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**Dynamics II course 2020**Lecture: Monday, 14-16, room N 3310

Prof. Dr. Gerrit Lohmann

Tutorial: Monday, 16-17, room N 3310

Tutors: Daniel Balting, Stephan Krätschmer

**go to the web site**

**starting April 20, 2020 with the lecture**

The focus of the course is to identify the underlying dynamics for the atmosphere-ocean system. This is done through theory, numerical models, and statistical data analysis. It has been recognized that the atmospheric and oceanic flow binds together the interactions between the biosphere, hydrosphere, lithosphere and atmosphere that control the planetary environment. The fundamental concepts of atmosphere-ocean flow, energetics, vorticity, wave motion are described. This includes atmospheric wave motion, extratropical synoptic scale systems, the oceanic wind driven and thermohaline circulation. These phenomena are described using the dynamical equations, observational and proxy data, as well basic physical and mathematical concepts. Exercises complement the lessons.

German Version:

In den letzten Jahren wurde erkannt, dass Wechselwirkungen zwischen Klimakomponenten wie der Atmosphäre und des Ozean für die Klimaforschung essenziell sind. Der Schwerpunkt des Kurses liegt auf den theoretischen Grundlagen der Dynamik im Atmosphäre-Ozean-Eissystem. Die grundlegenden Konzepte von Strömungen, Energie, großskalige Wirbel und Wellenbewegung werden beschrieben. Dies umfasst atmosphärische Wellenbewegungen, die ozeanische windinduzierte Strömung und die thermohaline Zirkulation. Anhand von Beispielen werden die grundlegenden Methoden erlernt.

Specific aspects:

- Dynamical concepts for climate dynamics: Bifurcations, Feedback analysis
- Instabilities in the atmosphere-ocean system and the dynamics of waves
- Statistical approach of fluid dynamics
- Ocean circulation and atmospheric dynamics
- Climate variability patterns
- Reconstruction of climate, instrumental and proxy data
- Fundamental models: Stochastic climate model, Stommel's box model etc.

Literature:

- Holton, J.R., Introduction to Dynamical Meteorology, Academic Press
- Gill, A., Atmosphere-Ocean Dynamics, Academic Press
- Dutton, J.A., The Ceaseless Wind, Dover
- Olbers, D.J., Ocean Dynamics, Springer
- Cushman-Roisin, B., ENVIRONMENTAL FLUID MECHANICS
- Cushman-Roisin, B. & Beckers, J.-M., Introduction to Geophysical Fluid Dynamics: Physical and Numerical Aspects
- J. Marchal, R. A. Plumb, 2008. Atmosphere, Ocean and Climate Dynamics: An Introductory Text. Academic Press, 344 pp; videos pdf
- R. H. Stewart, 2008: Introduction To Physical Oceanography, online Version: http://oceanworld.tamu.edu/home/course_book.htm
- T. F. Stocker, 2011. Introduction to Climate Modelling. Springer. SBN 978-3-642-00773-6
- B. Saltzman, Dynamical Paleoclimatology - A generalized theory of global climate change, Academic Press, San Diego, 2002, 354 pp.
- N. Gershenfeld, The nature of mathematical modeling, Cambridge University Press, Cambridge, 2003, 344 pp.
- H. Goose, Climate system dynamics and modelling, Cambridge University Press, Cambridge, 2015, 358 pp.
- The Princeton companion to mathematics / Timothy Gowers, editor ; June Barrow-Green, Imre Leader, associate editors. p. cm. Includes bibliographical references and index. ISBN 978-0-691-11880-2
- Statistical Analysis of Climate Series Analyzing, Plotting, Modeling, and Predicting with R Pruscha, Helmut 2013, VIII, 176 p. (link)
- Kämpf, J., 2009: Ocean Modelling for Beginners Using Open-Source Software. Springer. (link)
- Kaper, H.G., Engler, H., 2013: Mathematics and Climate. SIAM. Includes bibliographical references and index. ISBN 978-1-611972-60-3
- Michael Hantel, 2013: Einführung Theoretische Meteorologie. ISBN 978-3-8274-3055-7 DOI 10.1007/978-3-8274-3056-4 Springer-Verlag, Berlin Heidelberg.

**A script will be provided:**

Gerrit Lohmann: Ocean Fluid Dynamics: Concepts, Scaling and Multiple Equilibria.

132 pp. Lecture Notes 2018

with Examples

exercises on paleo server

studIP

Abstimmungssysteme

weathertank

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4 CP, Mandantory course in pep

There are two parts: Course achievements and examination achievements (Studienleistungen und Prüfungsleistungen)

**Course achievements:**50% of the points of the exercise sheets are required. Furthermore, we require active participation in the tutorial with at least one time at the blackboard showing a solution in front of the class.

**Examination achievements:**You have to pass the written exam.

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__Preliminary time table:__**go to the web site**

before

**April 20:**

Chapter 1;

Repeat the material of Dynamics I and other courses. For reading: A very short intro into R , and the Script of the lecture.

Prepare your own laptop (instal R) For programming issues, we will start to work with examples. Please download the open source software R (http://cran.r-project.org/),

for nice features, you may also download Rstudio: http://www.rstudio.com/ (there is also a nice tutorial, and hands-on courses for beginners and even R experts).

**April 20:**

14-16: Lecture 1 (GL)

Overview of Dynamics II (Chapter 4)

Fluid Dynamics, Non-dimensional parameters, dynamical similarity

Elimination of the pressure term and vorticity

16-17 Tutorial: (GL)

Exercise 1 distributed, preparation_NetCDF_CDO_tutorial.pdf, download_data.pdf

**April 27:**

14-16: Lecture 2 (GL)

Rayleigh-Bénard convection and the Lorenz system

Bifurcations

(Chapter 5.3; Chapter 2.3)

Experiments: trailer Cellules de Bénard, Rayleigh–Bénard convection made with mix of cooking oil and small aluminium particles, Was haben Benard-Zellen mit Kochen zu tun?

Simulations: Rayleigh Benard Thermal Convection with LBM, Rayleigh Benard Thermal Convection 3D Simulation

Sketch, Clouds, Cartoon

16-17: Tutorial (DB, SK)

Exercise 1 discussed, Exercise 2 collected, Exercise 3 distributed

**May 4:**

14-16: Lecture 2 (Christian Stepanek)

Lecture about programming: bash, csh, cdo (Chapter 2.2)

programming_course_intro_netcdf_cdo_shell 2019

cdo_examples

16-17: Tutorial (CS): Exercise 1 collected,

Exercise 2 distributed

**May 11:**

14-16: Lecture 4 about Ocean Dynamics (GL)

Coriolis effect

Scaling of the dynamical equations

Geostrophy

Vorticity

Wind-driven ocean circulation

(Chapter 6.1-6.6)

Water tank experiments: Taylor column. A Taylor column is a fluid dynamics phenomenon that occurs as a result of the Coriolis effect. It was named after Geoffrey Ingram Taylor. Rotating fluids that are perturbed by a solid body tend to form columns parallel to the axis of rotation called Taylor columns. At levels below the top of the obstacle, the flow must of course go around it. But the Taylor-Proudman theorem says that the flow must be the same at all levels in the fluid: so, at all heights, the flow must be deflected as if the bump on the boundary extended all the way through the fluid!

16-17: Tutorial (DB, SK)

Exercise 3 collected, Exercise 4 distributed

Projects in Dynamics II (please ask)

**May 18:**

14-16: Lecture 5 about Atlantic deep ocean circulation (GL)

Wind-driven ocean circulation

Vorticity dynamics

Simple model of meridional overturning

(Chapter 6.6, 6.7, 7.1, 7.2)

Model scenarios

16-17: Tutorial (DB, SK)

Exercise 3 discussed, Exercise 4 collected, Exercise 5 distributed

**May 25:**

14-16: Lecture 6 about Shallow water equations and waves (GL)

Rossby, Gravity, Kelvin waves

Plain waves

Scaling

(Chapter 8)

16-17: Tutorial (DB, SK)

Exercise 4 discussed, Exercise 5 collected, Exercise 6 Exercise 6 distributed

**June 1: Pentecost: Holiday in Germany**, no lecture

**June 8: AWI day**

Glaskasten, Bussestr. 24, Bremerhaven

09:00 - 09:20 Overview AWI (TK)

09:30 -10:20 Climate System (TK)

10:30 -11:20 Polar Oceanography (TK)

11:30-12:45: Lecture 7: Dynamics at AWI (GL)

Simple model of meridional overturning (Chapter 7.1, 7.2)

Application: Climate-Box-Model scenarios

Scenario of climate change as shown in the cinema movie The Day After Tomorrow: trailer 1, trailer 2, trailer 3, full movie .

Rossby waves naturally occur in rotating fluids. Within the Earth's ocean and atmosphere, these planetary waves play a significant role in shaping weather: Rossby wave animation, Extremes and Rossby waves, Jet streams,

Rossby wave in a tank, experiment in a tank, experiment in a tank

shallow2D_rossby.r for your R application

Equatorial waves: Theory of Matsuno

13:00-14:00 Lunch in the Mensa

14:00 - 15:00: AWI Ice core Lab (GL)

15:20-16:00 Tutorial (CS): Exercise 2 discussed, Exercise 6 collected, Exercise 7 distributed

**June 15:**

14-16: Lecture 8 about Climate variability and dynamics

pdf of the Lecture

16-17: Tutorial (DB, SK)

Exercises in R

Intro into R for Dynamics, Rmarkdown

(Chapter 2.1)

R in 2018

Exercise 7 collected

Exercise 8 distributed

**June 22:**

14-16: Lecture 9 about Stochastic climate model (GL)

Scaling: Brownian motion and stochastic climate model (Chapter 7.3)

Brownian Motion

16-17: Tutorial (DB, SK)

Exercises 5,6 discussed, Exercise 8 collected, Exercise 9 distributed

**June 29:**

Short: Coarse-graining and filtering, kinetic models, entropy production (Chapter 3.5)

The Boltzmann Equation and Navier Stokes Equation

Application: Simulation set-up of the Rayleigh-Bénard convection

**July 6:**

14-16: Test exam (GL) 16-17 Tutorial (DB, SK):

Exercises 7,8 discussed, Exercise 9 collected

**July 13:**

14-16: Lecture 11 (GL)

Summary of Dynamics II (pdf of the Lecture)

16-17 Tutorial (DB, SK): Exercises 9 discussed; Re-Questions to exercises and test exam

**August xx:**Exam (written, 10-12), room (see anouncement in the pep office)

The exam is based on the exercises and the general content of the lecture. The procedure follows the rules of pep.

The perfect score for the exam is 100 points, although the sum of the problems is 150. Therefore, you can choose among the problems to solve. 50 points are necessary for the course. Keep in mind that each problem has a different number of points. You are allowed to use a calculator & pen. Collaboration or use of alternative sources of information is not allowed.