arXiv subjects

John Brownfield

Publications and source records attributed to John Brownfield.

2 recordsLinked to original sources

arXiv2025

Stability of the Rankine Vortex and Perimeter Growth in Vortex Patches

We prove that for $\omega: \mathbb{R}^2 \to [0,1]$ sharing the same total vorticity and center of vorticity as the Rankine vortex, the $L^1$ deviation from the Rankine patch can be bounded by a function of the pseudo-energy deviation and the angular momentum of $\omega$. In the case of $m-$fold symmetry, the dependence on the angular momentum can be dropped. Using this, we affirm the results of prior simulations by demonstrating linear in time perimeter growth for a simply connected perturbation of the Rankine vortex.

math.AP↗

arXiv2023

Slowly traveling gravity waves for Darcy flow: existence and stability of large waves

We study surface gravity waves for viscous fluid flows governed by Darcy's law. The free boundary is acted upon by an external pressure posited to be in traveling wave form with a periodic profile. It has been proven that for any given speed, small external pressures generate small periodic traveling waves that are asymptotically stable. In this work, we construct a class of slowly traveling waves that are of arbitrary size and asymptotically stable. Our results are valid in all dimensions and for both the finite and infinite depth cases.

math.AP↗