 Deposit profile of a finite triangular-valley particle current

Under the same box-model assumptions, $M_0={\rho }_p{\varphi }_{0}W$ is initial particle mass and $m_d$ is final deposited mass per downstream length. Integrate the vertical particle deposition flux across the instantaneous triangular-valley width $2\lambda h$ from arrival of the front at $x$ until settling is complete. This gives the displayed profile on $0\le x\le R$ and zero beyond the runout. Its integral is $M_0$, verifying particle mass conservation. Areal deposit density also depends on the lateral coordinate because the wetted valley width changes as the current thins.

// Target: geophysics.bigb