The ‘Radcliffe Wave’ as a Kelvin–Helmholtz instability

The large-scale Galactic magnetic field B » 2 pG aligned with this shearing flow in the solar neighbourhood6 will suppress the KHI if Vrel < VA = B(4np)-1/2 » 20 km s-1, where VA is the Alfvén speed in the region4 and p = ßmHn » 2.3 x 10-25 g cm-3 is the mass density of the gas with particle density n » 10-1 cm-3 at the disk-halo interface, one scale height (H » 200 pc) above the Galactic midplane (ß = 1.38 is the mean molecular weight of the gas and mH is the mass of the hydrogen atom). Setting Vrel = 20 km s-1, the minimum velocity (VA) required for the KHI, for a 100 km s-1 kpc-1 falloff at the disk-halo interface (H)-with the understanding that such large velocity gradients are not known to exist near the Sun and are, together with any associated features, probably rare across our Galaxy-gives 4max » 2 kpc for О » 10-15 s-1 in the solar neighbourhood, in agreement with the observed undulation of the Radcliffe Wave. [...]although this study10 pertains to fluids in a uniform gravitational field, such as those encountered in laboratory and terrestrial environments, rather than to a self-gravitating middle layer, some enhancement of the KHI in the Galaxy can be expected for wavelengths greater than 2H /0.4 » 1 kpc. Three-layer modelling11 of the effect of rotation on the development of the KHI in protoplanetary disks shows that the Coriolis force removes the stabilizing effect of the velocity and density gradients on the KHI that can arise in the non-rotating, two-layer treatment4, and that the dominant unstable modes have wavelengths of several scale heights, kH » 1, where k = 2п/Л is the wavenumber of an unstable mode with wavelength Л.