The convection structure in a rectangular channel with a horizontal flow forΓ= 12 was studied. The simulations were preformed by solving the hydrodynamic equations using the SIMPLE method. The convective behavior in an absolutely and convectively unstable regime was studied. The results show that the two types of convection patts in this system appear depending on the convection intensity and horizontal flow. A periodically localized traveling wave state was found in this system.