Exner equationFrom Wikipedia, the free encyclopedia

This rock belonging to University of Minnesota Professor of Geology Chris Paola is inscribed with the Exner equation.TheExner equationis a statement ofconservation of massthat applies tosedimentin afluvialsystem such as ariver.[1]It was developed by the Austrian meteorologist and sedimentologistFelix Maria Exner, from whom it derives its name.[2]Contents[hide] 1The equation 1.1Basic equation 1.2Including external changes in elevation 2ReferencesThe equation[edit]The Exner equation describesconservation of massbetween sediment in the bed of a channel andsediment that is being transported. It states that bed elevation increases (the bedaggrades) proportionally to the amount of sediment that drops out of transport, and conversely decreases (the beddegrades) proportionally to the amount of sediment that becomes entrained by the flow.Basic equation[edit]The equation states that the change in bed elevation,, over time,, is equal to one over the grain packing density,, times the negativedivergenceof sedimentflux,.

Note thatcan also be expressed as, whereequals the bedporosity.Good values offor natural systems range from 0.45 to 0.75.[3]A typical good value for spherical grains is 0.64, as given byrandom close packing. An upper bound for close-packed spherical grains is 0.74048. (Seesphere packingfor more details); this degree of packing is extremely improbable in natural systems, making random close packing the more realistic upper bound on grain packing density.Often, for reasons of computational convenience and/or lack of data, the Exner equation is used in its one-dimensional form. This is generally done with respect to the down-stream direction, as one is typically interested in the down-stream distribution oferosionanddepositionthough a river reach.

Including external changes in elevation[edit]An additional form of the Exner equation adds asubsidenceterm,, to the mass-balance. This allows the absoluteelevationof the bedto be tracked over time in a situation in which it is being changed by outside influences, such astectonicor compression-related subsidence (isostatic compression or rebound). In the convention of the following equation,is positive with an increase in elevation over time and is negative with a decrease in elevation over time.