Lecture 6

Question 1

Which types of linear time depended waves do exist?

Answer 1

1. Compression waves
2. Expansion waves
3. Entropy waves

Question 2

What happens when M=1 with the wave speed for Ψ1?

Answer 2

This wave speed will be 0 (phi 1 is the characteristic: x_dot = u-c).

Basically because M=1 –> u=c.
Therefore, phi1 does not lead to any information transport downstream or upstream. The resulting characteristic velocity (x_dot) = 0.

Question 3

Are linear compression waves equal to shock waves?

Answer 3

No

They change the same way the properties of the fluid. However, we cannot have linear theory in shock waves because characteristics cannot intersect, and in a shock wave by definition the characteristics intersect (remember that we said that we have a shock wave when convergent characteristcs converge in a single point).
This was when the characteristic velocity (dlambda/dx) < 0.

Linear compression waves are like a limiting concept of shock wave when the shock intensity approaches 0.

There are never shock waves in linear theory.

Question 4

How does a leftward running compression affect the flow velocity?

Answer 4

It increases the velocity in the same way as it advances, so it increases the velocity to the left points.

Question 5

How does a leftward running expansion affect the flow velocity?

Answer 5

It increases the velocity in the opposite way as it advances, so it increases the velocity to the right points.

Question 6

How does a rightward running expansion affect the flow velocity?

Answer 6

It increases the velocity in the opposite way as it advances, so it increases the velocity to the left points.

Question 7

How does a rightward running compression affect the flow velocity?

Answer 7

It increases the velocity in the same way as it advances, so it increases the velocity to the right points.

Question 8

How are p and u across a Linear Entropy Wave?

Answer 8

Constant