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.