Multiscale low Mach number flows

There is a rich variety of low Mach number fluid flow
applications that are characterized by multiple spatial
scales. This presentation will begin by reviewing several
examples from thermoacoustics, combustion, and meteorology.

One systematic approach to analyzing such flows utilizes
multiple scales asymptotics. The second part of the
lecture will summarize a number of results in this
direction, all related to the examples given in the first
part of the lecture.

The asymptotic limit of vanishing Mach number is singular.
As a consequence, numerical computations of low Mach number
flows are challenging in various ways. This is true, in
particular, when variable densities, exothermal reactions,
or the effects of gravity and/or rotation are involved.
The third part of the lecture will outline current work
aiming at translating the insight gained in asymptotic
analyses into efficient numerical techniques.