[Paper Review] Bernhard Haurwitz Memorial Lecture (2017): Potential Vorticity Aspects of Tropical Dynamics

Wayne H. Schubert|arXiv (Cornell University)|Jan 24, 2018

Tropical and Extratropical Cyclones Research39 references3 citations

TL;DR

This paper presents a nonlinear potential vorticity (PV) framework for understanding tropical dynamics, showing that diabatic heating in the ITCZ and tropical cyclones generates PV towers through nonlinear evolution of PV anomalies. The key result is that reversed PV gradients form within days, triggering combined barotropic-baroclinic instability that drives easterly wave development and intensifies storms via boundary layer pumping.

ABSTRACT

This paper is the textual material accompanying the 2017 Bernhard Haurwitz Memorial Lecture, delivered by the author on 28 June 2017, at a joint session of the American Meteorological Society's 21st Conference on Atmospheric and Oceanic Fluid Dynamics and 19th Conference on Middle Atmosphere (26-30 June 2017, Portland, OR).

Motivation & Objective

• To reframe tropical cyclone and ITCZ dynamics through the lens of nonlinear potential vorticity (PV) evolution, moving beyond linear stability theories.
• To explain the rapid development of easterly waves and tropical cyclone intensification via PV anomalies generated by diabatic heating.
• To demonstrate that reversed PV gradients form within days due to zonally asymmetric heating, enabling combined barotropic-baroclinic instability.
• To challenge the traditional steady-state view of the ITCZ and Hadley circulation by showing a continuously evolving, unstable PV field.
• To highlight the role of nonlinear boundary layer dynamics in generating intense, localized pumping that shapes eyewall structure and storm intensity.

Proposed method

• Uses a zonally symmetric background state with potential vorticity increasing poleward to model the tropical environment.
• Applies a diabatic heating profile $ \dot{\Theta}(\Phi) = \dot{\Theta}_m \exp\left(-\frac{(\Phi - \Phi_m)^2}{\Phi_w^2}\right) $ to represent ITCZ heating centered at $ \Phi_m $ with width $ \Phi_w $.
• Solves the PV evolution equation (46) using the time-dependent heating profile to compute the time-evolving PV field in $ (\Phi, \theta) $-space.
• Derives the characteristic timescale $ \tau_c(\Phi) $ for PV evolution, with $ \tau_c(\Phi_m) = \frac{\pi \dot{\Theta}_m \tau}{\theta_T - \theta_B} $, linking heating rate to PV response.
• Analyzes PV isolines in $ (\Phi, \theta) $-space at different times to visualize the formation of PV towers and reversed gradients.
• Compares the nonlinear PV framework with classical linear theories (e.g., Charney and Eliassen, 1964), emphasizing the role of nonlinear dynamics in storm intensification.

Experimental results

Research questions

• RQ1 How does diabatic heating in the ITCZ generate potential vorticity anomalies that lead to instability and wave development?
• RQ2 What is the role of nonlinear PV evolution in the rapid intensification of tropical cyclones, particularly in relation to boundary layer pumping?
• RQ3 How quickly can reversed potential vorticity gradients form in response to localized diabatic heating, and what are the implications for instability?
• RQ4 In what ways does the nonlinear PV framework differ from classical linear stability theories in explaining tropical cyclone and ITCZ dynamics?
• RQ5 To what extent do boundary layer dynamics control the location and intensity of eyewall formation through localized PV anomalies?

Key findings

• Diabatic heating in the ITCZ produces a transient, localized PV tower in $ (\Phi, \theta) $-space, with the maximum PV anomaly forming at the latitude of maximum heating.
• Reversed poleward gradients of potential vorticity emerge within a few days due to the nonlinear evolution of PV anomalies, enabling combined barotropic-baroclinic instability.
• The timescale for PV evolution at the heating maximum is $ \tau_c(\Phi_m) = \frac{\pi \dot{\Theta}_m \tau}{\theta_T - \theta_B} $, linking heating rate and thermodynamic contrast to PV response.
• The PV framework explains the growth of easterly waves not through linear instability alone, but via the nonlinear development of PV anomalies and their interaction with the background flow.
• The modern nonlinear view supersedes classical linear models by showing that primary circulation can grow exponentially even with fixed diabatic heating, driven by PV dynamics.
• Boundary layer pumping, generated nonlinearly, plays a critical role in positioning the eyewall and determining the size of the eye in tropical cyclones.