Help Setting Up Equation To Find Curl of Navier-Stokes Equation

In summary, the person is struggling to use equations 2.1 and 2.2 in the article to find the curl of the Navier-Stokes equation. They understand how to find the curl, but are having trouble with the explanation and steps provided by their professor. They are asking for help and suggestions, but the equations in the attachments are not usable. The person responding suggests using LaTeX to make the equations easier to read and understand.
  • #1
AKBob
1
0
1.
Homework Statement

I'm having trouble using equation 2.1 or 2.2 in the article to find the curl of the navier-stokes equation. I understand how to find curl, but can't make sense of the explanation/steps in the document provided by the professor.

Homework Equations


All relavent equations are included in the two attachments.

The Attempt at a Solution


I'm really having trouble getting started. The document provided by my professor says to "First evaluate the '(Beta)yk X v' term, substitute that in (v is the vector discussed at the top)," but the equation at the top looks like a general equation, and I'm starting to get frustrated.

Any help/ideas/suggestions would really be appreciated.
 

Attachments

  • Project Doc 1.txt
    4.3 KB · Views: 397
  • Project Doc 2.txt
    47.6 KB · Views: 442
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  • #2
All the equations in the attachments are broken beyond repair.
 
  • #3
Yeah, sorry, use some LaTeX please. It'll be easier on everyone (well, except maybe you). Example:

[tex]\rho \left(\frac{\partial v}{\partial t} + v \cdot \nabla v \right) = - \nabla p + f + \overline T(\nabla)[/tex]

Is given by

Code:
[tex]\rho \left(\frac{\partial v}{\partial t} + v \cdot \nabla v \right) = - \nabla p + f + \overline T(\nabla)[/tex]
 

Related to Help Setting Up Equation To Find Curl of Navier-Stokes Equation

1. What is the Navier-Stokes equation?

The Navier-Stokes equation is a set of partial differential equations that describe the motion of a fluid. It takes into account factors such as viscosity, pressure, and velocity to predict the behavior of a fluid.

2. Why is finding the curl of the Navier-Stokes equation important?

The curl of the Navier-Stokes equation is important because it allows us to analyze the vorticity of a fluid flow. This information is crucial in understanding and predicting the behavior of fluids in real-world scenarios, such as in weather patterns or in the design of aerodynamic structures.

3. How do you set up an equation to find the curl of the Navier-Stokes equation?

The equation for finding the curl of the Navier-Stokes equation involves taking the cross product of the gradient of the velocity field with the velocity field itself. This can be represented mathematically as curl(v) = ∇ x v, where v is the velocity vector and ∇ is the gradient operator.

4. What are the steps to solving a curl of Navier-Stokes equation problem?

The first step is to understand the problem and identify the given variables and equations. Then, use the appropriate mathematical operations to find the curl of the Navier-Stokes equation. This may involve taking partial derivatives, using the product rule, and simplifying the equation. Finally, check your solution for accuracy and make sure it makes physical sense.

5. What are some real-world applications of the curl of Navier-Stokes equation?

The curl of the Navier-Stokes equation is used in many fields, including meteorology, engineering, and fluid dynamics. It can help predict the behavior of fluids in various scenarios, such as in weather forecasting, designing efficient pipelines, or understanding the flow of blood in the human body.

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