We investigate the behavior of a high-Reynolds-number polydisperse gravity current propagating along a channel of general cross-section form given by a width function $f\left(z\right)$ into a linearly stratified ambient fluid of density ${\rho }_a\left(z\right)$. The current of density ${\rho }_c$ is formed by $n$ types of particles of various densities and settling velocities suspended in an interstitial fluid of density ${\rho }_i$. We formulate shallow-water equations of motion and then solve the partial differential equation system of hyperbolic type by the Lax-Wendroff two-step finite-difference method. We present typical profiles for height ($h$) and velocity ($u$) of the current and mass concentration ($\mathrm{\Phi }$) of the particles. We show that initially the front of the current propagates with an almost constant speed. During the next stage the height and the speed of the nose decrease, which leads to the pseudosimilar final stage of propagation. The solutions are illustrated for flow in typical power-law geometry. The problem introduces two dimensionless parameters: (1) the stratification parameter $S$ ($0\le S\le 1$), which represents the magnitude of the stratification in the ambient fluid, and (2) the particle buoyancy parameter $\mathrm{\Pi }$ ($\mathrm{\Pi }\ge 0$). We show that increasing $S$ decreases the velocity of the propagation of the current. The effect of $\mathrm{\Pi }$ is the opposite: as $\mathrm{\Pi }$ increases, the current propagates faster. For a specific dependence between $S$ and $\mathrm{\Pi }$, an equilibrium is reached for a significant time and the system behaves like a system without particles propagating into the ambient of constant density.

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• Polydisperse systems
• Suspensions
• Direct numerical simulations