Boundary β‐plumes and their vorticity budgets

Abstract

Analytic solutions for the β‐plume near a solid boundary with Rayleigh drag are presented and their vorticity budgets calculated. It is shown that, when the boundary tilts into the westward plume of streamlines, the β‐plume decays exponentially with a characteristic e‐folding length‐scale that depends inversely as the cosine of the angle of the boundary. Most of the vorticity is extracted from the flow in a short range along the wall. By contrast, when the boundary tilts away from the westward plume of streamlines, the vorticity extraction is reduced by a factor that depends exponentially on the distance to the wall and the sine of the wall angle. Numerical solutions for horizontal viscous dissipation are also presented, and it is shown that they resemble the β‐plume with Rayleigh drag. However, the plume tail decays as an exponential modulated by a harmonic oscillation. The characteristic e‐folding decay scale is shorter than with Rayleigh drag by one to five times, depending on wall angle; the oscillation wavelength is about 3.4 times the e‐folding scale. These results suggest the relevant parameters and scalings controlling bathymetric interactions in more complex situations, such as the real ocean.