• The world ocean
• Dynamics I - Fundamental laws
• Dynamics II - The ocean and the Earth system
  
• Theory of ocean waves
• Ocean waves and eddies

at Bremen University. Lecture scripts and books can be downloaded. Please consider the note on copyright in these documents. The scripts are subject to continued work. Comments and corrections are welcome.

The Earth is a 'water planet'. A good two-thirds of its surface is covered with water. The large oceans are an essential prerequisite for the existence of the biosphere. They were the cradle of the first life on Earth and provide an indispensable habitat for numerous organisms

It is generally accepted that the oceanic circulation has a profound influence on the mean state of the earth's climate and on climate changes on decadal and longer time scales. Large-scale transports of heat and fresh water by ocean currents are key climate parameters. The stratification and circulation in the upper ocean is crucial for the penetration of heat and substances into the ocean. Vertical motions and water mass formation processes in high latitudes are an important controlling factor for the oceanic uptake of carbon dioxide through the sea surface and thus directly influence the radiative forcing in the atmosphere.

The world ocean plays a twofold role in the Earth's climate system. On the one hand climate fluctuations are caused by long-term changes in the heat distribution of the ocean. On the other hand the thermal 'inertia' of the great water masses slows down climatic changes. The close link between ocean and atmosphere is also effective on shorter time scales. This is seen by interaction between the surface temperature of the ocean and the air temperature close to the ground. The surface winds also contribute to changes in the oceanic circulation and thus regional weather conditions. Since such changes prevail for longer times in the oceans compared to the atmosphere, the ocean can be regarded as a long-term memory which imposes its 'knowledge' from previous climate conditions on future weather and climate.There is, however, also another factor which underlines the importance of the ocean for the global climate system. The ocean forms one of the largest carbon reservoir on Earth. Owing to its relatively large surface area compared with that of the land masses, it plays an important role in the carbon cycle through biological and chemical exchange processes. A small quantity of this carbon is deposited on the sea floor through dead organisms and their calcific shells. A much larger part of this carbon is given off again into the atmosphere. The ocean reacts relatively inertly to an increase in the carbon dioxide concentration in the atmosphere. However, the carbon dioxide content in the water close to the surface remains in a quasi-equilibrium with the atmosphere. Carbon dioxide is only withdrawn permanently from the atmosphere when the carbon which is chemically or biologically bound in the surface water sinks to lower levels in the ocean (biological pump) and is buried in the sediments.

The fundament of the physics of the fluidal envelopes of the Earth is based on the concepts of hydrodynamics and thermodynamics. Molecular structures of the media are not considered explicitly. Physical properties of small but finite volume elements are defined according to the continuum hypothesis. The corresponding state variables will thus be regarded as continuous fields in space and time. The equations which describe the evolution of the state of ocean and atmosphere are the macroscopic conservation theorems for partial masses, momentum, and internal energy, as used in conventional hydrodynamics and thermodynamics. In this lecture we follow a phenomenological derivation of hydrodynamics, residing on empirical knowledge such that mass, momentum and energy of small (material) volume elements moving in the fluid are conserved. The thermodynamics is also formulated for these elements, assuming that the properties are locally in a thermodynamical equilibrium. The macroscopic theory is built in this Lagrangian point of view, but the evolution equations are transformed to the Eulerian form of a field theory which is more useful in applications.

Purpose of this lecture:

The lecture introduces the fundamental physical laws governing the dynamics of atmosphere, oceans and ice. Various forms and approximations are considered and applied to learn from simple, preferably analytical models how equilibria are established and variability of the systems arises.

Scripts/Books/Material/Exercises

Gallery of simple models

Der feuchte Fussball

Complex models are questionable - the work you do is real, the outcome imaginary (Henry Stommel)

The Earth is made up of the geosphere, atmosphere, hydrosphere (the oceans and lakes), cryosphere (the great ice caps, sea ice and mountain glaciers), and the biosphere (the living world). Each obeys certain natural laws, mostly arising from physics. On short times scales, specific for each sphere, each subsystem is in a state of dynamic equilibrium. On longer periods of time, fluctuations and transitions from one state of equilibrium to another may become visible. These delicate states of equilibrium may be permanently disturbed by changes in external conditions. The Earth system is thus constantly in a state of change.

The Earth system is one of the most complex systems presently investigated by scientists. The physical compartments - atmosphere, hydrosphere and cryosphere - are usually combined as 'climate system' and can be described by mathematical equations which result from fundamental physical laws. The other 'nonphysical' parts of the system, as e.g. the vegetation on land, the living beings in the sea and the plentitude of chemical substances relevant to climate and life, can be represented by mathematical evolution equations as well. Comprehensive models spanning this broad range of coupled compartments are so complex that they are mostly beyond a deep reaching mathematical treatment, in particular when asking for general analytical solutions. Solutions are obtained by numerical methods for specific boundary and initial conditions. Simpler models have helped to construct these comprehensive models, they are also valuable to train the physical intuition of the behavior of the system and guide the interpretation of the results of numerical models.

Simple models may be stand-alone models of subsystems, such as stand-alone general circulation models of the ocean or the atmosphere or coupled models, with reduced degrees of freedom and a reduced content of the physical processes. They exist in a wide range of structural complexity but even the simplest model may still be mathematically highly complicated due to nonlinearities of the evolution equations.

Purpose of this lecture:

This lecture presents a selection of such models from ocean and atmosphere physics. The emphasis is placed on a brief explanation of the physical ingredients and a condensed outline of the mathematical form.

• describe the entire Earth system
• embedded in this is the ocean, including the physical systems (motion of water, sea ice, watermass properties), the bio-geochemical system (carbon, nutrients), the ecological system (food web, population dynamics)
• outline of the basic mathematical description, either of physical laws or of phenomenological considerations, of dynamics of ocean system compartments
• outline of model building and the mathematical techniques to solve problems
• examples of system modeling, stand-alone and coupled

 
Scripts/Books/Material/Exercises

The ocean and the atmosphere have highly variable circulations. Currents, temperature and other fields vary on time scales from seconds to decades with spatial scales from millimeters to thousands of kilometers. The variability is either imprinted by variable forcing (ocean by atmopheric winds and pressure) or by instabilities of larger scale currents.

Purpose of this lecture:

The dynamical equations describing linear oceanic waves are derived from basic principles. Dispersion, propagation, wave guides and energetics of sound waves, gravity waves, planetary waves, equatorial waves, and instabilities are analyzed and various mathematical techniques are presented (WKB, ray theory, wave reflections, turning and critical layer analyis, eigenfunctions, wave modes, stationary phase method). Most of the material is applicable to atmospheric waves as well. The role of waves in ocean dynamics is discussed.

 
Scripts/Books/Material/Exercises