A3 Drag Increase

Topic

The surface of the fish's body is the focal point of this model, as it is there that the two most common causes of increased drag in wild fish come into play: the external biological load adhering to the body and damage to the scales covering it. Ectoparasites and damaged or missing scales each independently alter the hydrodynamics of the boundary layer surrounding the fish; both ultimately increase the same physical forces—namely, the friction drag and pressure drag—that the fish must overcome while swimming.

Ectoparasites that attach to the body surface include isopods such as *Gnathia*, copepods such as *Lepeophtheirus*, and trematodes, among other similar organisms. By attaching to the body, these parasites directly alter the hydrodynamics of the boundary layer and markedly increase both friction drag and pressure drag. When an attached parasite is bulky—isopods, for instance, can reach up to two centimeters in size—it also creates additional local pressure drag. This drag increases in proportion to the parasite's frontal area and the square of the fish's swimming speed; thus, a larger parasite or a higher swimming speed both serve to increase this additional local pressure drag.

Damaged or missing scales affect the body surface in a different way than parasites do. When a scale is lost or damaged, the fish's body loses the surface microstructure that the scale provided to reduce drag—specifically the effect of the fine ridges found on ctenoid scales. Instead, a rough patch is exposed—with a height comparable to a grain of sand—causing the water flow around the body to transition to a turbulent regime sooner than it would over an intact surface. The impact of this roughness on drag can be summarized by a dimensionless number combining roughness height, flow friction velocity, and water viscosity: as long as this number remains low, frictional drag still depends on the general flow regime; however, once the number exceeds a value of approximately seventy, the surface becomes "hydraulically rough," and frictional drag ceases to depend on the flow regime, becoming determined solely by the ratio of roughness height to the fish's body length.

The additional drag generated by both parasites and damaged scales entails a tangible biological cost, which can be estimated by the fish's ability to escape a predator. The fish's maximum escape speed drops in direct proportion to the excess drag it incurs, while the "safe escape radius"—the distance at which the fish can still outpace a pursuing predator—shrinks quadratically as the relative speed between the two decreases; a slight drop in relative speed results in a much larger reduction in this safe escape radius.

The magnitude of this cost depends on the parasite load the fish carries: in severe infections—involving more than one hundred copepods per fish—the cost of transport can rise by 30% to 80%, and critical sustained swimming speed can drop by 20% to 40%. In general terms, the impact of this added drag scales with the ratio of the parasite's frontal area to the fish's own frontal area, and with the square of the swimming speed; consequently, larger parasites and higher swimming speeds impose the greatest penalty on the fish.

Thus, external biological load and scale damage—while affecting the fish's body surface through different mechanisms—converge on the same outcome: a fish that experiences more drag than it should and expends more energy to swim at the same speed, and which, when faced with the need to escape a predator, has less speed margin and a smaller safety buffer than an individual without such an external biological load.

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