Computer cabinets, such as supercomputer cabinets, having progressive air velocity cooling systems are described herein. In one embodiment, a computer cabinet includes an air mover positioned beneath a plurality of computer module compartments. The computer module compartments can be arranged in tiers with the computer modules in each successive tier being positioned closer together than the computer modules in the tier directly below. The computer cabinet can also include one or more shrouds, flow restrictors, and/or sidewalls that further control the direction and/or speed of the cooling air flow through the cabinet.