For 25 rolls, the dimensionless wave number is while it decreases to 1.88 for 15 rolls. This places the flow regime in a state of oscillatory instability [118]. The mild unsteadiness in the fringe patterns can be with the oscillatory instability mechanism corresponding to a Rayleigh number 1.39 x 10⁴ and a dimensionless wavenumber of 1.88.

The temperature surfaces on three horizontal planes at which respectively, are shown in Figure 4.53. To preserve visual clarity, these surface plots have been partially filtered, without any noticeable loss of signal strength. The ordering of the horizontal planes is from the cooled top plate where . The nature of the temperature field is three-dimensional but is similar at all the three planes. One can see rolls spreading over the entire length of the cavity. While this is a qualitative trend, distortions can also be seen in the form of nonuniformity in roll width and straightness, and possible interference between neighboring rolls. These aspects are brought out in the isotherms over horizontal planes of the fluid layer (Figure 4.54(a-c)) as the equivalent or the dominant rend, with other detail surfacing from increasing view angle. The patterns on two different planes obtained with the final set of four views are shown in Figures 4.54 (b-c). These figures have also been partially filtered for presentation. While the unfiltered plots satisfy the projection data, the isotherms in Figure 4.54 are quite close. Hence, the resulting influences of the apparently three-dimensional flow field Figure 45 (b-c) is akin to longitudinal rolls. While Figure 4.54(b-c) show three-dimensionality in the flow field, the similarity in the geometry of isotherms suggests the formation of a stable structure in the field layer. The situation is analogous to chaotic convection superimposed on a set of stationary rolls observed by Gollub and Benson at a Rayleigh number of 60000.

The local, the line-of-sight averaged (i.e., along a light ray) and the cavity averaged Nusselt numbers have been computed at both the walls. The Nusselt number has been computed using the reconstructed filed as well as the projection data. The average Nusselt number for the entire surface has been computed form the width-averaged temperature profile of the projection data. This corresponds to the slope of the S- shaped curve at the bounding planes. The average Nusslet number at both plates has been reported for various angles of projection. The angular projections other than Ra=4.02 x 10⁴ do not include the entire width of the test cell, but it is expected that the average Nusselt number over the partial length will be representative of the entire width of the cavity. The average Nussselt number for each of the plates has been compared with the experimental correlation reported by Gebhart et al. in air.

A summary of all the Nusselt numbers referred to above is given in Table 10. The Nusselt numbers computed form interferometric measurements are within of the globally averaged value of 2.14. the individual plate-averaged Nusselt numbers are 2.16 and 2.12 as shown within brackets in Table 10. As stated earlier, interferometric projections at were not utilized for reconstruction. The closeness of the average Nusselt numbers at these view angles with respect to other projections shows overall consistency in the measurements. The above equation gives a value of Nu=2.59 at Ra=1.39x10⁴. The Nusselt number obtained form the present set of experiments is thus approximately below the Nusselt number based on the above correlation. The agreement is much closer at the higher Rayleigh number and is discussed later. Within experimental uncertainty, the comparison with previous experiments at the lower Rayleigh number may be taken to be favorable.

Table 10: Comparision of Average Nusselt Number with Ra=1.39x10⁴

The temperature field derived form the interferograms suggest the formation of longitudinal rolls in the cavity. The presence of rolls can be deduced form local Nusselt number variation the distance. When the local Nusselt number is computed from the projection data, the value corresponding to the average computed along the light ray within the test cell is obtained. These line-of-sight Nusselt numbers are averaged along the direction of the light ray and are shown in Figure 46 for various projections angles for the top and the bottom plates. The rolls being parallel to the axis, the line-averaged Nusselt number along the axis that is the projection is expected to show similar trends over both the walls. This is evident in Figure 4.54 (a), where except for a small part of the test cell towards the ends, the local hot and cold wall Nusselt numbers are similar. Along the axis, that is the projection, the local Nusselt numbers at the two walls are expected to show a phase shift. This corresponds to the inclination of the major axis of the roll cross-section with respect to the vertical direction. This shift is seen in Figure 4.54 (b). Hence in a qualitative sense the variation of the line-averaged Nusselt number over the two plates supports the equivalent flow pattern in the cavity to be in the form of longitudinal rolls.