Abstract
We present a mathematical model of the growth of coral subject to unidirectional ocean currents using concepts of porous-media flow and nonlinear dynamics in chemical systems. Linear stability analysis of the system of equations predicts that the growth of solid (coral) structures will be aligned perpendicular to flow, propagating against flow direction. Length scales of spacing between structures are selected based on chemical reaction and flow rates. In the fully nonlinear system, autocatalysis in the chemical reaction accelerates growth. Numerical analysis reveals that the nonlinear growth creates sharp fronts of high solid fraction that, as predicted by the linear stability, advance against the predominating flow direction. The findings of regularly spaced growth areas oriented perpendicular to flow are qualitatively supported on both a colonial and a regional reef scale.
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