Stuck on Homework: Analyzing 2D Shear Velocity Field

In summary, the flow described in this conversation involves a barotropic fluid, with uniform density, and no time dependence in the x-direction. To achieve a steady state, energy must be supplied to the system.
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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?
 
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Please take note that at among the top of the listing of sections in PF, we DO have a homework help section.

Zz.
 
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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 [itex]\rho[/itex] 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 [URL [Broken] Oceanography. Part I: Fundamental Principles
 
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1. What is a 2D shear velocity field?

A 2D shear velocity field is a representation of the velocity of a fluid in two-dimensional space. It is often used in fluid mechanics and geophysics to study the flow of fluids, such as air or water, over a surface.

2. How is a 2D shear velocity field analyzed?

To analyze a 2D shear velocity field, scientists use mathematical equations and computer models to calculate the velocity of the fluid at different points in the field. They also use visualizations, such as color maps, to help understand the patterns and flow of the fluid.

3. What types of research can be done using 2D shear velocity fields?

2D shear velocity fields are useful in a variety of research areas, such as studying the movement of fluids in the atmosphere and oceans, understanding the behavior of earthquakes, and exploring the flow of blood in the human body.

4. Why is analyzing 2D shear velocity fields important?

Analyzing 2D shear velocity fields allows scientists to gain a deeper understanding of the behavior and movement of fluids, which can have practical applications in fields such as weather forecasting, earthquake prediction, and medical research. It also helps to advance our understanding of fundamental physical processes.

5. What are some challenges in analyzing 2D shear velocity fields?

One of the main challenges in analyzing 2D shear velocity fields is obtaining accurate and precise data, as it often involves complex and dynamic systems. Additionally, interpreting and visualizing the data can be difficult, as it requires advanced mathematical and computational skills.

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