An analytical solution for horizontal velocity profiles in the hurricane boundary layer

TL;DR

This paper develops an approximate analytical solution for horizontal wind profiles in the hurricane boundary layer, improving understanding of wind sensitivity to parameters outside the eyewall using a nonlinear model with series expansion.

Contribution

It introduces a nonlinear single-column model with a series expansion approach to derive an analytical solution for hurricane boundary layer winds, extending beyond linear analyses.

Findings

First order correction suffices for most practical cases.

Provides simplified understanding of wind profile sensitivity.

Helps analyze effects of parameters like eye distance and Coriolis force.

Abstract

Theoretical analyses of the hurricane boundary layer have traditionally relied on slab models, which provide a limited description of wind profiles. Literature on height-resolving methods is typically based on linear analyses, which may fall short of capturing the full sensitivity of the solution to variations in input parameters. This work proposes an approximate analytical solution of a nonlinear single-column model for horizontal winds based on a constant eddy viscosity assumption and valid outside the eyewall. Building on literature that uses a linearized system of equations, we account for the nonlinearities through a series expansion approach. We find that a first order correction is sufficient for most practical cases. This solution helps provide a simplified understanding of the sensitivity of the radial and tangential wind profiles to input parameters such as the distance from the hurricane eye and the Coriolis force.