The stability of inviscid Beltrami flow between parallel free-slip impermeable boundaries

Abstract

We present a family of exact inviscid three-dimensional Beltrami flows in a horizontally periodic domain lying between two parallel free-slip boundaries. Significantly, these flows are not stress free: the horizontal vorticity varies on each boundary. Using direct numerical simulations (employing horizontal hyperdiffusion only for numerical stability), we find that the largest-scale member of the family is unstable and breaks down into anisotropic turbulence, with relatively large horizontal vorticity at and near each boundary, and associated surface frontal features. We conjecture that all members of the family are similarly unstable. The free-slip boundaries play an important role in the late stages of the instability by constraining the deformation of vortex lines near the boundaries. This study appears to be the first to consider the role of boundary horizontal vorticity in an inviscid context.