats to control cross-flow, why is their number so variable? Two families—Istiophoridae and
Xiphiidae—have but a single finlet, whereas
the others have from five to eleven. This
146
VLADIMIR WALTERS
suggests that the istiophorids and the swordfish face boundary layer problems entirely
different from those of other scombroids.
This point will be returned to later.
Thirdly, the caudal peduncle is a lowdrag coupling for the caudal fin. Most
scombroids (except scombrids and istiophorids) have a knife-like keel on either
side of the caudal peduncle. In cross-section
the peduncle of a tuna, skipjack, and swordfish resembles a double-bladed axe. This
permits the peduncle to oscillate (in moving the caudal fin) with a minimum of disturbance to the surrounding water. If we
consider a cylinder undergoing reciprocating harmonic oscillation of low amplitude
(thus being analogous to a cylindrical peduncle), a steady streaming motion is imparted to the whole fluid over great distances even though the motion of the cylinder is purely periodic. Such induced streaming requires an energy expenditure by the
cylinder. It is suggested that the keeled peduncle imparts less energy (hence less drag)
to the water than does a cylindrical or vertically elliptical peduncle, and if so, then
the keeled peduncle is a more efficient coupling than is the circular or vertically elliptical fin base for scombroid locomotion."
Fourthly, the caudal fin may be regarded
as a high-speed hydrofoil flap having
cross-flow control measures. The caudal fin
is the source of most of the thrust developed in swimming. Nursall (1958, also this
issue) compares the caudal fin with a hydrofoil, pointing out that the scombroid fin has
a high aspect ratio. This reduces the cross* In this connection, a photograph taken of a
swimming porpoise demonstrates eddyless cross-flow
past an oscillating keeled peduncle (Rosen, M. W.
1961. Experiments with swimming fish and dolphins.
A. S. M. E. Pap. 61-WA-2O3: fig. 11). The keeled
scombroid peduncle may perform in the same manner, with smooth cross-flow between the last finlet
and the caudal fin. In scombroids with keeled peduncles the caudal fin thus resembles an externalhydrofoil flap with the slot bordering on the peduncle. In forms lacking peduncular keels the caudal fin is more comparable with a plain flap or
aileron which lacks a slot. The resemblance to a
plain flap would be greatest in forms having a deep
peduncle and small fin span.
flow around the tips of the fin lobes, thereby reducing drag. Since an ordinary hydrofoil or airfoil exhibits a negative pressure
gradient between the middle and the tips,
a certain amount of cross-flow will occur regardless of aspect ratio. Scombroids (with
the exception of the Xiphiidae) possess a
pair of short fleshy keels on either side of
the caudal fin root. Since the keels are convergent caudad, they accelerate the flow between them to direct a high velocity jet
across the middle of the fin. The keels
themselves may serve as boundary layer
fences, reducing the slippage of the boundary layer toward the tips of the lobes. The
high velocity jet which they produce causes
a pressure drop along the middle of the fin;
this would also prevent the slippage of the
boundary layer toward the tips by reducing
the negative pressure gradient.
Having compared scombroids with hydrofoils possessing various movable drag reduction devices, we shall now consider how
modification of the body profile (in plan
view) can alter drag coefficients. The Joukovsky profile can be satisfactorily used at
Reynolds Numbers below 2 X 10° (practically speaking, the upper limit for laminar boundary layers). This is a mathematically defined shape, derived from the conformal mapping of eccentric circles. It is
the shape one thinks of whenever the word
"streamlined" is mentioned, and it is the
shape of many fast-swimming fishes of small
to moderate size, such as the trout. It is the
shape exhibited by the Scombridae.
When Reynolds Number exceeds 2 X 10°,
the simple Joukovsky profile develops transitional, then turbulent skin friction; the
boundary layer finally separates from the
body surface, mixes with the external fluid,
and drag increases. Separation can be delayed and drag reduced by shifting the hydrofoil's plane of maximal width rearward,
thus creating a laminar profile. The lami
nar profile has 50 to 70 percent less drag
than the Joukovsky profile in the Reynolds
Number range 2 X 10* to 5 X N>7. A tendency for a rearward shift in the plane of
SWIMMING IN SCOMBROID FISHES
maximal body width can be seen in the
scombroids as body size increases (this is
roughly indicated in Table 1, column on
head length); in forms having a laminar
profile, the maximal width tends to lie farther behind the gill covers, which in turn
are farther back due to the increased relative length of the head.
Thus far we have scarcely considered
pressure or form drag. This results when
the boundary layer separates and mixes
with the surrounding fluid. There is some
form drag present when separation does not
take place, owing to the displacement of the
external flow by the boundary layer. At
low Reynolds Numbers, for a streamlined
object the skin friction drag is much gieater
than form drag, which can practically be
disregarded. At high Reynolds Numbers,
where separation takes place, form drag becomes important. The computation of form
drag is a very complicated matter.
As we have already noted, separation can
be delayed by modifying the body shape
and shifting the plane of maximal width
backward; it can also be delayed by use of
a compensating leading-edge slat (synchrony
between respiration and swimming). But
once the water has progressed beyond the
scombroid's gill covers, what then? Separation becomes more of a possibility as the
water flows back along the body. The likelihood that separation may take place is
greatest when the boundary layer must flow
against a positive pressure gradient; such a
gradient exists between a point near the
plane of maximal width and the posterior
end of the caudal base. Separation can be delayed by converting the laminar boundary
layer into a turbulent one near the plane
of maximal width; the increase in surface
friction is much less than the reduction in
form drag. Separation is delayed because
the high energy content of a turbulent
boundary layer enables it to travel against
an adverse pressure gradient for a longer
time than can a low energy content laminar
boundary layer. The cybiids, thunnids,
and katsuwonids all possess a structure
147
which could make the laminar boundary
layer turbulent near the plane of maximal
body width. This is the corselet, an area of
thickened scales and thickened skin which
projects slightly above the body surface; beyond the corselet the scales are either small
and smooth or entirely absent.
The Cybiidae, which operate at 3.7 X
10"' to 1.6 X 107, illustrate a fourth method
by which form drag is reduced, namely by
alteration of the thickness ratio. The thickness ratio (width:length) of large cybiids is
smaller than for small cybiids; all cybiids
which exceed a length of one meter are noticeably more slender-bodied than shorter
species. The form drag for slender bodies
is less than for broad bodies of the same
profile type.
The Thunnidae and Katsuwonidae operate at 3.7 X 1°5 t o 7-3 X 1°7> n a v e m o r e °£
a Joukovsky than a laminar profile, yet exhibit no tendency to slim the body with increasing length. Both families possess a
corselet, indicating the boundary layer is
turbulent along much of the trunk and tail,
but it is puzzling that they have not altered
their body thickness to further reduce form
drag. They may control form drag some
other way, for example, by energizing or accelerating the boundary layer along the
full length of the body behind the corselet.
A simple way to accelerate the boundary
layer would be to lower its kinematic viscosity, which can be accomplished by increasing its temperature. Thunnids and
katsuwonids are said to have body temperatures 6° to 12° C higher than their surroundings (Kishinouye, 1923; Berg, 1940:
footnote p. 491; Morrow and Mauro, 1950;
Van Oosten, 1957). The thunnids and
katsuwonids possess a cutaneous vascular
system, which is unique to these families
(Kishinouye, 1923; Godsil and Byers, 1944).
The vessels supplying the trunk musculature are arranged in countercurrent fashion, with the main vessels situated just beneath the skin surface from the corselet
caudad. In view of recent studies on countercurrent systems (Scholander, 1958) the
148
VLADIMIR WALTERS
arrangement of the blood vessels indicates
that thunnids and katsuwonids cannot lose
any appreciable amount of muscular heat
through the gill surfaces; the heat loss must
take place through the skin behind the
corselet. If these fishes have as high a body
temperature as has been reported, they
might reduce the kinematic viscosity of a
thin film of water adjacent to the skin by as
much as 10 or 20%. This could have importance in the control of boundary layer
separation. However, if the fish travels 10
lengths/sec the boundary layer would be in
contact with the post-corselet part of the
body for only about 0.05 sec. Heat transfer
may not be rapid enough to significantly
alter the kinematic viscosity of a thick layer
of water, but it may be sufficiently rapid to
energize a layer measuring molecules in
thickness. The problem certainly bears
looking into.
there may be a positive pressure gradient between the bill tip and gill cover
(other scombroids have a negative gradient, according to their head shape). Beyond this it becomes very difficult to guess
how the istiophorid body may perform at
its estimated Reynolds Numbers, since we
do not know what kind of pressure gradient exists between the gill covers and the
caudal fin. If it is a negative gradient the
hydrodynamics must be extremely interesting. In view of this uncertainty with respect to the post-cranial pressure gradient,
we cannot speculate on the possible functions of the remarkable integuments found
in these fishes (N.B. Marshall's comments
at the end of Bainbridge, 1961; Walters, in
press).
The final scombroid family to be considered is the Xiphiidae, or swordfish. As with
the istiophorids, the swordfish also possesses
The istiophorids are billed fishes with a bill. Its head length is about 50% greater
laminar profiles. They lack a corselet, have than in the Istiophoridae. As with the istiono cutaneous vascular system, but do have phorids, little can be said about the swima slender build. They display a tendency ming performance of the swordfish because
to shift the gill openings backward by its concave head surface indicates a relengthening the head, although head versed pressure gradient and a fully turbulength is only slightly greater than for thun- lent boundary layer between the bill tip
nids and katsuwonids. At their indicated and the gill cover. Its skin is naked, in conReynolds Numbers of 1.3 to 7.3 X 10T» a trast to the istiophorids, but the swordfish
laminar boundary layer cannot be main- is said to have a peculiar system of pores
tained. The head surface, which is convex (Walters, in press). Since the swordfish has
in most fish, is concave for more than half a horizontally-elliptical, keeled peduncle
its length in the istiophorids (the bill may and no caudal keels, while the istiophorids
be nothing more than an incidental result have a vertically-elliptical, keelless peof boundary layer mechanics which dic- duncle but do have caudal keels, we pretates a concave profile). We must presume sume that the swimming performance is
that istiophorids have a fully turbulent quite different in the two families.
boundary layer along the entire head surSUMMARY AND CONCLUSIONS
face, since it has been demonstrated that
when flow takes place along a concave sur- 1) The Reynolds Numbers are conservaface the faster-moving fluid particles are tively estimated to range from 3.7 X J 0 6 to
forced against the surface by centrifugal 7.3 X 107 for actively swimming scomforces while slower-moving particles are de- broids, and thus their shape and body
flected (the reverse is true of a convex sur- structure are postulated to reflect the inface)—a concave surface thus intensifies teractions between the fish and its immediturbulence in the boundary layer (while a ate environment. The immediate environconvex surface favors laminar flow). The ment is the boundary layer, the mechanics
istiophorid head shape further suggests that of which governs swimming performance.
SWIMMING IN SCOMBROID FISHES
149
2) Scombroids are compared with hydro- Bainbiidge, R. 1958. The speed of swimming of
fish as related to size and to the frequency and
Toils having movable drag reduction deamplitude of the tail beat. J. Exptl. Biol. 35:
vices. The head and gill covers constitute
109-33.
. 1960. Speed and stamina in three fish. J.
a compensating leading-edge slat, and deExptl. Biol. 37:129-53.
lay boundary layer separation. The finlets
-. 1961. Problems of fish locomotion. Symp.
control cross-flow and prevent separation in
Zool. Soc. London 5:13-32.
a manner similar to the slotted wing tips of Berg, L. S. 1940. Classification of fishes both recent and fossil. Trav. Inst. Zool. Acad. Sci. URSS
birds. The keeled peduncle serves as a low
5:517 pp.
drag coupling for the caudal fin. Cross-flow Breder,
C. M., Jr. 1926. The locomotion of fishes.
and separation are reduced by the high asZoologica 4:159-297.
pect ratio of the caudal fin, and also by the Godsil, H. C, and R. D. Byers. 1944. Systematic
study of the Pacific tunas. Calif. Div. Fish Game,
caudal keels which act both as boundary
Fish'Bull. 60:131 pp.
layer fences and boundary layer energizers. Golenchenko, A. P. 1960. The swordfish. [In Russian] Priroda 4:115.
3) The Scombridae have a Joukovsky profile. Since they operate below R = 2 X 1°G Gray, J. 1957. How fishes swim. Sci. Am. 197:4854.
they have no boundary layer separation Harris, J. E. 1936. The role of the fins in the equiproblem, and they show no other apparent
librium of the swimming fish: 1. Wind tunnel
tests on a model of Mustelus canis (Mitchell). J.
mechanisms to reduce form drag.
Exptl. Biol. 13:476-93.
4) The corselet of the Cybiidae, Thunni- Jones,
R. T., and D. Cohen. 1960. High speed
dae, and Katsuwonidae may reduce form
wing theory. Princeton Aeronautical Paperbacks
no. 6.
drag by making the boundary layer turbulent, thus delaying separation in their R Kishinouye, K. 1923. Contributions to the comparative study of the so-called scombroid fishes.
range of 3.7 X 105 to 7.3 X 107.
j . Coll. Agr. Imp. Univ. Tokyo 8:293-475.
5) The Cybiidae have a laminar profile and Lane, F. W. 1941. How fast do fish swim? Counhave altered their thickness ratio to reduce
try Life, London:534-5.
form drag. The thunnids and katsuwonids Morrow, J. E., Jr., and A. Mauro. 1950. Body temperatures of some marine fishes. Copeia: 108-1(5.
have not done this, and they may reduce
Nursall,
J. R. 1958. The caudal fin as a hydrofoil.
form drag by thermally energizing the
Evolution 12:116-20.
turbulent boundary layer between the
. 1962. Swimming and the origin of paired
corselet and the caudal fin.
appendages. Am. Zoologist (this issue).
6) The istiophorids and xiphiids apparent- Shapiro, A. H. 1961. Shape and flow: the fluid dynamics of drag. Anchor Books, Doubleday and
ly have a reversed pressure gradient and
Co., Garden City, L. I.
fully turbulent boundary layer between Schlichting, H. 1960. Boundary layer theory. Mcbill tip and gill covers. This makes it diffiGraw-Hill, N. Y.
cult to say anything about how the rest of Scholander, P. F. 1958. Counter current exchange:
a principle in biology. Hvalradets skrifter no. 44:
the body may perform in swimming. Owing
24.
to differences in caudal fin and peduncle
V. V. 1949. Essays on physics of the sea.
structure, the families are presumed to have Shuleykin,
[In Russian] Akad. Nauk, SSSR.
different swimming performances.
Van Oosten, J. 1957. Chapter V. The skin and
REFERENCES
Abbott, I. H., and A. E. von Doenhoff. 1959.
Theory of wing sections. Dover Publications,
Inc., New York.
scales. Vol. 1. In M. E. Brown, [ed.], The physiology of fishes. Metabolism. Academic Press,
Inc., N. Y.
Walters, V. in press. The trachipterid integument
and an hypothesis on its hydrodynamic function.
Copeia.