Basic Concepts Involved in Tropical Cyclone Boundary Layer Shocks

TL;DR

This paper explores fundamental concepts of boundary layer shocks in tropical cyclones, linking wave phenomena to eyewall structures and presenting analytical models that reveal how boundary layer dynamics influence cyclone eyewalls.

Contribution

It introduces the connection between wave solutions and eyewall formations and provides analytical models demonstrating boundary layer discontinuities affecting cyclone structure.

Findings

Triangular waves relate to single eyewalls

N-waves relate to double eyewalls

Discontinuities influence eyewall dynamics

Abstract

This paper discusses some basic concepts that arise in the study of the tropical cyclone frictional boundary layer. Part I discusses the concepts of asymptotic triangular waves and asymptotic N-waves in the context of the nonlinear advection equation and Burgers' equation. Connections are made between triangular waves and single eyewalls, and between N-waves and double eyewalls. In Part II, analytical solutions of a line-symmetric, $f$-plane, slab model of the atmospheric boundary layer are presented. The boundary layer flow is forced by a specified pressure field and initialized with $u$ and $v$ fields that differ from the steady-state Ekman solution. With certain smooth initial conditions, discontinuities in $u$ and $v$ can be produced during the transient adjustment to the steady-state Ekman solution. Associated with these discontinuities in the horizontal wind components are singularities in the boundary layer pumping and the boundary layer vorticity, which can be either divergence-preferred or vorticity-preferred. These models serve as a prototype for understanding the role of the atmospheric boundary layer in the dynamics of primary and secondary eyewalls in tropical cyclones