Buoyancy production in a particle-laden current (${\partial }_t(g^{\prime }h)+B_x=S_B-v_s{g}^{\prime }$)

The integrated budget is ${\partial }_t(g^{\prime }h)+B_x=S_B-v_s{g}^{\prime }$. A steady spatial increase needs a source $S_B$ exceeding deposition, for example sediment resuspension or lateral particle input. In unsteady flow, local depletion can produce $B_x>0$ even without particle addition.