Code
Φ-406
Level
Undergraduate
Category
B
Teacher
N. Flytzanis
ECTS
6
Hours
4
Semester
Spring
Display
Yes
Offered
No
Teacher Webpage
Goal of the course
The course is designed for 3rd and 4th year students. Use of the basic conservation laws of mechanics and thermodynamics to study phenomena in hydrodynamics, and wave propagation. The student is introduced to new concepts of description (continuum, fluid particle, velocity field, material derivative ) which he/she should be able to apply not only in hydrodynamics but in other areas of physics. Mathematics are introduced as needed. Mastering of tensors and tensor calculus. Ability to understand and qualitatively explain several interesting phenomena in fluid dynamics as well as Applying the conservation laws both on the microscopic and macroscopic level. Use dimensional analysis along with physical arguments to obtain important dimensionless quantities and solve scaled down problems. It is advised that students have a good command of Classical Mechanics and some Differential Equations including Differential calculus (Grad, div, curl in curvilinear coordinates, surface and volume integrals)
Program
Monday,15:00-17:00, Room 2
Wednesday, 15:00-17:00, Room 2
Wednesday, 15:00-17:00, Room 2
Syllabus
Basics and kinematics: Fluid properties and forces. Continuum model and velocity field. Euler and Lagrange description. Kinematics and material derivative. Continuity of mass. Incompressible fluid and conservation of momentum (Euler) and energy (Bernoulli and extensions). Potential Flow. Kelvin Theorem (conservation of circulation) and Magnus phenomenon (lift). Hydrodynamic mass. Flow in non-inertial systems (Coriolis force, gradient flow). Reynolds Theorem. Viscous flow Stress and rate of strain tensors. Viscous forces. Laminar flow. Navier-Stokes equation and applications in creeping flow. Vorticity diffusion. Stokes flow around a sphere.Thermodynamics of viscous flow. Dimensional analysis, Buckingham theorem, dimensionless numbers and applications. Vorticity sources and vortex models and interactions. Boundary layers and flow separation. Turbulence flow and experimental techniques of flow characterization. Instabilities and convection. Diffusion. Surface waves ( gravity and interface). Nonlinear waves. Tsunami waves. Compressible fluids (isothermal and adiabatic flow) Waves in 1-dimension. Sound waves.
Application (6 hours): One of the following : Oceanography, Geophysical flow, turbulence and chaos, Blood flow, hydrodynamics of charged fluids, diffusion of polutants.
Application (6 hours): One of the following : Oceanography, Geophysical flow, turbulence and chaos, Blood flow, hydrodynamics of charged fluids, diffusion of polutants.
Bibliography
N. Flytzanis, Notes on Hydrodynamics.
