Research papersPhysically sound formula for longitudinal dispersion coefficients of natural rivers

•A concise form for longitudinal dispersion coefficients is put forward.•A formula for the longitudinal dispersion coefficients in natural rivers is obtained.•Genetic method is used to obtain a predictor without pre-given form.

The longitudinal dispersion coefficient (k) is necessary for a plethora of mass transport applications in fluids, but a general formulation for k remains lacking. In this study, we propose a canonical form for k that reflects the physics of dispersion and suits complex flow conditions encountered in natural streams. This general form is much more concise than previous predictors. A predictor for k of natural streams is also obtained using a genetic programming(GP) without pre-specified correlations among field data or a pre-specified form of the predictor. This predictor is physically sound (i.e. exhibits the aforementioned canonical form) and appears to be commensurate to or better than previous estimates of k. A grey model, which measures the proximity of data to a target shape (i.e. the proposed physically sound form), is also used to verify that the canonical form is appropriate. A formulation for k in natural rivers is obtained by utilising a GP. Its form is consistent with the canonical form.