MC-6496

## Candidate

Chengzhu
(William)
Xu

Applied
Mathematics,
University
of
Waterloo

## Title

Wave-Mean Flow Interaction and Its Applications

## Abstract

A
common
practice
in
the
study
of
environmental
and
geophysical
fluid
dynamics
is
to
divide
the
overall
flow
field
into
a *mean
flow* and
a
departure
from
the
mean
flow,
often
referred
to
as
a *wave*.
Because
of
the
various
length
and
time
scales
involved,
interaction
between
the
waves
and
the
mean
flow
leads
to
a
number
of
phenomena.
Here,
we
study
wave-mean
flow
interaction
in
two
different
areas,
internal
wave
dynamics
and
large-scale
atmospheric
circulation.
For
internal
waves,
the
mathematical
formulation
is
based
on
the
WKB
theory.
It
is
well
developed
for
a
weakly
nonlinear
environment,
but
less
so
for
a
fully
nonlinear
environment.
For
this
part
of
the
project,
we
investigate
internal
wave
dynamics
with
numerical
simulations
performed
of
a
fully
nonlinear
background
flow,
which
cannot
be
expressed
in
analytical
form.
For
large-scale
atmospheric
circulation,
wave-mean
flow
interaction
leads
to
the
Eliassen-Palm
theorem,
which
describes
the
dynamics
controlling
the
response
of
the
extratropical
atmospheric
circulation
to
climate
perturbations,
for
example
wave
teleconnections
originating
in
the
tropics.
In
this
part
of
the
project,
we
examine
two
different
topics,
the
linear
interference
effects
and
Rossby
wave
critical
layer
dynamics.
While
wave-mean
flow
interaction
is
used
to
describe
fluid
flow
in
different
context,
the
general
conclusion
is
the
same
in
both
cases:
energy
exchange
between
the
waves
and
the
mean
flow
occurs
while
the
wave
action
(or
wave
activity)
is
conserved.