CONTACT INFORMATION
Dr. Jahrul Alam
HH-3054, (709) 864 8071
email: alamj_at_mun_dot_ca
http://www.math.mun.ca/~alamj/
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MEETING
The class will meet M W F 16:00-17:15 in HH-????.
OFFICE HOUR
M W 09:00-11:00 in HH-3035 or by appointment. Students may drop by my office any time between 09:00 and 17:00. An appointment is required ONLY to check if I have other scheduled tasks outside designated office hours.
Background knowledge
If you have taken math3202 (vector calculus), math 3260 (differential
equation), and phys 2820 (computational
mechanics), you are fully prepared for taking
math 4180.
In principle, the course uses partial differential equations. However, knowledge from math 4160 will not applied directly. Students must know partial derivatives, and techiques for solving differential equations. Laws of fluid mechanics will be expressed using partial derivatives, however, thoories of PDEs are not essential, but an important aspect of fluid mechanics.
OBJECTIVES
This course is a basic introduction to the subject of
fluid mechanics and is intended for undergraduate and
beginning graduate students of applied mathematics and
physics. This course introduces the general equations
(both rotating and non-rotating) that result from the
conservation of mass principle, Newton's second law, and
the first law of thermodynamics. From these a number of
particular situations will be considered that are of
special interest - such as boundary layers and
turbulence. After completing this course the students
should be able to apply the basic principles and methods
of mechanics to new and different situations.
This course
also aims to prepare undergraduate students, who are
interested in graduate studies in the area of Fluid
Dynamics as well as to prepare students who plan to work
in industries.
COURSE OUTLINE
Governing equations of fluid motion (ch 3-4)
A brief introduction to continuum
hypothesis, Lagrangian and
Eulerian description, rotating and non-rotating frame of
reference, kinematics, stress and other forces,
conservation of mass and momentum.
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Vortex motion, irrotational flow, and water wave (ch 5-7)
Students will learn briefly fundamental laws of vortex motion -
such as - circulation, vortex lines/tubes, vortex rings,
vortex filaments, vortex instability, effects of
viscosity, decay of trailing vortices, velocity
potential, irrotational votex, sources/sinks, doublet, flow
past a solid body, water wave etc.
Laminar boundary layer flow (ch 8-10)
We will discuss flow past solid obstacles, lift/drag on
airfoils, boundary layer theory, perturbation techniques
etc.
Introduction to turbulence and geophysical fluid
dynamics (ch 11, 13-14)
A brief introduction to geophysical fluid dynamics and turbulence will present the
gateway to the rich world of turbulence, introducing
many open questions and unsolved puzzles. Students will
be introduced the direct numerical simulation (DNS)
method - for example - challenges of DNS, how intermittency
affects DNS etc.
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Text book
Most students may find lecture notes are sufficient. However, I
strongly recommend to use at least one of the following
text books. In the above outline, chapters are mentioned from Kundu and Cohen, but the course will not cover details of each chapters.
Main text book: Fluid Mechanics (5th Ed.) by
Pijush K. Kundu and Ira M. Cohen(all lectures are prepared according to this text book).
Secondary text books are: Vortex dynamics by Saffman,
P. G., Introduction to fluid dynamics by Batchelor, G. K.,
and Introduction to dynamic meteorlology by Holton, J. R.
Calendar description
(Same as Physics 4205). Basic observations, mass conservation,
vorticity, stress, hydrostatics, rate of strain, momentum
conservation (Navier-Stokes equation), simple viscous and inviscid
flows, Reynolds number, boundary layers, Bernoulli's and Kelvin's
theorems, potential flows, water waves, thermodynamics.
Prerequisite
Physics 3220 and either AM4160 or Physics 3821.
Note: Please talk to your Professor if you do not meet the
prerequisite. You may be able to take the course if you have
taken m3202, m3260, p2820.
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