# why inviscid flow have vortices?

#### amaelle

Good day all
I have a question : we know that that vorticity comes from velocity gradient and viscosity, so in this case how can vortices form in such a fluid?

#### Woody

The simple answer is they cannot.
Calculations which use the inviscid approximation have to insert vortices artificially.
From experimental evidence the starting points and strengths of any vortices that might be expected can be estimated
and then and then a mathematical model of a vortex imposed onto the otherwise inviscid model.

A connected question to others out there (I don't know the answer),
Does this mean that vortices cannot be formed in super-fluid helium?
Can super-fluid helium be stirred?

amaelle

#### amaelle

Thanks a lot!
but still i have another question
irrotational flow= vorticity equal to zero
if no vortices are there so does this mean that inviscid flows =irrotational flows? I know they are not but this point confuses me
Thanks!

#### Woody

They are different approximations used to make the calculations easier.
Which is used depends on the circumstances being modeled.
If the flow is known to be irrotational, (or at least to a close approximation)
then a lot of simplifications can be made to the calculations.
Similarly, for simple flows an inviscid model is often a good enough approximation to provide useful answers.
Often the calculations do not have to be accurate to the last detail to provide an answer that is good enough for the required purpose.

amaelle

#### studiot

Good day all
I have a question : we know that that vorticity comes from velocity gradient and viscosity, so in this case how can vortices form in such a fluid?
The simple answer is they cannot.
Calculations which use the inviscid approximation have to insert vortices artificially.
From experimental evidence the starting points and strengths of any vortices that might be expected can be estimated
and then and then a mathematical model of a vortex imposed onto the otherwise inviscid model.

A connected question to others out there (I don't know the answer),
Does this mean that vortices cannot be formed in super-fluid helium?
Can super-fluid helium be stirred?
Of course they can.

Amaelle, Why do you think viscosity is necessary for vortex flow?

There are different types of vortex.
One distinction is the difference between what are called free vortices and forced vortices.

A forced vortex can be forced in any fluid.

A free vortex can form due to change in flow conditions in any fluid.

Basically viscosity is an energy dissipative mechanism.

amaelle

thanks a lot!

#### studiot

Thanks a lot!
but still i have another question
irrotational flow= vorticity equal to zero
if no vortices are there so does this mean that inviscid flows =irrotational flows? I know they are not but this point confuses me
Thanks!
Is this really a high school topic?
I ask because it is difficult to produce auseful high school level answer.

The vorticity is a measure of the local rotation or spin of the fluid. It is a point function.
It has nothing to do with the global rotation of the fluid, which may be due to external forces (including torques) generating a forced or line vortex.

Consider two short lines of fluid, momentarily at right angles to each other at some point in the fluid.

The vorticity represents the average angular velocity of these two lines.

So if we let one fluid line lie along the x axis with velcoity u and the other along the y axis with velocity v then
the vorticity, omega, is given by

$$\displaystyle \omega = \left( {\frac{{\partial v}}{{\partial x}} - \frac{{\partial u}}{{\partial y}}} \right)$$

In fact this definition makes omega twice the average rate of rotation, which is why I said it is a measure of the average.