Rayleigh number

As the Rayleigh number increases, the gravitational forces become more dominant.

Figure 22.10 shows another space-time representation of the same type at a higher Rayleigh number.

The next development with increasing Rayleigh number does produce such fluctuations - periodic ones.

In other words, what sort of flow pattern will be found when the Rayleigh number is above, but not too much above, its critical value?

For most engineering purposes, the Rayleigh number is large, somewhere around 10 to 10.

The onset of instability in these flows is best described as an electric Rayleigh number.

The balance of these two forces is expressed by a non-dimensional parameter called the Rayleigh number.

At a critical Rayleigh number of 1708, the instability sets in, and convection cells appear.

At high Rayleigh number the heat transport is large, in the sense that Nu > 1.

The later stages, at still higher Rayleigh number, have not yet yielded to theoretical analysis and our knowledge of them comes entirely from experimental observation.

At low enough Rayleigh number this pattern persists indefinitely (Fig. 22.3).

At higher Rayleigh number spontaneous changes occur.

However, we must first remember that the above account of evolution with increasing Rayleigh number derived from experiments with pattern control.

Ultimately, however, at the highest Rayleigh numbers, the thermals lose their identity before reaching the opposite boundary.

The onset of natural convection can be determined by the Rayleigh number (Ra).

Although the critical Rayleigh number is independent of the Prandtl number, subsequent developments are not.

To understand the processes occurring at high Rayleigh number, it is helpful to look at the mean temperature distribution across the layer.

Inserting these substitutions produces a Rayleigh number that can be used to predict thermal convection.

They showed that thermomagnetic convection can be correlated with a dimensionless magnetic Rayleigh number.

The Rayleigh number () is a measure determining the relative strength of conduction and convection.

Figure 24.8 shows a sequence of spectra for increasing Rayleigh number measured in a Bénard apparatus.

The most generally used dimensionless number would be the Richardson number and Rayleigh number.

Figure 22.1 shows an example of the observed variation of Nusselt number with Rayleigh number.

The permanent spatial structure is not present at the highest Rayleigh numbers at which observations have been made (Fig. 22.8).

A Rayleigh number for bottom heating of the mantle from the core, Ra can also be defined: