Kelvin-Helmholtz waves

Crapper, G.D., N. Dombrowski, W. P. Jepson, and G. A.D. Pyott. 1973. A note on the growth of Kelvin-Helmholtz waves on thin liquid sheets. J. Fluid Mechanics 57 671-72. 

Crapper GD, Dombrowski N, Pyott GAD, Large amplitude Kelvin-Helmholtz waves on thin liquid sheets, Proc. R. Soc. London Ser. A Math. Phys. Sci. 342(1629), 209-224, 1975. 

As described previously, in the atomization sub-model, 232 droplet parcels are injected with a size equal to the nozzle exit diameter. The subsequent breakups of the parcels and the resultant droplets are calculated with a breakup model that assumes that droplet breakup times and sizes are proportional to wave growth rates and wavelengths obtained from the liquid jet stability analysis. Other breakup mechanisms considered in the sub-model include the Kelvin-Helmholtz instability, Rayleigh-Taylor instability, 206 and boundary layer stripping mechanisms. The TAB model 310 is also included for modeling liquid breakup. 

Presence of the imaginary part with negative sign implies temporal instability for all wave lengths. Also, to be noted that since the group velocity and phase speed in y-direction is identically zero, therefore the Kelvin-Helmholtz instability for pure shear always will lead to two-dimensional instability. 

As described above, instability of the interface between the electrolyte and molten metal is a significant problem that is one root cause of the energy inefficiency of Hall cells. Expressed simply, the interface is deformed by the electromagnetic body forces arising from the interaction between currents in the cell and the magnetic field. The currents are themselves affected by the interface position because it determines the distance between the top surface of the aluminum and the bottom of the anode. There is therefore the possibility that interface deformation leads to further interface deformation. Other mechanisms for generating waves at the interface may be significant, for example, the Kelvin-Helmholtz... 

Kelvin-Helmholtz instability arises because of shear along an interface between two different fluids. Being related to turbulence and transition phenomena, it also describes the onset of ocean wave formation, jetting instabilities, and cloud formation. In microfluidics, it is commonly seen in fluid-fluid interfaces. It is not to be confused with Rayleigh-Taylor or Rayleigh instability ( Rayleigh-Taylor instability). 

We now turn to interfaces in systems not initially at rest. From the manifold possible situations of this type we choose two for detailed study. One is the so-called Kelvin-Helmholtz instability at the interface between two fluids initially moving in a direction parallel to the interface, but at different velocities. The other is wave motion on a falling liquid film, a situation of great practical interest. 

The Kelvin-Helmholtz (KH) instability causes the sheared interface between two fluids that move horizontally at different velocities to form waves (Figure 1.4d). Below a threshold value, surface tension stabilizes the interface. Above the threshold, waves of small wavelength become unstable and finally lead to the formation of drops (liquid-liquid flows) or bubbles (gas-liquid flows), defined by the microchannel dimensions. Surface tension will suppress the KFl instability if [57]... 

Kordyban, E. S., Some Characteristics of High Waves in Closed Channels Approaching Kelvin-Helmholtz Instability, ASME J. Fluids Engng., Vol. 99, pp. 339-346 (1977). 

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