Introduction

Different friction laws and coefficients


                         No friction on the bottom
                         Strickler law
                                      K = 20
                                      K = 150
                         Interpretation          
                         Manning law


Introduction : working of the code

A case is basically ran based on the cas200 file, fluvialp stores the results. We launch an application starting from any initial condition, the profile we get is the analytical solution of the initial problem. In order to use it later as an initial condition itself, for time convergence matters, we copy this file into fluvialnum. Therfore, we affect the key word "SUITE DE CALCUL" the value OUI, and specify that "FICHIER DU CALCUL PRECEDENT" will be fluvialnum.


    Different friction laws and coefficients

Listing of available laws :

In the cas200 file, we can change the bottom friction law and adjust its coefficient, under the key words "LOI DE FROTTEMENT SUR LE FOND" and "COEFFICIENT DE FROTTEMENT".
For the law, you can put a number between 0 and 5. Each matching corresponds to a certain law:

Each time, we vary the chosen law, and run a simulation using Telemac 2d. We finally vizualise the results with Rubens.

No friction on the bottom

Case of no friction on the bottom

Strickler law with K = 20

Strickler law with K = 150

Case Strickler law (K = 150)

Interpretation :

The Strickler coefficient is known to be the quantifier of the bottom rugosity. The more K is, the less rugous is the channel bottom.

Chezy law :

We remmember Chezy law: Q = Ch S (Rh I)1/2 where    Ch, the Chezy coefficient depends on thef low regime. The Reynolds number is :

Re = (U Dh) / v        U= Q / S = 8.858893836 /(2*2) =2.21 m/s                         

Re = 8.86*10-6     turbulent regime

The Chezy coefficient is Ch = (8*g/lamba)1/2, where lambda will be calcutated via Nikuradse formulae :

lambda = 0.0032 + (0.221/Re0.237) = 0.01 SI

                                               Ch = 88.59 SI

Working :

We will proceed twice :

The aberant value of 0.001 will be afected to Chezy's coefficient. See how this works:

 

Back to plan

Here are the results:

 

Much better this time! We see that the water stays around 2 meters. The froude number has normal values. Nevertheless, it stays lesser than 1.

Back to plan

Manning law:

The other case has been launched for the Manning law. The coefficient n was set to 10.

 

Manning law with coefficient :10.

It looks like this case is not ohysical at all, the coefficient of Manning is probably not correct at all. However, note that the aval cote value is respected : 2m on the end od the channel. During the last step on the run, the Froude number never become greater than 1, which means that the regime stays subcritical all over the channel.

Notes:

1. 6 bottom friction laws, listed below, are available. But they are not all useble in concrete cases. Each flow regime has its own laws, that best describe bottom phenomenons.
Therefore, we must determine the flow regime and find the matching laws and coefficients. The criterias are almost based on the Reynolds number.