Computation of the mixing energy in rivers for oil dispersion

The formation of oil droplet from an oil slick in rivers plays an important role in the transport and fate of oil. We provided a means to compute the mixing energy (energy dissipation rate) in streams, which is needed to estimate oil dispersion in streams. The formulation allows on to estimate the mixing properties of a stream based on easily measurable quantities, such as stream slope, average water speed, and the roughness coefficient. By assuming a roughness height at the streambed, one could also predict the value of the local energy dissipation rate at various depths. The formulation provides also a direct relation between the energy dissipation rate and the shear stress at the bottom of the stream. An example is provided for illustration, and it shows that for a stream that is 30 m wide and has a natural slope of 1/1000, the average energy dissipation rate is equal to 0.001 watt/kg and the maximum value is at the streambed and is around 0.01 watt/kg. The latter value is comparable to spilling breakers of 0.30 m high waves.