I want to have insight over fluid-flow vector field, as I have an ordinary differential equation (ode): dv/du=-2(u2+v2)/(v2 - 5u2)
where u and v are horizontal and vertical velocity components inside the fluid-flow velocity vector-field.
Please also hint on using MATLAB "quiver" or "streamline" syntax to visualize the fluid flow based on the ode.
Notice that from elementary fluid mechanics dy/dx=v/u, where x and y are the streamline coordinates.
As theoretical guideline, solving for v=v(u) and inserting in dy/dx=v(u)/u allows to get the streamline y=y(x) along which the vector velocity is tangent
@Filippo Maria Denaro. Thank you. I had a similar idea. But assume v(u) = u^2, or v(u)=sin (u), therefore: dy/dx=u,
or dy/dx=sin (u)/u, then how you get y=y(x)?! Notice that in my case, the solution of the ode, does not yield an explicit solution as v=v(u) or u=u(v), and I need to directly exploit the unsolved ode to get a sense or visualization of the fluid flow field.
could you post the original reference for this problem?
I assumed the functions u(x,y) and v(x,y) are known
This is my own research and the ode is the solution to my own methodology.
The functions u(x,y) and v(x,y) should be found.
The ode is only a portion of my research, and I have not given further details as the statement of the question might be ill-conditioned. Getting the functions u(x,y) and v(x,y) is not simple in my methodology, and I am looking to have some insight on the fluid flow visualization through a weak-form solution to the ode. But if this is not possible, I should numerically calculate the velocity vector-field.
But the first ODE dv/du you wrote could be assumed for any regular functions u(x,y) and v(x,y) that satisfies that equation. Without an explicit representation of the two velocity components, the streamline equation can be only solved formally as
y(x)-y0 = Int [x0,x] (v/u) dx
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