Ocean Dynamics: steady circulation


Gasser, Marc

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


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 – Equations of motion
1.1 Mass conservation equation
1.2 Volume and surface forces
1.3 Momentum conservation equation
1.4 Equation of state
1.5 Heat and salt conservation equations
1.6 Turbulent diffusion
1.7 Decomposing the flow: Reynolds fluxes
1.8 System of equations of motion
1.9 Non-dimensional equations

Practical: Introducing Matlab with simple applications
1.10 Introductory concepts
1.11 TEOS' routines for computing thermodynamic ocean variables
1.12 Reading actual oceanographic data, plotting properties profiles, plotting T-S diagrams and computing derived quantities such as the buoyancy frequency
1.13 2-D kriging and spatial interpolation

Day 2 – Lineal addition of simple solutions
2.1 General solution for the linear problem
2.2 The Coriolis force
2.3 Geostrophic balance (homogeneous ocean)
2.4 Ekman transport
2.5 Inertial oscillations
2.6 Tide generating force
2.7 Equations of motion for an homogeneous ocean
2.8 Geostrophic balance in a continuously stratified ocean
2.9 Geostrophic balance in a layered ocean
2.10 Box models for the thermohaline circulation

Practical: Simple algebraic and built-in applications
2.11 A simple model of the sea breeze
2.12 The wind-driven ocean-interior circulation (Sverdrup 1947)
2.13 A Coriolis tutorial: the motion of a particle using an inertial and non-inertial reference system (Matlab code by James Price, WHOI)

Day 3 – Energy
3.1 Thermodynamic variables and internal energy
3.2 Total energy equation
3.3 Mechanic energy equation
3.4 Internal energy equation
3.5 Bernoulli relation
3.6 The gradient Richardson number
3.7 Simple models for the upper ocean
3.8 Ocean-atmosphere box models

Practical: Matlab tools for differential equations
3.9 Solving ordinary differential equations (ODE’s)
3.10 Mathematical analysis of ODE’s, including phase portraits, stability points and bifurcation analysis (Lorenz, 1963)
3.11 Solving partial differential equations (PDE’s)
3.12 Creating the domain (simple and realistic domains), setting the initial and boundary conditions

Day 4 – Vorticiy and potential vorticity
4.1 Vorticity and angular velocity
4.2 Potential vorticity and angular momentum
4.3 Vorticity equation
4.4 Potential vorticity conservation equation
4.5 Coastal upwelling
4.6 Quasi-geostrophic model for homogeneous flow
4.7 Sverdrup relation
4.8 Boundary layer solutions (Munk and Stommel)
4.9 Subduction and thermocline circulation

Practical: Student-group projects (one project for every 2-3 students)
4.10 Shallow water equations
4.11 Coastal upwelling (Pedlosky 1978)
4.12 Wind driven circulation gyres (Stommel 1948, Munk 1950, Laiz 2001)
4.13 Convection box models (Stommel 1981)

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

Past course editions: 

Editions: 2015 - November

2017 - January
"Great experience. What I liked best was that lessons incorporated real life examples and concept-based illustrations as much as possible. This has enabled me to follow physical mechanisms of ocean dynamics more easily than before. Good balance between the theory and practical sessions. Kudos to the instructors and organisors for doing such a great job!”
Vandhna Kumar, LEGOS France, Ocean Dynamics: steady circulation Spring 2017

Number of hours: 





9:00-12:30 h 14:00-17:30 h


Institut de Ciències del Mar

Maximum number of places: 


Lab or field work description: 

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

Special requirements: 

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

Contact for further information: 

For additional information, please check our Contact section or get in contact directly with the Lecturer of this course.


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).


Bring own lap-top with Matlab language installed.
Price: 450.00€

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• If you cancel less than 10 working days before the event you will not be entitled to a refund.
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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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