SO513 Assignment 2 (45 35 pts)
Name: ________________________
1. (5 pts) Given that salinity, s, or any passive material concentration for that matter obeys the
non-diffusive conservation equation,

  s       su   0
t
derive the Material tracer equation
s
Ds
 u s 
 0.
t
Dt
2. (5 pts) If a fluid is irrotational, its vorticity  is zero and the flow u can be expressed as the
gradient of a scalar function  called the velocity potential: u   . Using this expression,
show that for an irrotational fluid, the rotation tensor rij is also zero. (See end of Lesson 1 notes
for an expression for the rotation tensor).
3. (5 pts) Problem 4.1, Kundu, Cohen, and Dowling (pg. 151).
4. (5 pts) Problem 4.2, Kundu, Cohen, and Dowling (pg. 151).
5. (5 pts) Problem 4.33a, Kundu, Cohen, and Dowling (pg. 162).
6. (10 pts) Problem 4.40 (all parts, a-c), Kundu, Cohen, and Dowling (pg. 163).
Modified 5-Feb-2015: 6. (10 pts) Problem 4.40 (only parts a and b), Kundu, Cohen, and Dowling
(pg. 163).
7. (10 pts) Problem 4.41 (all parts, a-c), Kundu, Cohen, and Dowling (pg. 163).
Modified 5-Feb-2015: 7. No problem 7.