Final Report Summary - FIBOSI (Flow Interaction between the ocean surface and the interior)
In recent times, data have revealed an unexpectedly dynamic ocean, exhibiting ever-changing highly-complex structures such as swirling vortices or eddies and a plethora of jets (the largest example being the gulf stream). The ocean is not as predictable as previously thought; jets or currents shift position, intensify and diminish, meander, and spin off vortices, some of which get swept back into the jets and re-incorporated. The true picture is more aptly called 'turbulent'. This turbulence - it is now recognised - plays a major role in organising the overall ocean circulation; in short, the organised flow patterns intimately depend on the turbulence.
The research project conducted aimed to better understand this relationship by focusing on key fundamental processes thought to occur widely throughout the oceans. We primarily considered a problem which has been poorly studied to date, namely the interaction between surface vortices and the deep interior. Specifically, we aspired to understand the way in which surface vortices interact with vortices and jets (currents) in the interior.
This alone is a highly complex problem, potentially depending on many parameters. It is necessary to simplify to begin to be able to comprehensively explore important controlling parameters and arrive at any useful, informative conclusions. We began by employing the so-called 'quasi-geostrophic' model governing the motion of a three-dimensional rotating stratified fluid, when the background effects of the Earth's rotation and density stratification are in some sense 'dominant'. This model is regarded as an excellent approximation to the full system of equations over large parts of the ocean, and it is the most widely used model by the geophysical fluid dynamics community, particularly in 'process' studies aiming to understand fundamental aspects of atmospheric and oceanic dynamics.
The quasi-geostrophic model, despite its relative simplicity, is itself capable of a rich array of solutions, most of which remain unexplored. This is because the model is nonlinear, depends on three space dimensions, and depends on time. As a result, few analytical solutions are known, and few of these are relevant to the turbulent dynamics of the ocean. Instead, we must rely on numerical simulations, and obtaining accurate solutions is computationally very challenging.
To meet this challenge, we made a decisive advance in this project by developing a new, state-of-the-art, highly-versatile, adaptable computational method capable of modelling an enormous variety of flow situations, within the quasi-geostrophic approximation. The new method was built from a much simpler two-dimensional 'single-layer' method called the 'combined Lagrangian advection method' (CLAM, see Dritschel & Fontane, J. Comput. Phys. 229, p.5408 2010), which combines the accurate and efficient parts of several numerical modelling approaches to achieve an unprecedented gain in accuracy and efficiency. The three-dimensional quasi-geostrophic counterpart of CLAM is likewise vastly more efficient and accurate than other computational methods widely used by the scientific community - this is likely to have a major, long-term impact on basic research, by providing the community with a carefully-designed, easy-to-use method for studying fundamental dynamical processes in the oceans.
The development of this new model was a huge research effort, and unfortunately it took more time than expected. There were many issues to sort out concerning the efficient representation of the vertical structure of the flow, and throughout we insisted on creating a method which would be more generally useful by the community. The PI has developed innovative computational methods for nearly three decades, and this new method was undoubtedly the most challenging undertaking to date.
Less time was therefore available for studying all of the problems described in the original proposal. However, we did address the 'core' problem of the interaction between a surface vortex and an interior vortex. This problem depends on a number of parameters, such as the size ratio and intensity ratio of the two vortices, as well as their horizontal and vertical separation. We have comprehensively examined this parameter space, identifying distinct regimes where the two vortices align themselves vertically, where one vortex is split into several vortices, or is stripped of its periphery, or is altogether destroyed. A few striking examples are provided as attached images, and movies can be found on the project website http://www-vortex.mcs.st-and.ac.uk/~dgd/FIBOSI(opens in new window). Two papers are in preparation, the first describing and testing the computational method, and the second studying the interaction between a surface vortex and an interior vortex.
The PI and the research fellow continue to collaborate on this research, and further publications connected to the project will be reported to the REA in due course. This research has greatly strengthened existing ties to Professor Xavier Carton's group at the Universite de Bretagne Occidentale, with whom there is now a strong collaboration with several members of the PI's research group in St Andrews.
As already mentioned, this research is relevant to other researchers studying fundamental aspects of ocean dynamics. We will shortly make available the entire software package for modelling a very wide range of problems under the quasi-geostrophic approximation. This includes not only basic vortex-vortex and vortex-jet interactions, but also the effects of wind-stress forcing and buoyancy forcing at the ocean surface, and bottom drag. All of these features have been built into the computational method and have been thoroughly tested.
The research project conducted aimed to better understand this relationship by focusing on key fundamental processes thought to occur widely throughout the oceans. We primarily considered a problem which has been poorly studied to date, namely the interaction between surface vortices and the deep interior. Specifically, we aspired to understand the way in which surface vortices interact with vortices and jets (currents) in the interior.
This alone is a highly complex problem, potentially depending on many parameters. It is necessary to simplify to begin to be able to comprehensively explore important controlling parameters and arrive at any useful, informative conclusions. We began by employing the so-called 'quasi-geostrophic' model governing the motion of a three-dimensional rotating stratified fluid, when the background effects of the Earth's rotation and density stratification are in some sense 'dominant'. This model is regarded as an excellent approximation to the full system of equations over large parts of the ocean, and it is the most widely used model by the geophysical fluid dynamics community, particularly in 'process' studies aiming to understand fundamental aspects of atmospheric and oceanic dynamics.
The quasi-geostrophic model, despite its relative simplicity, is itself capable of a rich array of solutions, most of which remain unexplored. This is because the model is nonlinear, depends on three space dimensions, and depends on time. As a result, few analytical solutions are known, and few of these are relevant to the turbulent dynamics of the ocean. Instead, we must rely on numerical simulations, and obtaining accurate solutions is computationally very challenging.
To meet this challenge, we made a decisive advance in this project by developing a new, state-of-the-art, highly-versatile, adaptable computational method capable of modelling an enormous variety of flow situations, within the quasi-geostrophic approximation. The new method was built from a much simpler two-dimensional 'single-layer' method called the 'combined Lagrangian advection method' (CLAM, see Dritschel & Fontane, J. Comput. Phys. 229, p.5408 2010), which combines the accurate and efficient parts of several numerical modelling approaches to achieve an unprecedented gain in accuracy and efficiency. The three-dimensional quasi-geostrophic counterpart of CLAM is likewise vastly more efficient and accurate than other computational methods widely used by the scientific community - this is likely to have a major, long-term impact on basic research, by providing the community with a carefully-designed, easy-to-use method for studying fundamental dynamical processes in the oceans.
The development of this new model was a huge research effort, and unfortunately it took more time than expected. There were many issues to sort out concerning the efficient representation of the vertical structure of the flow, and throughout we insisted on creating a method which would be more generally useful by the community. The PI has developed innovative computational methods for nearly three decades, and this new method was undoubtedly the most challenging undertaking to date.
Less time was therefore available for studying all of the problems described in the original proposal. However, we did address the 'core' problem of the interaction between a surface vortex and an interior vortex. This problem depends on a number of parameters, such as the size ratio and intensity ratio of the two vortices, as well as their horizontal and vertical separation. We have comprehensively examined this parameter space, identifying distinct regimes where the two vortices align themselves vertically, where one vortex is split into several vortices, or is stripped of its periphery, or is altogether destroyed. A few striking examples are provided as attached images, and movies can be found on the project website http://www-vortex.mcs.st-and.ac.uk/~dgd/FIBOSI(opens in new window). Two papers are in preparation, the first describing and testing the computational method, and the second studying the interaction between a surface vortex and an interior vortex.
The PI and the research fellow continue to collaborate on this research, and further publications connected to the project will be reported to the REA in due course. This research has greatly strengthened existing ties to Professor Xavier Carton's group at the Universite de Bretagne Occidentale, with whom there is now a strong collaboration with several members of the PI's research group in St Andrews.
As already mentioned, this research is relevant to other researchers studying fundamental aspects of ocean dynamics. We will shortly make available the entire software package for modelling a very wide range of problems under the quasi-geostrophic approximation. This includes not only basic vortex-vortex and vortex-jet interactions, but also the effects of wind-stress forcing and buoyancy forcing at the ocean surface, and bottom drag. All of these features have been built into the computational method and have been thoroughly tested.