A Coupled Reduced Theory for Depositional Onset on a Prescribed Two-Layer Bypass Background

A recent two-layer theory for long-runout turbidity currents explains sustained bypass by allowing a dense lower layer to exchange mass with a more dilute upper layer while avoiding rapid over-thickening. Here, a morphodynamic extension is developed that couples suspended load and bed exchange while treating the two-layer hydrodynamics as a prescribed background. A suspended-sediment balance with bed exchange and Exner’s equation are written on that background, the depositional state variable B=Es/(rC) is introduced, and an exact nonlinear evolution equation for B is derived within the prescribed-background setting. In the weak-exchange limit this equation reduces to an algebraic onset criterion, thereby identifying the regime in which the simpler threshold is valid. Applied to an Amazon-like local-normal-flow reconstruction, the model shows that finite exchange shifts depositional onset upstream relative to the weak-exchange estimate. Background-fidelity checks, grid-refinement tests and closure/inlet sensitivities are reported to delimit the quantitative use of the reduced application. The framework is therefore best interpreted as a coupled reduced theory for suspended load and bed exchange on a prescribed two-layer bypass background rather than a fully hydro-morphodynamic closure.