Ocean Dynamics: propagating anomalies


The participant will be introduced to the main concepts of Ocean Dynamics for rotating and stratified turbulent fluids. The course is structured around ten main topics, each to be covered in one day. Each topic will have a theoretical background, where fundamental concepts will be discussed, and a practical exercise, where a laboratory and/or computer exercise will be discussed, developed and applied. After completing the course the participant will have an intermediate knowledge of the major blocks underlying the dynamics of ocean circulation and mixing.

Programme information: 

Day 1 – Surface waves
1.1 The inviscid equations of motion
1.2 Surface gravity waves: the Laplace equation
1.3 Sinusoidal solutions to the Laplace equation
1.4 Wave kinematics
1.5 Phase and group velocity
1.6 Waves in hydrostatic balance: the long wave approximation
1.7 The wave equation

Practical: Surface wave propagation
1.8 Numerical simulation of the wave equation in 1D and 2D
1.9 Shoaling, refraction, difraction and reflection

Day 2 – Internal waves
2.1 Buoyancy frequency
2.2 Internal gravity waves
2.3 Internal waves with rotation
2.4 Long waves at the interface of two fluids
2.5 Long waves in stratified fluids: normal modes

Practical: Internal waves
2.6 Buoyancy frequency computation
2.7 Sturm-Liouville problem, eigenvalues and eigenvectors
2.8 Decomposition of an internal wave field into normal modes

Day 3 – Effects of rotation
3.1 The Rossby adjustment problem
3.2 Transient free (Poincaré) waves
3.3 Boundary effects: Poincare and Kelvin waves
3.4 Bottom effects: topographic Rossby waves

Practical: Rotation-related motions
3.5 Inertial oscillations
3.6 Classical harmonic tidal analysis

Day 4 – Planetary waves
4.1 Equatorially trapped waves
4.2 Quasigeostrophic scaling for long waves
4.3 Quasigeostrophic Rossby waves
4.4 Analogy between topographic and planetary waves

Practical: Student-group projects (one project for every 2-3 students)
4.5 Forced inertial oscillations
4.6 Rossby adjustment problem and Poincaré waves
4.7 Kelvin and Rossby waves
4.8 Wave propagation in complex domains (including tsunamis)

Day 5 – Recent papers and wrap up
5.1 Discussion on recent papers
5.2 Course wrap up

Practical: Student-group projects (continued)
5.3 Student presentations
5.4 Course summary


Gasser, Marc

Research Assistant
Physical and Technological Oceanography Department
Institute of Marine Sciences - CSIC
Barcelona, Spain

Course dates: 

No edition programmed


9:00-12:30 h and 14:00-17:30 h, Monday to Friday

Past course editions: 


Institut de Ciències del Mar

Number of hours: 


Contact for further information: 

For additional information, please contact the program coordinator at

Lab or field work description: 

It will include both laboratory experiments and program development and application. As described in the course information.



Maximum number of places: 



Full price of this course is 450€. A reduced registration fee of 360€ is applied for early registrations (20 days before the opening of the course).

Special requirements: 

Good background in Calculus and Physics. Good general programming background.

The student is encouraged to have previously participated in the “Ocean Dynamics: Steady Circulation” course.

Price: 450.00€

Cancelation policies

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• If you cancel less than 10 working days before the event you will not be entitled to a refund.
There will be no refund for non-attendance to the course.

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In the case of a complete course cancellation, attendants will either be offered an alternative date, a credit note or a full refund. Barcelona Ocean will not compensate for travel fees or any other expense incurred by you as a result of such cancellation. Every effort will be made to avoid the cancellation of any planned courses.

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