Essence
of Atmospheric Dynamics
A book in progress
by
Mankin Mak
Department of Atmospheric sciences
This book is a self-contained text
on atmospheric dynamics for students in atmospheric/physical sciences. It has 12 main chapters containing more
than enough materials for two semester courses. Physical, dynamical and mathematical
concepts are introduced at the fundamental level. The discussions are
supplemented with schematics, weather maps and plots of statistical
structure of the atmospheric general circulation. Students would learn how to formulate and solve dynamical problems
through a large number of substantive analyses in maximally simplified
model settings. Those
analyses illustrate the dynamics of different classes of atmospheric
disturbances. The broad objective
of the book is to help students develop
a feel for the essence of atmospheric dynamics.
The first half of the book covers the materials prerequisite for developing a quantitative understanding of disturbances and circulation in the atmosphere. They are written for students who are learning these materials for the first time.
Chapter 1
presents the most pertinent concepts and the laws of physics to be extensively
applied in the rest of the book.
Chapter 2
introduces the rudimentary approximations that help clarify the dynamical
nature of the simplest aspects of atmospheric flow. The kinematic of flows is also discussed. The governing equations are transformed to different coordinate systems for
atmospheric studies.
Chapter 3
discusses concepts such as vorticity, circulation and
potential vorticity for quantifying the rotational
properties of a flow in a fluid.
The related governing equations and theorems are
elaborated in details.
The concepts are illustrated with sample
analyses of sea-breeze circulation, broad distribution of wind in a hurricane, orographic response in a barotropic
fluid and excitation of jet by stirring.
This chapter ends with a discussion of the impermeability theorem for
potential vorticity and of generalized potential vorticity as a means of incorporating the influence of
boundaries.
Chapter 4 reviews
a simple representation of the impact of small turbulent eddies on their
background flow. The flows in
different boundary layers mostly in the atmosphere are analyzed
to illustrate the effect of friction.
Chapter 5 covers
the fundamentals of wave dynamics in the context of internal gravity waves and Rossby waves.
It specifically discusses how to deduce the functional relationships of
all wave parameters, the structural characteristics of the waves, their
dispersion and energy propagation.
Chapter 6
presents the quasi-geostrophic theory
which is the central theory for large-scale flow in the atmosphere. The governing equations and their
specific form in a two-layer version of such model are derived and
elaborated. The various
dynamical concepts in the context of this model are
illustrated with a diagnosis of an idealized baroclinic
jet streak and a prognosis of its short-term evolution.
The second half of the book elaborates on the more complex mechanisms that are associated with different types of disturbances. Those chapters are written for students who are familiar with the basic materials in the first half of the book.
Chapter 7
discusses how and why the velocity and pressure fields in the atmosphere would
rapidly adjust towards a new balanced state whenever their existing balance is upset by unspecified causes. The adjustments from two canonical forms
of initial imbalance are analyzed.
Chapter 8 is a
relatively long chapter consisting of five parts. Its content is a potpourri of
instability theories/analyses that could give rise to small-scale, meso-scale or large-scale disturbances. Much greater emphasis is
placed on the dynamics of the different aspects of instability for
large-scale disturbances. The broad
scope of this topic alone is highlighted with
instability analyses of several classes of basic flows with increasing
structural complexity.
Chapter 9 inquires
into the dynamics of stationary planetary waves including the characteristics
in their propagation through a shear flow and their excitation by thermal and
topographic mechanisms. An analysis
of the Asian summer monsoon as a forced circulation serves to illustrate the
dynamical properties of this class of wave disturbances in a recognizable
setting.
Chapter 10 addresses
the dynamical nature of interaction between a zonal mean flow and an ensemble
of waves. Particular wave-mean flow interaction is illustrated with a model analysis of the time-mean
residual circulation in response to empirical frictional, diabatic
and eddy forcing.
Chapter 11 is
concerned with three illustrative analyses of the equilibration dynamics of
fully nonlinear baroclinic waves. One delineates the dynamics of life
cycle of baroclinic waves in the absence of external
forcing. Another brings to light
the symbiotic relation between synoptic-scale waves and planetary-scale waves
in a forced dissipative system. The
third looks into the dynamical nature of the relative intensity of the two
major observed storm tracks.
Chapter 12 focuses on the nature of nongeostrophic
dynamics. It is illustrated
with three model analyses concerning with frontogenesis,
Hadley circulation and non-supercell tornado-genesis.
An appendix summarizes the mathematical tools and methodology used in the book for easy reference. The Hamiltonian formulation of fluid mechanics is however separately presented in chapter 12 in the context of a particular application.
This book is by no means
comprehensive, as some important topics such as geostrophic turbulence and
moist dynamics are not touched upon.
However, I believe that this book is distinctly different from and
complementary to the existing texts on atmospheric dynamics.
Overall outline of the book
Length of the first draft
(double space, font size 12) as of 6 May 2009
|
Chapter |
Topic |
Pages |
Figures |
|
1 |
Fundamental
Concepts and Physical Laws |
45 |
12 |
|
2 |
Basic
Approximations and Elementary Flows |
47 |
20 |
|
3 |
Vorticity
and Potential Vorticity Dynamics |
66 |
23 |
|
4 |
Friction and
Boundary Layers |
37 |
9 |
|
5 |
Fundamentals
of Wave Dynamics |
51 |
18 |
|
6 |
Quasi-Geostrophic Theory and Two-layer Model |
56 |
21 |
|
7 |
Dynamic
Adjustment |
35 |
15 |
|
8 |
Potpourri of
Instability Theories |
|
|
|
|
8A Small and Meso-scale Instability |
29 |
9 |
|
|
8B Purely Barotropic Instability |
35 |
12 |
|
|
8C Purely Baroclinic Instability |
59 |
24 |
|
|
8D Instability
of Baroclinic Jets |
14 |
8 |
|
|
8E Instability
of Localized Jets |
28 |
16 |
|
9 |
Stationary
Wave Dynamics |
72 |
43 |
|
10 |
Wave-Mean
Flow Interaction |
46 |
26 |
|
11 |
Equilibration
Dynamics of Baroclinic Waves |
40 |
26 |
|
12 |
Nongeostrophic Dynamics |
69 |
28 |
|
Appendix |
Mathematical
tools and Analysis Techniques |
21 |
|
|
Total |
|
747 |
310 |