THE KELVIN-HELMHOLTZ INSTABILITY IN PHOTOSPHERIC FLOWS - EFFECTS ON CORONAL HEATING AND STRUCTURE

The continual motion of the photosphere is essential to a wide range of solar phenomena, from the formation of fluxules and the structure of the granulation network to coronal heating. The velocity structure in and around intergranular lanes is unknown at scales below a few hundred kilometers. Both theoretical and observational arguments lead us to believe, however, that a significant sheared component exists in these locations. For example, largely random, strongly sheared flows have been observed down to the smallest resolved scales in Halpha and continuum images. Sheared flows can be susceptible to the Kelvin-Helmholtz instability, which breaks down the laminar velocity patterns into smaller scale components with significant transverse structure. Any morphological alteration in the velocity field will be reflected in the magnetic field, due to the frozen-in condition. Because the footpoints of the coronal magnetic field move with the photospheric flows, the fine structure of the entire solar atmosphere can be affected. We have performed a series of hydrodynamic numerical simulations which investigate the nonlinear evolution of driven, subsonic velocity shears under a range of typical photospheric conditions. Here the hydrodynamic assumption is justified because the magnetic field is primarily perpendicular to the surface of the high-beta photosphere, thus affecting the characteristic time scales but not the qualitative behavior of the instability. Our calculations show that typical photospheric flows are indeed susceptible to the Kelvin-Helmholtz instability, with rapid nonlinear growth times roughly half of a typical granule lifetime. Approximately half of the initial kinetic energy is transferred to smaller spatial scales, the bulk being concentrated at the scale of the persistent Kelvin-Helmholtz vortices (approximately 100 km). Hence the KHI produces vortical structures in intergranule lanes comparable to a typical fluxule radius, which is precisely the right scale for maximum power transfer to the corona. Relevant photospheric observations and implications for wave-resonance heating and coronal structure also are discussed.