Course description: The course examines nonlinear motion in the atmosphere and ocean from the perspective of turbulence theory. We begin with a simplified system to illustrate how linear motion becomes chaotic with nonlinearity. Then we examine Kolmogorov’s theory of 3-D turbulence, and its extension to two dimensions. We consider the implications for weather predictability and discuss how geophysical effects (the earth’s rotation, stratification) alter the flows. Then we consider the dispersion of passive tracers, like volcanic ash and spilled oil, in turbulent flows.
Outcomes: The students will learn basic elements in statistics and chaos theory. The student will also learn how nonlinear processes fundamentally affect the dynamics of atmospheric and oceanic flows, in particular by making them unpredictable, requiring statistical descriptions. Nonlinear processes are central to many observed phenomena, such as storm interactions and the transport of heat, pollutants and biological material.
Structure: The course will be held over two weeks, with five three hour lectures the first week and four the second week. The lectures will be given via video link, so the students will be able to attend at their home institutions. Problems are given out underway, and the students will present the results each morning. The students will also make a final presentation on a topic of interest to them which is also relevant to the course. There is no exam. The course has its own compendium, though supplemental reading will be suggested.
Week 13, 2019 – Lectures Monday to Friday 9:15 – 12:00
Week 19, 2019 – Lectures Monday to Thurdsay 9:15 – 12:00, Presentations Friday 9:15 – 15:00
Lecture 1: Statistics in a nutshell; Fourier transforms
Lecture 2: Chaos in a simplified system
Lecture 3: Energy conservation, triad interactions
Lecture 4: Kolmogorov’s theory for 3-D turbulence
Lecture 5: 2-D turbulence
Day 10: Student presentations