Dear all,
Dear Christophe: I appear on this forum always as a private person and I also take the risk of complaining as a private person. My opinions or requests on this forum do not reflect in any way the opinions and requests of my employer. This said, thank you very much for considering this small development! But see below....
Dear Jean-Michel: This is an excellent idea! Yes, the output of the longitudinal value would be enough -- users could then easily deduct the transversal values even if they changed the values of the Elder constants. This would be probably also a very appropriate output to be compared with the isotropic viscosity value delivered by other methods.
Dear all:
The trouble with 2D modelling is that you have to take into account the dispersion (of a tracer, but also of the momentum) due to the vertical integration -- here, just of the vertical velocity profile. This is simply a mathematical artefact, but without it you may not succeed with calibrating your model across a broader range of discharges and water levels -- at least in terms of river modelling.
The most effective and popular method is to represent this dispersion by some kind of diffusion and, again for rivers, to compute the "dispersion viscosities" applying the intuitively well understood and liked Elder model, making them proportional to the shear velocity and the depth. (The physicists among us may protest here, because they may prove that the dispersion cannot be always represented by some diffusion.)
And what makes the things even more awkward for many, the vertical integration of a turbulent(!) viscosity model based on the mixing length -- again, very popular and liked, delivering efficiently in 3D the parabolic vertical distribution of the turbulent viscosity over the depth -- has the very similar form of the now "turbulent viscosity" proportional to the shear velocity and depth -- but with an isotropic coefficient much lower than the Elder *dispersion* model. (kappa/6 if I remember correctly compared with [6.0,0.6], with kappa=0.41.)
And this allows many of us to throw the turbulence and the (artificial) dispersion together and just manipulate the Elder coefficients to represent both turbulence and dispersion together. Practical, isn't it?
And therefore it is important to have the output right in order to compare different calibration methods. And to sort out the all the sources and reasons for the "velocity diffusion". Not to mention the case of the tracer transport.
And, by the way, I would be very happy to have the (artificial) dispersion and the turbulent viscosity models separate clearly and understandably in 2D models. I find this mixed-up treatment one of the largest weaknesses of the 2D modelling.
Best regards,
jaj
PS. Note in 3D you do not have these problems at all. This is the very advantage of 3D models. jaj