Rayleigh number, Darcy-modified

Using these values the Darcy-modified Rayleigh number based on the height of the bottle... 

The solution discussed above has, as parameters, Raw, the Darcy-modified Rayleigh number based on the enclosure width, and A. the enclosure aspect ratio HfW. Some typical results computed with the above program are shown in Figs. 10.29 and 10.30. 

Hence, this analysis indicates that instability will first occur, i.e., convective motions will first occur, when the Darcy-modified Rayleigh number based on the thickness of the layer reaches 39.5. If Ra is greater than this value, convective motion will occur. This value for / amjn is in good agreement with experiment, some experimental results being shown in Fig. 10.35. 

The Darcy-modified Rayleigh number, based on characteristic dimension L, is defined as follows... 

Analyze the linear stability of the fluid layer. The analysis is similar to the classical Rayleigh-Benard problem, but simpler because the Navier-Stokes equations are replaced with Darcy s law. It can be solved analytically. In place of the Rayleigh number, you should find that the stability depends on a modified Rayleigh number,... 

---