Hello
to reproduce this kind of waves, you need to use less diffusive advection schemes and to turn off all diffusive terms. It is not a matter of turbulence model, in my opinion.
You can try to use the characteristic scheme (MOC), this has the advantage to be completely implicit with no stability restriction. Furthermore, if your problem is not too large, you can use the second order kinetic scheme with finite volume kernel. The WAF scheme also can give satisfactory results also.
I hope that this helps,
With my best regards,
Riadh ATA