Box model for colliding turbidity currents via equation discovery methods

Box models have been widely used in the study of singular turbidity currents since the 1990s and have been popular in the more general gravity current community long before that. As a system of ordinary differential equations the box model is easily interpretable and computationally expedient. To achieve this model all horizontal variations are neglected and therefore the classical box model is unable to capture the dynamics when distinct turbidity currents collide. With the prospect of deep-sea mining for polymetallic nodules on the rise it is becoming increasingly important to consider the interaction of neighboring turbidity currents. Using numerical data obtained by solving the shallow-water equatons for turbidity currents, we take advantage of modern equation discovery techniques (SINDy) to generate a system of ordinary differential equations as a box model for colliding turbidity currents. A comparison of the resulting sediment deposition patterns from the shallow-water equations versus the discovered box model system is provided as these patterns give the clearest interpretation of the environmental impact after the suspended sediment settles.