Kelvin-Helmholtz

Fig. 13. Sketch of Kelvin-Helmholtz instabiHty, where C, the convex side of fluid M, is at a lower pressure than D, the concave side of fluid B.

If Comte had lived long enough to see the development of thermodynamics and its applications, he might have retracted these words. However, he died well before the work of Black, Rumford, Hess, Carnot, Joule, Clausius, Kelvin, Helmholtz, and Nernst that established different aspects of the sciences, followed by the contributions of Gibbs, Lewis, and Guggenheim that unified the science into a coherent whole.a... 

PMS stars with M < 0.35 M0 have a simple structure - they are fully convective balls of gas all the way to the ZAMS. As the star contracts along its Hayashi track the core heats up, but the temperature gradient stays very close to adiabatic except in the surface layers. Li begins to burn in p, a reactions when the core temperature, Tc reaches c 3x 106 K and, because the reaction is so temperature sensitive (oc Tc16-19 at typical PMS densities) and convective mixing so very rapid, all the Li is burned in a small fraction of the Kelvin-Helmholtz timescale (see Fig. 1). 

William Rankine was the first to propose the first law of thermodynamics explicitly, in 1853 (he was famous for his work on steam engines). The law was already implicit in the work of other, earlier, thermodynamicists, such as Kelvin, Helmholtz and Clausius. None of these scientists sought to prove their theories experimentally only Joule published experimental proof of the first law. 

Kelvin, defined, 24 434-435 Kelvin, Lord, 24 433 Kelvin equation, 9 113 19 182 Kelvin-Helmholtz instability, 11 762-763, 765, 772... 

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. 

The first simulations of the collapsar scenario have been performed using 2D Newtonian, hydrodynamics (MacFadyen Woosley 1999) exploring the collapse of helium cores of more than 10 M . In their 2D simulation MacFadyen Woosley found the jet to be collimated by the stellar material into opening angles of a few degrees and to transverse the star within 10 s. The accretion process was estimated to occur for a few tens of seconds. In such a model variability in the lightcurve could result for example from (magneto-) hydrodynamic instabilities in the accretion disk that would translate into a modulation of the neutrino emission/annihilation processes or via Kelvin-Helmholtz instabilities at the interface between the jet and the stellar mantle. 

To test whether the Kelvin-Helmholtz instability, induced by convection, is capable of... 

In this report the results of old calculations (Mayle 1985 Woosley, Wilson, Mayle 1986 Mayle, Wilson, Schramm 1987) of collapse driven explosions and new calculations of the Kelvin-Helmholtz proto-neutron star cooling will be compared with the neutrino observations of supernova 1987a. The calculations are performed by a modern version of the computer model of Bowers and Wilson 1982. (See Mayle 1985 for more recent improvements). 

If we plot the Kamiokande and IHB data together as in Figure 3, we see that for the first two seconds a fairly high luminosity is followed for 10 seconds by a much lower luminosity. We infer from this fact that there may have been a 2 second period of accretion, followed by the explosion and subsequent Kelvin-Helmholtz cooling of the proto-neutron star. 

However numerical simulations of early supernova-driven winds fail to find any evidence for substantial gas ejection from luminous ( L ) galaxies. One can ask what is wrong with the hydrodynamic simulations Certainly, the simulations lack adequate resolution. Rayleigh-Taylor instabilities enhance wind porosity and Kelvin-Helmholtz instabilities enhance wind loading of the cold interstellar medium. Both effects are certain to occur and will enhance the wind efficacity. Yet another omission is that one cannot yet resolve the motions of massive stars before they explode. This means that energy quenching is problematic and the current results are inconclusive for typical massive galaxies. 

Another role of the surfactant is to initiate interfacial instability, e.g., by creating turbulence and Raykleigh and Kelvin-Helmholtz instabilities. Turbulence eddies tend to disrupt the interface since they create local pressures. Interfacial instabilities may also occur for cylindrical threads of disperse phase during emulsification. Such cylinders undergo deformation and become unstable under certain conditions. The presence of surfactants will accelerate these instabilities as a result of the interfacial tension gradient. 

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... 

Figure 6.1 Three regimes of canopy flow. Three scales of turbulence are present. The smallest scale (black circles) is set by the canopy morphology, specifically the diameter of and spacing between individual canopy elements, such as stems and branches. Drag discontinuity at the canopy interface generates a shear-layer that produces vortices via Kelvin-Helmholtz (K-H) instability (shown as solid, black ovals). Boundary layer vortices are present above the canopy (dashed gray). When H/h is small the water surface constrains the boundary layer eddy scale.

Figure 11 Phenomena connected with drop breakup (a) deformation (splitting) of droplets, (b) deformation into lenticular shape, (c) development and separation of the boundary layer, (d) velocity distribution near the separation point of the boundary layer, (e) Kelvin Helmholtz instability, and (f) Rayleigh Taylor instability, pi < P2-...

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