Per R. Jonsson, Kent M. Berntsson, and Ann I. Larsson. 2004. Linking larval supply to recruitment: flow-mediated control of initial adhesion of barnacle larvae. Ecology 85:2850–2859.

Turbulent diffusion and larval motility potentially control the contact rate of larvae with settlement surfaces. To explore the relative importance of these mechanisms we formulated a simple model of contact rate as a function of hydrodynamic regime and larval motility. The model was based on a random-walk representation of turbulent diffusion (Massel 1999). The settlement panel plane was modelled parallel to the flow (x-axis) and the vertical axis. Advective flow parallel to the settlement panels was characterized by the free-stream velocity U.  The turbulent diffusivity (K_y) was only considered in the direction perpendicular to the panel (y-axis):

(E.1)

where y is the distance to the panel surface, k is the von Karman constant (0.41), C_d is the drag coefficient for a flat plate (C_d is a function of the Reynolds number), and M is the motility of the cyprid larva. The motility component in the y direction was estimated as:

(E.2)

where u_c is the swimming speed of cyprids in the y direction (6 cm/s from Crisp 1955) and l_c is the characteristic length between random changes of directions (1–2 s from Walker et al. 1987). The water passing over the leading edge of the panel was assumed to be fully turbulent and the boundary-layer thickness () growing as:

(E.3)

(Schlichting 1979). The local flow speed, u(y), along the panel was modelled as:

(E.4)

(Schlichting 1979). The path of larvae released at the leading edge at different distances from the panel was simulated on a computer using MATLAB 5.2 for Macintosh. The turbulent displacement (l) in the y direction for each time step (t = 0.01s) was evaluated as:

(E.5)

(Massel 1999) where R is a uniform random number between –0.5 and 0.5. For each distance (y) from the panel surface the paths of 500 larvae were simulated and the probability (p) of contact was recorded. A larva was considered to make contact with the panel if the distance to the panel was less than 0.1 mm (the approximate length of cyprid antennules). The total number of encounters was calculated from the measured larval concentration (C) in the water-column and was integrated over the probabilities of encounter for each distance from the panel. The rate of encounters was calculated as:

(E.6)

where L is panel size and  is average flow speed along the panel (very close to U).

LITERATURE CITED

Crisp, D. J. 1955. The behavior of barnacle cyprids in relation to water movements over a surface. Journal of Experimental Biology 32:569–590.

Massel, S. R. 1999. Fluid mechanics for marine ecologists. Springer-Verlag, Berlin, Germany.

Schlichting, H. 1979. Boundary Layer Theory. (Seventh edition). Mc Graw-Hill, New York, New York, USA.

Walker, G., A. B. Yule, and J. A. Nott. 1987. Structure and function in balanomorph larvae. Pages 307–328 in A. J. Southward, editor. Barnacle biology, Crustacean issues 5. Balkema, Rotterdam.