LAUSR

Deposits within caves are often used to interpret past landscape evolution and climate conditions. However, cave passage shapes also preserve information about past conditions. Despite the usefulness of passage shape, no previous models simulate cave cross‐section evolution in a realistic manner. Here we develop a model for evolving cave passage cross‐sections using a shear stress estimation algorithm and a shear stress erosion rule. Our model qualitatively duplicates observed cave passage shapes so long as erosion rates vary with shear stress, as in the case of transport limited dissolution or mechanical erosion. This result provides further evidence that erosion rates within caves are not typically limited by surface reaction rates, even though current speleogenesis models predict surface‐rate limitation under most turbulent flow conditions. By adding sediment transport and alluviation to the model we successfully simulate paragenetic channels. Simulations duplicate the hypothesized dynamics of paragenesis, whereby: 1) the cross‐section of a phreatic passage grows until shear stress is sufficiently reduced that alluviation occurs, 2) the floor of the passage becomes armored and erosion continues on the ceiling and walls, 3) negative feedback produces an equilibrium cross‐sectional area such that shear stress is sufficient to transport incoming sediment. We derive an approximate scaling relationship that indicates that equilibrium paragenetic channel width scales with the square root of discharge, and weakly with the inverse of sediment supply. Simulations confirm this relationship and show that erosion mechanism, sediment size, and roughness are secondary controls. The inverse scaling of width with sediment supply in paragenetic channels contrasts with surface bedrock channels, which respond to larger sediment supplies by widening. Our model provides a first step in simulating cave cross‐section evolution and points to the need for a better understanding of the dominant erosion mechanisms in soluble bedrock channels. © 2020 John Wiley & Sons, Ltd.