A non-hydrostatic multi-phase mass flow model

Modeling mass flows is classically based on hydrostatic balance equations. However, if momentum transfers scale similarly in slope parallel and flow depth directions, then the gravity acceleration can have same order of magnitude effects, urging for a non-hydrostatic model formulation. Here, we extend existing single-phase Boussinesq-type models by developing new multi-phase consisting solid fine-solid particles viscous fluid (Pudasaini & Mergili, 2019). The includes enhanced dispersion considering various interfacial transfers. We outline contributions waves emerging from phase-interactions. present general, well-structured framework with dispersion, setting foundation comprehensive simulations. discuss situations where non-hydrostatic, dispersive effects are more pronounced such flows. Reduced demonstrate importance contributions. Simplified analytical solutions reveal how be reduced to non-dispersive ones, yet largely generalizing models. postulate novel, spatially varying dissipative force, called prime-force, which physically controls dynamics run-out precise way. Practitioners engineers may find this force very useful technical applications. This illuminates need formally including prime-force A simple equation derived highlighting essence dynamics. Dispersion produces wavy velocity field about reference state without first kind avalanching debris mass. intensity increases energetically as volume fraction or friction decreases.