According to Landau&Lifshitz, an ideal fluid is one with zero viscosity and a negligible thermal conductivity. This is also the FR.wikipedia version:
En mécanique des fluides, un fluide est dit parfait s'il est possible de décrire son mouvement sans prendre en compte les effets de viscosité et de la conductivité thermique
On the other hand, EN.wikipedia says:
In physics, a perfect fluid is a fluid that can be completely characterized by its rest frame mass density ρ and isotropic pressure p […] Specifically, perfect fluids have no shear stresses, viscosity, or heat conduction.
I'm not sure about how does the first characterization (before […]) implies the second one, however I take them to be equivalent (I'd be grate if someone could clarify about this point, but this is not my question).
The confusion arises from IT.wikipedia:
Un fluido ideale è un fluido che ha densità costante e coefficiente di viscosità nullo.
that is: "an ideal fluid is one with constant density and null viscosity coefficient". Apart from the fact that this doesn't specify which viscosity coefficient is zero, I've found that lots of people (mostly italians, I have to say) define an ideal fluid as an incompressible one.
So my question is:
Which is the conventional, commonly accepted, definition of ideal (or perfect) fluid?
Best Answer
For a newtonian fluid, you can write the total stress tensor $\sigma_{ij}$ as $$\sigma_{ij} = -p \delta_{ij} + \tau_{ij}$$ with $$\tau_{ij} = \mu \left(\frac{\partial u_i}{\partial x_j} + \frac{\partial u_j}{\partial x_i}\right).$$
$-p \delta_{ij}$ is the classic pressure term and $\tau_{ij}$ is the shear stress tensor with $\mu$ the shear viscosity.
When considering a perfect fluid, the shear stress tensor is considered null which lead to take a viscosity equals to 0. You can write the same formula for the thermal component in the energy equation which will give a thermal conductivity also equals to 0.
It is possible to write different behaviour law for the total stress tensor but the main idea will be the same: by neglecting the shear stress, you neglect the viscosity.
These hypothesis leads to consider Euler equations instead of Navier-Stokes equations.
One last thing :
Be careful! The fluid is never incompressible. The flow may be, depending on Mach number and continuity equation. All fluids are compressible at some point.