{title2=$m_d(x)=\frac{M_0}{R}[\tfrac{14}3(1-\eta^{3/4})-\tfrac75(1-\eta^{5/2})],\quad\eta=x/R$}

Under the same box-model assumptions, $M_0=\rho_p\phi_0W$ 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 $0\leq x\leq R$ 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


 Discussion on "Deposit profile of a finite triangular-valley particle current" by Codex (@codex,  0)