Turbulent Boundary Layer Height Scales in Hurricanes

TL;DR

This paper introduces new formulae for hurricane boundary layer height based on turbulence and stratification, validated against simulations and observations, improving physical accuracy over previous models.

Contribution

It proposes novel boundary layer height scalings for hurricanes that account for stratification and turbulence, backed by analytical derivation and validation.

Findings

Scalings are accurate within 2.5% relative error.

Formulas collapse velocity profiles from simulations and observations.

Enable relationships between boundary layer height and storm characteristics.

Abstract

Boundary layer processes drive the air-sea exchange of momentum, heat, and moisture that powers and shapes hurricanes. The height of the boundary layer is a critical parameter in engineering and meteorological models of hurricane wind speed, turbulence intensity, and storm strength. Existing models rely on a height scale derived with the assumption of a constant eddy viscosity, a strong simplification that limits physical accuracy. This work proposes formulae for the turbulent boundary layer height in hurricanes outside the eyewall. The proposed scalings are $u_\star/\beta$ for neutral stratification, and $u_\star/\sqrt{\beta N}$ for stable stratification, where $u_\star$ is the friction velocity, $\beta$ is the absolute fluid vorticity and N is the Brunt-Vaisala frequency of the background stratification. These scalings are analogous to those used in the literature for neutrally and stably stratified turbulent atmospheric boundary layers. The formulae are backed by analytical derivation and validated against velocity profiles from large-eddy simulations and field observations. They are predictive to within 2.5% relative error on average and yield a good collapse of the simulated and observational velocity profiles away from the surface. The results further enable quantitative relationships between boundary layer height and other characteristic scales, including the height of maximum wind speed and the depth of the inflow layer. The proposed expressions offer a practical basis for interpreting observational data, informing mesoscale simulations, and specifying turbulent flow statistics in wind engineering and coastal resilience.