Instability waves

Steady skirt lengths increase with Re (B3, H5, W2). Wairegi (W2) and Bhaga (B3) also reported skirt lengths which increased with time. The length of steady skirts is controlled by a balance of viscous and capillary forces at the rim of the skirt (B3), whereas the length of wavy skirts appears to be determined by growth of Helmholtz instability waves (H5). 

The near-field response created due to wall excitation is shown here as due to the essential singularity of the bilateral Laplace transform of the disturbance stream function. So far we have seen that the occurrence of transition from laminar to turbulent boundary layer over plane surface proceed as growth of spatially growing instability waves -as was theoretically shown by Heisenberg (1924), Tollmien (1931) and Schlichting (1935) and later verified experimentally by Schubauer Skramstad (1947). 

R has been demonstrated that attachment-line boundary layer supports instability waves, the kind predicted in linear theory (shown by very careful experiments in Pfenninger Bacon 1969 Poll 1979 Arnal, Coustols Jul-lien 1984 Hall, Malik Poll 1984 Poll, Banks Yardley 1996). However, they do not cause transition occurring at the attachment-line, as no linear or nonlinear theories have explained transition at the attachment-line. In the literature, this premature transition is referred to as the Leading Edge Contamination (LEG) problem. In Sengupta et al. (2004) and in Sengupta... 

Homsy, G. M., El-Kaissy, M. M. Didwania, A. 1980 Instability waves and the origin of bubbles in fluidized beds - II. Comparison with theory. International Journal of Multiphase Flow 6, 305-318. 

Homsy, G.M., El-Kaissy, M.M., and Didwania, A. (1980). Instability Waves and the Origin of Bubbles in Fluidized Beds—11 Comparison with Theory, Int. J. Multiphase Flow 6, pp. 305-318. 

Figure 27.7 provides the classic result from Hoyt and Taylor showing the growth of instability waves near the orifice exit. More recent work from Portillo and Blaisdell [24] is shown in Fig. 27.6b that provides insight into the development of 3-D structures on the surface of the jet. The wave patches are attributed to instabilities in the boundary layer as it exits the orifice. 

G. A. BlaisdeU, Collicott, S. H., and Portillo J. E., Measurements of instability waves in a high-speed liquid jet, 61st Conference of the American Physical Society, Division of Fluid Dynamics, San Antonio TX, 2008. 

Fig. 2 Time series images of instability waves due to an electrokinetic instability in a conductivity gradient at an applied field of 1.25 kV/cm. The two solutions are Borate buffers of 1 and 10 mM which are introduced into the device at a stable electric field of 0.25 kV/cm. The high-conductivity stream is seeded with a neutral fluorescent dye [6]...

Figures 8.21 and 8.22 show visualized images taken by a CCD camera from the side and top of the experimental apparatus. Instability does not appear near the end walls of the vessel due to end effect. In Fig. 8.21, a silicone oil droplet can be seen after the rupture of instability waves. It is evident in Fig. 8.22 that the instability initiates over the entire horizontal cross-section. Figure 8.23 shows velocity vectors of salt water flow around the silicone oil/salt water interface just after the onset of KHI. Figure 8.24 shows some examples of the histories of the salt water flow velocity measured with the PIV. The mean velocity ranges from 0 to 32 cm/s, and the acceleration ranges from 0 to 20 cm/s. It can be concluded that PIV is adequate for the measurement of such an unsteady velocity field.

A detailed experimental study of the chemical conditions for which instable wave fronts appear was carried out, as previously, in the cerium-catalyzed BZ reaction [46]. The purpose of this study was to verify a simple hypothesis by Pertsov et al. [47] from which the authors calculated that the onset of instabilities at a marginal excitability is strongly associated with the critical curvature relative to the width of the autocatalyst band in the wave front, L. In a series of solutions with decreasing excitability the critical diameter. 

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