Double shear test
This 2D test examines the model’s ability to capture thin vortex filament. Two vorticity bands with opposite signs are placed in a doubly-periodic domain, corresponding to a jet flowing from left to right. The velocity profile suffers from barotropic instability, and the two vorticity bands entangle with each other. As the fluid is inviscid, it finally forms concentrated vortices.
Zhang et al., 2009, J. Comput. Phys.

Density current test
This test examines the ability to treat shear zone and sharp scalar gradient. A cold bubble falls down from the mid-layer, and splashes on bottom. All boundary conditions are slip-free and adiabatic. It then splits into two streams of horizontal propagating cold currents, driven by baroclinic torque. The current moves much faster than the fluid above, forming Kelvin-Helmholtz instability. The frontal zone has sharp temperature gradient.
Skamarock et al., 1992, Mon. Wea. Rev

Driven cavity flow test
The fluid is placed in a cubic cavity, and the lid moves at constant speed. The boundary condition is no-slip, so the lid drives a circulation with viscosity. There are boundary layers at each wall, so this test examines the model’s capability to reproduce viscous boundary layer with sharp gradient. The only nondimensional number is Ra, and standard data of horizontal vorticity field, u and w velocity profiles are available for comparison.   
Lo et al., 2005, Int. J. Numer. Meth. Fluids

Rotating Rayleigh-Benard convection

Turbulent convection between two parallel plates has thin thermal boundary layers near the plates. Thermal bubbles eject from the boundary layer, ascend to the upper boundary and merge into it. Rotating makes the fluid vertically-aligned, and bubbles “freeze” into plumes. Those vertical plumes entangle with each other, forming thin filaments.

Cloud self-aggregation
When water phase change is included in Rayleigh-Benard convection, the convection could be statically stable (Ra<0) in unsaturated region and unstable (Ra>0) in saturated region. That is, convection and gravity wave co-exist. Acending region is small and strong, with a large area of compensating descent. Direct numerical simulation shows that moist convection tends to organize into a “cloud cluster”, in analog to the cloud self-aggregation in real tropical atmosphere.

Pauluis, et al., 2011, Proc. Natl. Acad. Sci.