Geochemical Effects of Magmatic Solitary Waves .2. Some Analysis

As a complement to the numerical solutions of Watson & Spiegelman (1994; hereafter known as Paper I), we present some analytic solutions and proofs to illustrate more generally how a single magmatic solitary wave affects the transport of trace elements. In the absence of any diffusion or dispersion, the equations for trace element transport can be solved by the method of characteristics. This analysis shows that without diffusion, a solitary wave can transport chemical signals but cannot permanently change the shape of an initial trace element distribution. The solitary waves, however, can locally steepen trace element gradients by a distortion factor S which depends only on the ratio of initial and local transport velocities. These results are quite general and are expected for any solitary wave of permanent form and constant velocity because these waves always provide a frame of reference where the melt and solid velocities are steady state.