The object of geophysical fluid dynamics is the study of naturally occuring, large-scale flows on Earth and elsewhere, but mostly on Earth. Such flows, for example, describe large anticyclones of our wether, Gulf Stream and Jupiter's Great Red Spot. Typical problems in GFD concern the variability of the atmosphere (weather and climate dynamics), of the ocean (waves, eddies
and currents). Without its atmosphere and oceans, our planet would not sustain life. Therefore, understanding of natural fluid motions is important. Since a natural water is not homogeneous but stratified, this gives a rise to another important object of study in GFD. This is internal waves in the oceans and rivers.

Internal waves occur in density stratified fluids in the presence of a gravitational field. They arise as a result of perturbations which force the stratified fluid to move vertically (i.e, against gravity). Interfacial waves occurring between two superimposed layers of different density are a familiar phenomenon, in particular at the upper free surface of the ocean in the form of surface waves. In the continuously stratified interior of the ocean the restoring force of gravity is much weaker, and as a consequence the periods of internal waves are much larger than those of surface gravity waves.

Perhaps the first explanation of an oceanic phenomenon in terms of internal waves was V. Bjernes' explanation of "dead water," a hitherto mysterious effect in which ships in certain coastal localities would be unable to maintain their normal speed. Ekman (1904) cites a large number of examples of the phenomenon goinf back as far as Pliny the Naturalist, who reported that the effect was attributed either to a mollusk or a certain type of fish that attached itself to the keel. In a preface to Ekman's paper, Bjernes says:

"The present investigation of "dead water," was occasioned by a letter in November 1898 from Prof. Nansen asking my opinion on the subject. In my reply to Prof. Nansen I remarked that in the case of a layer of fresh water resting on the top of salt water, a ship will not only produce the ordinary visible waves at the boundary between the water and the air, but will also generate invisible waves in the salt-water fresh-water boundary below; I suggest that the great resistance experienced by the ship was due to the work done in generating these invisible waves"

Internal waves are ubiquitous in the oceans and therefore they are nowadays a field of paramount importance in fluid mechanics and are the subject of intense study through laboratory experiments, numerical models and theory. But their importance to mixing in the deep ocean and hence the dynamics of the ocean circulation has been recognized only in recent years.

Today internal waves are generally accepted to be responsible for a large fraction of mixing in the deep ocean. Internal waves can interact with one another and exchange energy among themselves. This is possible because of the nonlinear advective terms in the governing equations of motion for a stratified medium. The nonlinear interactions between the waves lead to a nonlinear coupling and energy transfer from large to small vertical scales. Away from direct forcing, the oceanic internal wave field appears to be remarkably uniform and described by the Gurrett-Munk (GM) spectrum which quantifies the observed distribution of wave energy in wave number and frequency space.

The need to estimate the energy exchange inside the ocean arises from the need to estimate the rate of ocean mixing in different regions. There are two key reasons for focusing on ocean mixing: ocean mixing plays an important role in climate variability; and mixing is the most uncertain component of modern general circulation models. Understanding of mixing is also important because the mixing internal wave produce disperses pollutants in the deep ocean (and so do internal waves in the atmosphere).

My current research interests in GFD:  

• I am currently interested in understanding of the spatial and temporal structure of tidal mixing, how and where energy is transferred out of the internal tide. This is necessary in order to better understand the structure of the global ocean circulation, which requires both a map of the tidal generation sites, as well as a dynamical understanding of how much energy from the internal tide is lost to dissipation.

• I am interested to investigate the rate at which wave breaking extracts energy from the internal wave spectrum.
  The energy distribution is well understood for the case of a single triad only. No theoretical studies of this process for two or more resonant triads have ve been reported up to the date. From the practical standpoint, the extension to the case of many resonant triads is important since internal wave field in the the real world's oceans consists of a superposition of many waves with different frequencies, wavnumbers, and amplitudes. Waves are generated at different locations by whatever mechanisms that prevail at each, propagate, and fill the ocean interior, undergoing strong, rapid nonlinear transfer of energy between frequencies in the process, before they dissipate and contribute to internal mixing in the oceans. Therefore, to describe the energy spectrum in the ocean, statistical and numerical models have neen used. However, such models don't explaine the nature of the energy spectrum or energy distribution in the ocean.
  
  However, we can use the recent model in which I described the resonant
  interactions of many internal waves to model the dissipation mechanism.
  The approach is based on finding the correct approximation rate at which energy is dissipated from the initially flat spectrum and comparison the result with the Garrett-Munk (GM) spectrum which represents the stable state of the energy spectrum (see Figure below). The idea is the following:
  
  if the GM model represents the stable state of the energy spectrum then what happens if we start our model with an energy spectrum far from the GM? Will it go to the GM or will it go to some other state?
  
  The simulations in my previous studies (see figure below) yield quantitative predictions of the time evolution of the GM spectrum and the flat spectrum without dissipation. Little change in the GM spectrum occurs (suggesting that the GM spectrum is an equilibrium state). We can see from the results (shown in this figure) that the flat spectrum does not go to the GM spectrum. Instead, it approaches another equilibrium state about which it then oscillates. If the dissipation will be added correctly to the model, then the equilibrium state in the form of the GM spectrum must be achieved. I have recently discussed this in another report and proposed the algorithm which works for the case of few resonant waves so far. More work is needed to generalize this approach to the case of many resonant waves.