# METEO 521: Dynamic Meteorology

Instructor: Prof. Fuqing Zhang,

Syllabus for METEO521: Dynamic Meteorology

Spring 2017

Instructor: Prof. Fuqing Zhang, 627A Walker Building, fzhang@psu.edu, 865-0470

Office hours: By appointments

Scope: This course does not cover the entire spectrum of atmospheric motion; this course focuses on large-scale atmospheric motion for which rotation and stable stratification are central. However, as the concepts to be covered in this course are fundamental to atmospheric motion, the same conceptual approach (e.g., scaling, adjustment, concept of balanced flows) can often be applied to other atmospheric phenomena at smaller scales.

Basic mathematics such as calculus, vector calculus, and partial differential equations will be extensively used.

Homework: Problem sets will be assigned roughly every other week. You are expected to work independently to solve the problems though discussions among classmates are allowed. Plagiarism will not be tolerated. Late homework will be penalized 20% each day after the due date; it will not be accepted after the 5th day past due.

Grading: Homework (20%), two in-class exams (25% each), and a final exam (30%).

Textbook: Atmospheric and Oceanic Fluid Dynamics (Vallis 2006)

References:

1. Introduction to Dynamic Meteorology (Holton and Hakim 2013)
2. Atmospheric-Ocean Dynamics (Gill 1983)

Course Outline

1. Preliminaries
• Review equations of motion (read T1.1-1.6)
• Incompressibility
• Sound waves (T1.8)
• Compressible and incompressible flow (T1.9)
• Incompressibility approximation
• Boussinesq approximation (T2.4)
• Anelastic approximation (T2.5)
1. Effect of rotation and stratification
• Equations of motion in rotating, spherical coordinates (read T2.1-2.3)
• Hydrostatic balance/approximation (T2.7)
• Geostrophic balance/approximation (T2.8)
• Thermal wind balance (T2.8)
• Static stability (read T2.9)
• Introduction and gravity waves (T2.10.1)
2. Gravity Waves
• Shallow water system as a tool (T3.1)
• Reduced gravity equations (T3.2; read T3.3)
• Thermal wind balance revisited (T3.4)
• Introduction of potential vorticity (PV) (T3.6)
• Shallow water waves (T3.7)
• Geostrophic adjustment (T3.8)
• Isentropic coordinates (read T3.9)
1. Vorticity and Potential Vorticity
• Preliminaries (read T4.1-4.4)
• Potential vorticity conservation (T4.5)
•  Potential vorticity and Kelvin’s circulation theorem
•  General form of PV; application to various fluids and flows (T4.6-4.8)
1. Simplified equations for ocean and atmosphere
• Quasi-Geostrophic scaling (T5.1)
• The shallow water quasi-geostrophic equations (T5.3)
• The continuously stratified quasi-geostrophic system (T5.4)
• Rossby waves (T5.7, 5.8; read T5.A)
1. Instabilities
• Synoptic dynamics (extratropical cyclones and fronts)
• Synoptic dynamics (tropical cyclones and hurricanes)
• Kelvin-Helmholtz instability (read T6.1)
• Instability of parallel shear flow (T6.2)
• Necessary condition for instability (T6.3)
• Baroclinic instability (T6.4)
• The Eady problem (T6.5)
• The two-layer baroclinic instability (T6.6, 6.7)
1. Planetary boundary layer
• Planetary boundary layer and its structure
• Atmospheric turbulence
• Secondary circulations and Ekman pumping