CSIC – Instituto de Ciencias Matematicas

The main goals of this project are exploring the applications of sophisticated mathematical tools in the area of nonlinear dynamical systems to the description of mixing and transport processes in oceanic and atmospheric flows. Several contexts have been chosen to analyze transport processes. The Arctic ocean, the troposphere in the Sahel area during the West Africa Monsoon period. These tools are also applied to the search of efficient navigation routes for Underwater Autonomous Vehicles in first transoceanic missions. Despite the diversity of the application areas there exist and underlying common basis in the study of all these problems, which is exploring the potential of dynamical systems tools to provide new and valuable information in all these domains. Our thesis is that these tools are able to provide novel insights.

This project supports the organization of a meeting that was structured along three days (6, 7 and 8 July 2016). The meeting was designed for allowing cross-disciplinary interaction among mathematicians, physicists, oceanographers and atmospheric scientists in a wide sense. The meeting focused on nonlinear dynamics of atmospheric and oceanic phenomena and created an international forum where prominent researchers investigated the power and impact of Mathematics in these areas and at the same time explored new mathematical challenges proposed by open problems in ocean and atmosphere sciences. In this way, it built on the momentum and interest resulting from the first and second meeting on this topic held respectively in 2008 at Castro Urdiales and 2012 at Madrid, Spain. These meetings lead to the publication of two Special Issues in the Journal Nonlinear Processes in Geophysics
http://www.nonlin-processes-geophys.net/special_issue103.html
http://www.nonlin-processes-geophys.net/special_issue147.html
Topics addressed in this forum were closely related to the following Science and Technology research areas: Modeling and Simulation Tools, Physical Oceanography, Littoral Geosciences and Biology, Unmanned Sea Vehicle Technology, Computational Decision Making, Applied & Computational Analysis, Data Science, etc. which are highlighted in focus areas quoted by the US Naval Science & Technology Plan: Platform Design and Survivability, Assure Access to Maritime Battlespace, Autonomy and Unmanned Systems and Information Dominance.

This Project of fundamental research tackles several problems which are listed within the Challenges for the Society Government Program, in particular they are listed among the priorities in Climate Change and Secure, Efficient and Clean Energy. Our approach to these problems is via the applications in geophysics of mathematical tools developed by our team. Our applied perspective requires: a numerical and computational approach to these goals, experience with data sets and observations and an interdisciplinary interaction with oceanographers, atmospheric scientists and geophysicists.
From the mathematical point of view one aspect of our research addresses dynamical systems with a general aperiodic time-dependence. These provide a theoretical framework suitable for describing the dispersion of passive scalars in fluids. Theoretical objects such as invariant manifolds of hyperbolic trajectories are useful for determining transport routes or identifying transport barriers and mixing. Our team has recently developed novel tools for describing the geometrical template underlying geophysical flows, which usually are aperiodic and defined in finite time. We aim to further pursue theoretical advances on these tools and foreseeing new applications on the topics highlighted in Challenges for the Society Government Program. A second aspect of our research lies on bifurcation theory and evolution problems. These tools provide a predictive frame for geophysical fluids. Our goals are focused in the study of complex fluid dynamics as those in the Earth’s interior. We will develop applications in conduits and chimneys of interest for geothermal energy exploitation and for addressing fundamental questions in volcanism.

The goal of this project was an improved understanding of transport processes in geophysical flows through the application of novel Lagrangian tools to the analysis of observational and numerical model datasets. Further development of those tools is also envisaged.
The research team members represent a combination of theoretical and applied fluid dynamicists, who have collaborated in the past among themselves in different projects directly related to the topics and objectives of this proposal. The results obtained and experience gained in past collaborations will be applied to ensuring the project success.

The goal of this proposal was exploring the applicability of techniques coming from nonlinear physics, dynamical systems and multifractal techniques to the operational management of natural resources using oceanic data, mainly satellite data. The participant researchers have contributed with relevant results. It has been demonstrated that abstract mathematical objects such as invariant manifolds of hyperbolic trajectories are useful to determine transport highways in oceanic flows and identifying transport barriers and even defining mixing measurements in specific geographical areas.
Additionally multifractal techniques applied to thermal images have allowed estimating surface ocean currents that could be applied in an operational context. As multifractal structures are a result of an advection process in a turbulent fluid, there exist connections between Lagrangian tools and Multifractal techniques that could support new theoretical advances and new operational techniques.