E6 Benthic Locomotion and Crawling on Substrate

Topic

Benthic locomotion describes the movement patterns of fish that live and travel on or near the seabed—such as flatfish (soles and rays), gobies, and scorpionfish. This mode of movement is dominated by three types of forces that are secondary in open-water swimming: the force of gravity, viscous fluid drag, and friction against the substrate itself. These fish move within the benthic boundary layer—a high-shear region adjacent to the bottom where the water velocity profile follows a logarithmic law: water velocity at a given height above the bottom increases in proportion to the logarithm of that height (measured relative to the substrate's roughness). This proportion is determined by the benthic friction velocity, which is the square root of the shear stress exerted by the bottom on the overlying water, divided by the water's density.

In addition to imposing this velocity profile across the benthic boundary layer, the substrate exerts two types of forces directly on the body of a fish resting or sliding upon it: a normal force (the reactive upward push exerted by the bottom on the fish) and a tangential friction force (which arises when the fish moves by sliding across the surface).

Hydrodynamic pressure is distributed differently between the dorsal and ventral surfaces of the fish when it swims very close to the bottom—a phenomenon known as the ground effect. This pressure difference significantly alters both the drag and the hydrodynamic lift experienced by the fish compared to what it would encounter while swimming in open water, far from the seabed. Both the drag and lift generated by this ground effect depend on the fluid density, the square of the swimming speed, and the area of ​​the fish's body projected onto the bottom, all multiplied by a coefficient specific to each force—which, in turn, depends on the ratio between the fish's height above the bottom and its half-body length. When this ratio falls below one-half—that is, when the fish swims at a height less than half its own body length—the lift generated by the ground effect can become negative; this occurs because the fluid accelerates as it passes through the narrow space beneath the fish's body, creating suction that pulls it toward the substrate rather than lifting it away.

The tangential friction force exerted by the substrate on the fish as it slides along the bottom follows the same Coulomb law describing friction between any two surfaces: it is proportional to a friction coefficient specific to the substrate multiplied by the net normal force the fish exerts against the bottom—specifically, the fish's weight minus the lift generated by the aforementioned ground effect and minus the buoyant force exerted by the water on its body.

Fish that crawl along the bottom using modified pectoral fins—with muscular rays acting like legs—generate propulsive forces against the bottom during each fin-contact cycle; this mechanism can be modeled as locomotion involving multiple contact points maintained by static friction against the substrate. The power required by the fish for this type of benthic crawling locomotion is proportional to the sum of the ground-effect drag and the substrate friction force described above, multiplied by the speed at which the fish crawls along the bottom. The flow regime within this benthic boundary layer is characterized—as is any flow—by a Reynolds number specific to that layer, which depends on the water velocity near the bottom, the thickness of the boundary layer itself, and the fluid's kinematic viscosity.

The expected outcome is that the energetic efficiency of benthic locomotion is substantially lower than that of open-water swimming—precisely due to the frictional losses against the substrate described in this model—yet the very ground effect that can generate suction and adhesion may also work to the fish's advantage: in flatfish well-adapted to benthic life, this ground effect can reduce effective drag by as much as thirty percent compared to what they would experience swimming away from the bottom, within the same benthic boundary layer described at the start of this model as the distinctive physical environment for this mode of locomotion.

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