Gas Dynamics

1. May 19, 2005

rolandk

I am stuck on some homework - I see many options, but not which is the correct set.

A simple 2D shear velocity field: v (x-direction) = v (x-dir)(y,t), v (y-dir) = 0, a barotropic flow with uniform density. Does this flow involve expansion, contraction, rotation and or deformation? How does the motion of the fluid look like in the vicinity of an arbitrary point x(0) - streamlines and particle paths? and what is the resulting volume force.

Concavity and convexity of the structure of the velocity field are important and four possible cases are possible - which ones? and in which direction is the x-momentum transferred in each case?

How much energy density per unit time must be given to the system to sustain the staionarity of the flow?

By which other mean can a steady state be achieved when the flow is given by: v(x-dir)=v(x-dir)(y,t), v(y)=v(y-dir)(y) ?

Can anyone out there give me some guidance?

2. May 19, 2005

ZapperZ

Staff Emeritus
Please take note that at among the top of the listing of sections in PF, we DO have a homework help section.

Zz.

3. May 19, 2005

Staff: Mentor

Given: A simple 2D shear velocity field, with v (x-direction) = v (x-dir)(y,t), v (y-dir) = 0.

or vx = vx(y,t), i.e. the x-component of velocity is a function of 'y' and is time dependent, and

vy = vy(y), which implies steady-state (i.e. no time dependence), and if vy=0, then there is no flow velocity in the y-direction.

A barotropic fluid is defined as that state of a fluid for which the denisty $\rho$ is a function of only the pressure. The condition of barotropy of a fluid represents an idealized state. See barotropic fluid

Also - Streamfunction for two-dimensional flow

In general, refer to Dynamical Oceanography. Part I: Fundamental Principles