Fluid physics

The subject of Fluid Physics aims to deepen the knowledge of fluids. The dynamic equations of conservation of mass, momentum and energy will be introduced that will allow solving several classic problems (Poiseuielle, Stokes, boundary layer, movement of a bubble, introduction to aerodynamics, etc.).

Subsequently, once the basic dynamics of fluids has been developed, they are perturbed to study the waves that propagate in them with applications in the atmosphere or ocean. Next, the different instabilities that can develop within fluids are introduced with examples that can be observed daily. Finally, the student is introduced to turbulence.

Studies are complemented by carrying out numerical simulations and exercises that help to more clearly visualize the concepts that are intended to be stated in the theory classes.

1. Introduction.
Definitions and notations. Examples.
Lagrangian and Eulerian systems.
Balance Equations. Mass, momentum and energy. Stress and strain tensors.
Navier-Stokes equation. Continuity equation.
Approaches to Navier-Stokes: Euler, Bernoulli, Boussinesq and Hydrostatics.
Newtonian and non-Newtonian fluids.
Rheology of viscoelastic materials: Characteristic function. Wetting effect on materials. Polymers. Granular fluids.
Potential/irrotational fluids.
2. Viscous fluids.
Navier-Stokes solutions for incompressible viscous fluids: laminar flow between two parallel plates, Couette flow, Poiseuille flow, flow in a channel of regular section, thin film, etc.
Stokes law. Forces on a rigid sphere and a bubble. Small Reynolds.
Boundary layer equations. Falkner-Skan and Prandtl/Blasius solutions. Reynolds high.
Drag and lift forces. Aerodynamics.
Oscillatory movement of a viscous fluid.
3. Waves
Definitions. Wave parameters.
Surface gravitational waves. Effect of surface tension and viscosity. Stokes drift.
Internal waves in stratified fluids. Topographic waves. Lee waves.
Waves in rotating fluids.
Geophysical waves.
4. Instabilities.
Stability and instability. Landau equation.
Rayleigh-Taylor instability.
Rayleigh-Plateau instability.
Saffman-Taylor instability. Diffusion Limited Aggregation (DLA).
Kelvin-Helmholtz instability.
Convection. Rayleigh-Bénard instability. Lorenz model.
Marangoni effect. Tears of wine.
Taylor-Couette instability or flow between two concentric cylinders. Taylor vortices.
Clumping instability
5. Turbulence.
Turbulence. Properties.
Averaged conservation equations. Reynolds tensor.
Closure problem. Turbulent kinetic energy (TKE) equation. First order RANS models.
Energy cascade. Kolmogorov's Law 5/3.

• D.J. Achenson. Elementary Fluid Dynamics. Clarendon Press. Oxford (1990).
• C. Bailly and G. Comte Bellot. Turbulence. Springer, Heidelberg (2015).
• G. Batchelor. An Introduction to Fluid Dynamics. Cambridge Univ. Press (1967).
• H. Bruus. Theoretical Microfluidics. Oxford Univ. Press (2008).
• S. Chandrasekhar. Hydrodynamic and Hydromagnetic Stability. Dover Pub. NY (1961).
• A.J. Chorin and J.E. Marsden. A Mathematical Introduction to Fluid Mechanics. Springer-Verlag. NY (1993).
• A.J. Chorin. Vorticity and Turbulence. Springer-Verlag. NY (1994).
• I.G. Currie. Fundamental Mechanics of Fluids. McGraw-Hill (1974).
• T.E. Faber. Fluid Dynamics for Physicists. Cambridge Univ. Press. (1995).
• U. Frisch. Turbulence. Cambridge Univ. Press (1995).
• E. Guyon, J.P. Hulin et L. Petit. Hydrodynamique Physique. Savoirs Actuels, Editions du CNRS (1997).
• P.K. Kundu. Fluid Mechanics. Academic Press (1990).
• L. Landau y E. Lifchitz. Mecánica de Fluidos. Curso de Física Teórica. Tomo 6. Ed. Mir. (1989).
• J. Lighthill. An Informal Introduction to Theoretical Fluid Mechanics. Clarendon Press. (1986).
• W.D. McComb. The Physics of Fluid Turbulence. Oxford Sci. Pub. (1990).
• B.R. Munson, D.F. Young and T.K. Okiisho. Fluid Mechanics. John Wiley & Sons. NY (1990).
• P. Oswald. Rheophysics. Belin (2005).
• S.B. Pope. Turbulent Flows. Cambridge University Press (2000).
• M. Rieutord. Fluid Dynamics: An Introduction. Springer (2015).
• A.H. Shapiro. The Dynamics and Thermodynamics of Compresible Fluid Flow. Wiley (1953).
• D.J. Tritton. Physical Fluid Dynamics. Oxford Sci. Pub. (1988).
• J.S. Turner. Buoyancy Effects in Fluids. Cambridge Univ. Press (1973).
• M. van Dyke. An Album of Fluid Motion. The Parabolic Press, Stanford CA (1982).
• F.M. White. Fluid Mechanics. McGraw Hill (1994).

BASIC
CB6 - Possess and understand knowledge that provides a basis or opportunity to be original in the development and / or application of ideas, often in a research context
CB7 - Knowledge about how to apply the knowledge acquired and their ability to solve problems in new or unfamiliar environments within broader (or multidisciplinary) contexts related to their area of study
CB8 - Ability to integrate knowledge and face the complexity of making judgments based on information that, being incomplete or limited, includes reflections on social and ethical responsibilities linked to the application of their knowledge and judgments
CB9 - Ability to communicate conclusions and the knowledge and ultimate reasons that sustain them to specialized and non-specialized audiences in a clear and unambiguous way
CB10 - Learning skills allowing to continue studying in a way that will be largely self-directed or autonomous.

GENERAL
CG01 - Acquire the ability to perform team research work.
CG02 - Be able to analyze and synthesize.
CG03 - Acquire the ability to write texts, articles or scientific reports according to publication standards.
CG04 - Become familiar with the different modalities used to disseminate results and disseminate knowledge in scientific meetings.
CG05 - Apply knowledge to solve complex problems.

TRANSVERSAL
CT01 - Ability to interpret texts, documentation, reports and academic articles in English, scientific language par excellence.
CT02 - Develop the capacity to make responsible decisions in complex and / or responsible situations.

SPECIFIC
CE12 - Provide specialized training in the different fields covered by Fundamental Physics: from environmental physics, fluid physics or acoustics to quantum and radiation phenomena with their technological, medical applications, etc.
CE13 - Master interdisciplinary tools, both theoretical and experimental or computational, to successfully develop any research or professional activity framed in any field of Physics.

Along the semester, master lectures will be combined with seminars of problems and computer seminars. All the basic material will be provided. The student will have the tutorial.

The evaluation of the subject will consist of a combination of the different activities carried out in class, so attendance is essential. Among the evaluable activities are exercises, small assignments, and resolution of numerical simulations. At the end of the course, a more complete work will be done that must be presented and shared with the rest of the class.

The evaluation of the subject will be made up of a combination of:
- Exercises and small class assignments: 60%
- Final work of the subject and presentation: 40%

This type of evaluation implies that the student must attend most of the classes and maintain a participatory attitude. In case of an absence of more than 20% of the total class hours, the student must be evaluated through a global exam of the subject.

The fraudulent performance of any exercise or test required in the assessment of this subject will involve the qualification of fail in the corresponding call, regardless of the disciplinary process that may be followed against the student. To be considered fraudulent, among others, to carry out works plagiarized or obtained from sources accessible to the public without reworking or reinterpretation and without citations to the authors and the sources.

It will be necessary 36 hours of classroom attendance (100%) of the student to the subject distributed as follows,
- Theoretical teaching 20h
- Interactive teaching 5h
- Practical laboratory teaching 10h
- Individual tutoring of students 1h

Besides, it is necessary to have approximately one hour for each hour of dedication to the subject.
- Student's personal work and other activities 39h

Continued study of the different aspects explained along the daily class is the key to be able to achieve the main goals of the course.
Reading of the recommended references is also valuable.

This course combines very well with Non Linear Physics and Microfluids.