Gone With the Headwind. Characterizing Erosion Using Lattice-Boltzmann Method : and its Implication in Planet Formation

Abstract: Erosion has a long history in science and is used in many different fields today, for example in geology for coastal erosion and in the oil industry for pipe erosion. It is very difficult to study erosion both analytically. Numerically it is difficult due to moving and shape-changing boundaries. Here we develop a numerical model in 3D using the Lattice-Boltzmann method, which is good at simulating complex moving boundaries, and erosion capabilities are implemented. Both laminar and turbulent flow can be modelled with this program. Using an experimentally derived model for the mass change due to erosion in clay and mud-type objects, one can derive equations predicting that the volume of a sphere should, due to erosion, scale as V ∼ −t2. This is also observed with simulations. The shapes of a double sphere with different orientations and a cube in laminar flow we find to have similar power law exponent P, P = 2±0.1. But a cube eroding in Re = 800 had no power law behaviour, meaning that the current analytical framework is incomplete. The possibility of a more general framework is presented for future research. Different Reynolds number also affected the power law behaviour and the shape change over time for the different solids. Very little research has been made for erosion of planetesimals, but it has been argued that erosion can be relevant to their fate. Using the same erosion model, an equation of the erosion time is found for laminar flows and for a sphere. Simulation results find that the equation works within an order of magnitude for turbulent flows, a double sphere and a cube. This gives an estimate of the erosion time t∗ of planetesimals to be t∗ ∼ 1s, given a size of radius equal to 10cm and 1km, an orbital eccentricity e > 10−2 and a distance at r = 1 a.u. Implying that orbits for planetesimals with low eccentricity might be favoured.