## Knowledge Expectations for METR 3123 Atmospheric Dynamics II: Theory of Atmospheric Flows

Purpose: This document describes the principal concepts, technical skills, and fundamental
understanding that all students are expected to possess upon completing METR 3123, Dynamics II:
Atmospheric Dynamics and Kinematics. Individual instructors may deviate somewhat from the specific
topics and order listed here.

Pre-requisites: Grade of C or better in METR 3113, METR 3213, MATH 3113.

Students should be able to apply the mathematics from their prerequisite courses, including,
calculus, vector analysis, ordinary differential equations (including use of complex exponential),
geometry and trigonometry.

Goal of the Course: This course continues the study of basic concepts of atmospheric dynamics and
kinematics begun in Dynamics I.

Topical Knowledge Expectations

I. Natural Coordinates and Idealized Flow Types
• Understand the qualitative meaning of trajectories and streamlines. Know how to derive their
differential equations and know how to solve them in simple flows.
• Understand the two-dimensional natural coordinate system (e.g., center/radius of curvature,
normal and tangential vectors). Work with the tangential and normal components of the equations of
motion in natural coordinates. Demonstrate a qualitative and quantitative understanding of the
force balances.
inertial flows, and understand the legitimacy of these approximations.
• Know how to derive the wind fields in these cases (quadratic equation), and solve problems using
the associated wind/pressure fields

II. Thermal wind
• Have a qualitative and quantitative understanding of the thermal wind. Be able to explain its
meaning and significance with and without equations.
• Know how to derive the thermal wind equation and be able to quantitatively solve problems related
to the thermal wind.

III. Circulation and Vorticity
• Know the mathematical definition and physical meaning of circulation and vorticity, and be able
to calculate them from information about the velocity field.
• Know how to derive the vertical component of the vorticity equation.
• Explain the meaning of terms in the vertical vorticity equation, and to use this equation to
explain a variety of meteorological phenomena (e.g., thunderstorm rotation).
• Explain the meaning of analogous terms in the horizontal vorticity equation and apply the
concepts to meteorological phenomena (e.g., baroclinic vorticity generation in gust fronts).
• Derive and understand the Bjerknes and Kelvin Circulation theorems, and be able to apply these
theorems in quantitative problem solving.
• Derive the Rossby potential vorticity theorem, and understand its limitations. Be able to
apply it
to atmospheric flows (e.g., topographic Rossby waves).