2D shear velocity field: expansion, rotation, deformation and energy

[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?

 

[ZapperZ]

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

Zz.

 

[Astronuc]

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

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

v_y = v_y(y), which implies steady-state (i.e. no time dependence), and if v_y=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 http://stommel.tamu.edu/~baum/reid/book1/book/node61.html

Also - http://stommel.tamu.edu/~baum/reid/book1/book/node22.html

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