The motion of linear and circular DNA molecules is studied under pressure driven buffer flow in a 50 nm slit channel with arrays of transverse 150 nm deep nanogrooves. Transport occurs through two states of propagation unique to this nanogroove geometry, a slow, stepwise groove-to-groove translation called the “sidewinder” and a fast, continuous tumbling across the grooves called the “tumbleweed”. Dynamical transitions between the two states are observed at fixed buffer velocity. Molecules exhibit size- and topology-dependent velocities.