Exner equation

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The exner equation describes the conservation of mass of sediment in a fluvial system such as a river. In its most commonly-used form, it is a conservation of mass between the sediment in the bed and the sediment in transport.

The equation states that the change in bed elevation, η, over time, t, is equal to one over the grain packing density εo, times the negative divergence of sediment flux through an infinitesimally small control volume.

\frac{\partial \eta}{\partial t} = -\frac{1}{\epsilon_o}\nabla\cdot\mathbf{q_s}

Note that εo is also expressed as (1 − λp), where λp equals the bed porosity.


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