PHY206 - Waves in Fluids, with illustrations from geophysics (2022-2023)

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.

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.