PHY206 - Waves in Fluids, with illustrations from geophysics (2023-2024)

Prerequisites: PHY101, PHY102, PHY201, PHY202

The course provides an introduction to waves in fluids. A necessary first step is to derive a minimal set of equations for fluid motions. In consequence, the course constitutes a partial introduction to fluid mechanics, restricted to inviscid fluids. One goal of the course is to demonstrate how one proceeds to obtain wave solutions starting from a physical description of a system and its equations of motion. Two families of waves are derived and examined in detail: acoustic waves and surface gravity waves. These serve to discuss key notions regarding waves: the methodology to obtain wave solutions, the dispersion relation and its implications, the phase and group velocity, the polarization relations. The above constitutes the core of the course. In complement and as openings to other topics, the three last sessions discuss nonlinearity, different families of waves present in the atmosphere and ocean, and propagation into an inhomgeneous medium.

At the end of the course, the students will understand how to obtain, in a given system, wave solutions if they exist, and how to characterize a family of waves. The illustrations, for acoustic waves and for geophysical waves, will have introduced general culture elements regarding music and musical  instruments, and certain oceanic and atmospheric motions.

Prerequisites: PHY101, PHY102, PHY201, PHY202

The course describes waves in fluids, with a preference for illustrations coming from the Earth system, in particular the atmosphere and ocean. Waves are one essential type of motion present in many fluids. One goal of the course is to demonstrate how one proceeds to obtain wave solutions starting from a physical description of a system and its equations of motion. Acoustic waves will be considered as a first example, surface water waves at different scales (from ripples in the pond to tsunamis) will be derived as further examples. Basics of fluid mechanics (Euler equations, kinematics) will be introduced in order to make these developments possible. Similarities in the behavior of fluid waves and optical waves seen in PHY202 will be discussed.

At the end of the course, the students will understand how one characterizes a family of waves (dispersion relation, polarisation relations), and how to proceed to obtain, in a given system, wave solutions if they exist. Some preliminary considerations for exploring behaviors beyond linearity will have been introduced, as an opening. Finally, some elements of the study of the Earth, and of the atmosphere in particular, will have been introduced.