I: Motivation and Fundamentals
The course begins with a general motivation to the study of Fluid Dynamical Systems, by introducing their fundamental concepts and illustrating their relevance to a wide spectrum of scientific, engineering and operational challenges.
II: Classical Fluid Dynamics
The classical part of the course builds on basic knowledge in Fluid Mechanics and Thermodynamics to formulate the basic principles governing fluid flow.
The notion of fluid is then revisited and generalised to a broad class of dynamical systems, paving the way for an integrated treatment of fluidstructure interactions with overarching span.

 Fundamental Definitions and Governing Principles
 Fluids in Motion: Descriptive Kinematics
 Fluids in Action: Fundamental Dynamics
 Fundamental Constraints: Thermodynamic Limits
 Dynamic Similarity and Scaling Physics
 Boundary Layers, Instability and Turbulence
 Numerical and Computational Fluid Dynamics (CFD)
III: Fluid Dynamical Systems
Fluid Dynamical Systems are then formulated in the light of Mathematical Physics, providing an intuitive yet rigorous treatment of complexity in a simple, coherent framework, shedding light over empirical Classical Fluid Dynamics, and providing a physical background to stochastic behaviour and uncertainties in complex fluid regimes.

 Fundamentals of Dynamical Systems: Diagnostic and Prognostic Laws
 Beyond the Mechanistic Paradigm: the Stochastic Physics of Fluids
 Beyond StochasticDynamics: new Mathematical Physics of Fluids
 Fluid Flow as a Dynamical System: Complexity made Simpler
 Thermodynamics of Fluid Dynamical Systems: Finding Order in Chaos
 Redefining Thermodynamic Limits: Coevolution in Transient Systems
 Nonlinear Interactions and Emergence: The role of Synergies
 Regime Dynamics and Clustering: Leptogenesis, Accretion and Coalescence
 Information Physics in Fluids: Beyond Statistics and Kinematic Geometry
 Predictability Laws: Dynamics of Uncertainties in Fluid Dynamical Systems
IV: RealWorld Applications
Realworld applications are presented for natural and built environments, along with their interactions, relevant for engineering design and decision support in the wake of hydrometeorological hazards and fluidstructure interaction challenges in a changing world. The course is concluded with frontier topics on fluid dynamical systems ranging from quantum mechanical to cosmological applications.

 Geophysical Fluid Dynamics: Multiscale Fluid Dynamics in the Earth System
 Magnetohydrodynamics: Understanding and Predicting Solar and Geomagnetic “Weather”
 Numerical Prediction Systems: Operational CFD and decision support in hydrometeorological applications
 FluidStructure Interactions: AeroHydrodynamics in built and natural environments
 ‘Big data’ analytics and model optimisation: Information retrieval, lossless data compression, dynamic model design and optimisation
 Frontier Topics: Fluid Dynamical Systems across scales: from Quantum Mechanics to Astrophysics and Cosmology.
TAKEHOME MESSAGES:

 Unify complex fluid laws into a simple, overarching framework
 Understand dynamical regimes, transitions, and extreme events ￼
 Find the order in chaos for improved understanding and prediction ￼
 Realworld applications for engineering design and decision support
Course Coordinator: Rui A. P. Perdigão