drag and pressure drag, both of which can best be understood by boundary-layer theory. Water moving across the body of a fish, either by the fish moving through water or holding position in flowing water, has a gradient in relative velocity that increases from 0, where water molecules are in contact with the fish, to that of the free-stream velocity, the velocity of the undisturbed water at some distance from the fish (Blake 1983a). The region between the free-stream velocity and the velocity at the fish is referred to as the boundary layer (Figure 7.1). Flow in the boundary layer can be laminar, resulting in low friction drag, or turbulent, where the resultant eddies form a thicker boundary layer compared to laminar flow and overall friction drag is increased (Webb 1975; Blake 1983a). The change from laminar to turbulent flow is predicted by the Reynolds number, a hydrodynamic measure calculated as
where L = fish length; U = speed; and ν = the kinematic viscosity of water, which is approximately 0.01 cm2s−1 (Webb 1975; Purcell 1977).
Friction drag arises from the viscosity of water in the boundary layer. The greater the surface area of the body, the greater the friction drag. Friction drag also increases exponentially with swimming speed. For laminar flow, the exponent is 1.5, rising to 1.8 for turbulent flow in the boundary layer (Alexander 1967a). Pressure drag is caused by eddies generated along and behind the body by the separation of the boundary layer from the body of the fish (Figure 7.1A). The farther back that boundary separation occurs, the lower the underpressure and the size of the wake. Because turbulent boundary layers separate farther back than laminar boundary layers (Figure 7.1B), the pressure drag resulting from separation of a laminar boundary layer is higher than that for a turbulent one (Blake 1983a). Streamlining also reduces boundary layer separation and thus lowers pressure drag. Other things being equal, pressure drag increases at approximately the square of velocity (Alexander 1967c). Because of how friction and pressure drag are formed, a body shape that reduces friction drag has the opposite effect on pressure drag. Friction drag is related to surface area, so a body shape that minimizes the surface-to-volume ratio, such as a sphere, would have the lowest friction drag. Among freshwater fishes, a more globular shape, such as shown by some sunfishes, would have lower friction drag but a higher pressure drag in contrast to a more elongate, streamlined fish such as a trout, which would have higher friction drag but a lower pressure drag (Alexander 1967c).
FIGURE 7.1. Flow separation around a fish holding position in flowing water.
A. Flow lines, friction and pressure drag, and the boundary layer at a point tangential to the body. The relative thickness of the boundary layer is greatly exaggerated. The length of the arrows indicates the relative velocity of water, ranging from zero in contact with the body of the fish to the free-stream velocity indicated by the arrows of identical length on the right.
B. Changes in flow separation from the body in laminar (dashed lines, black arrows) and turbulent (dotted lines, white arrows) flow. Based on Webb (1975) and Blake (1983a).
Generated Forces
Water flowing over the body and fins of a fish can generate lift because the shapes are acting as hydrofoils—such lift is often referred to as dynamic lift. Bernoulli’s equation predicts that pressure will decrease as the velocity of fluid increases across a surface, so lift for a hydrofoil occurs when flow across the upper surface exceeds that of the lower, resulting in a pressure differential (Webb 1975). Such conditions occur when the angle incidence (α) of the hydrofoil increases from zero (Figure 7.2). The lift generated by a hydrofoil acts normal to the drag force and increases with the angle of incidence up to a point where flow lines begin to separate from the hydrofoil (usually about 15°), resulting in a sudden increase in pressure drag and a sudden decrease in lift so that a stall occurs. Because the amount of lift generated by turbulent flow is greater than for laminar flows, as a consequence of later separation of flow lines as described previously, higher values of lift occur at higher Reynolds numbers (Webb 1975; Blake 1983a).
FIGURE 7.2. Flow lines, lift, drag, and the resultant pressure force at three angles of incidence (α) of a hydrofoil. Drag is parallel to the axis of flow (or motion) while lift is normal to the axis of flow or motion. Based on Webb (1975) and Blake (1983a).
Freshwater fishes occupy a wide range of habitats with a correspondingly high range of current speeds and degrees of turbulence. To maintain hydrodynamic stability, change posture, initiate changes in course, or change location, fishes must control translational and rotational forces. Translational forces refer to movement of a body from one point in space to another without rotation and occur in three planes: surge, slip, and heave (Figure 7.3). Surge refers to movement forward or backward, slip refers to sideways movement, and heave refers to movement up or down. Rotational forces refer to movement around the center of mass and occur along three axes: yaw, pitch, and roll (Figure 7.3). Yaw describes the rotation about the center of mass from side to side, pitch is the rotation up or down, and roll is the rotation along the horizontal axis of the body. Some actions do not result in a change of rotational or translational state because they result in keeping the body in the same location (e.g., hovering) (Alexander 1967c; Webb 2006).
Body Shape, Fin Location, and Maneuverability
Control and maneuverability during hovering or active movement are related closely to fin placement relative to the center of mass, the control of fin rays and fin area by muscles, and swimming speed (Alexander 1967c; Webb 2006). Four zones are recognized relating to fin placement and function (Figure 7.4): (1) an anterior body zone of rudders and lift surfaces positioned anterior to the center of mass that are important in translational forces; (2) a zone of keels located at the center of mass that are particularly important in controlling roll; (3) a zone of stabilizers located immediately posterior to the center of mass and important in controlling yaw, pitch, and roll; and (4) a zone of locomotion and rudders located well posterior to the center of mass that is again important in translational forces (Aleev 1969; Gosline 1971). Anterior control surfaces (zone 1) can include pectoral fins, the head, or the anterior part of the spinous dorsal fin, with the head particularly important in turning motion in elongate body shapes (Webb 2006). A fin, such as the spinous dorsal in zone 1, acts to deflect the fish away from its forward course, but during rapid forward progress in a straight line, it is advantageous for it to be folded down, which also helps to reduce drag. Pectoral fins can also be furled during high swimming speeds (Webb 2006). A single dorsal fin located over the center of mass (zone 2) serves as keel but does not stabilize or deflect the forward course of the body. Many lower teleosts, such as herrings, minnows, suckers, catfish, and trout (groups in the Clupeomorpha, Ostariophysi, and Protacanthopterygii; Figure 7.5), have dorsal fins in this general position or in a position slightly posterior to the center of mass where the fin can also function as a stabilizer (rudder) or aid in propulsion (Figure 7.4B) (Aleev 1969; Gosline 1971). In higher teleosts, such as Moronidae, Centrarchidae, and Percidae (groups in the Acanthomorpha; Figure 7.4A), the dorsal fin consists of two parts, the more anterior spinous dorsal fin and the more posterior soft dorsal fin. The spines can be raised or lowered depending on need. It is important to remember, however, that fins can serve multiple purposes, including camouflage, communication, and in the case of spines, defense.
FIGURE 7.3. Terms used in describing translational (black font and arrows) and rotational (gray font and arrows) changes in state about the center of mass in fishes. Photograph of Colorado Pikeminnow (Ptychocheilus lucius) courtesy of Tom Kennedy. Based on Alexander (1967a) and Webb (2006).
