# Free-slip boundary conditions

Hi all,
This may be a naive question but reading multiple sources got me confused. In the manual, free-slip is indicated (section 2.12) by ‘no normal velocity’ and Eq. 65 makes it clear: {u}_m\cdot n = 0 on \partial \Omega_{free-slip}. So far so good.
However, reading somewhat famous textbooks in geodynamics, I have come across other definitions: the above condition is common to all, but it is supplemented by either \partial v_y/\partial x =0, or by \sigma_{xy}=0 (on the side walls of a cartesian domain).
Rather surprisingly I was not able to find much info in other books, hence my asking on this forum
Cedric/

• slip: the normal component of the velocity is zero, i.e., no flux
across the boundary
• free: the tangential force is zero.

The tangential force is (sigma.n).t where sigma is the stress, n is the
normal vector, and t is the tangent vector. sigma.n is the total force
acting, and it can of course have a nonzero normal component (sigma.n).n
to ensure that the velocity is in fact zero in normal component. “Free
slip” then implies that the tangential force is in fact zero.

We should probably fix this in the manual. Want to take a stab at it? Or
at least open a github issue?

There is more material on this whole topic here:
https://dealii.org/developer/doxygen/deal.II/step_22.html#Weakform

Cheers
W.

Thank you for this very clarifying answer.

Is it then the question of simply changing Eq.(65) from
u_m \cdot n = 0
into
u_m \cdot n=0 \quad \& \quad (\sigma \cdot n) \times n = 0 ?
Or do we want to explain also that the first bit stands for impermeable conditions while the second insures that the tangential stress at the boundary is zero?

I like explaining what a formula means