A numerical model is used to study the "Denver Cyclone," a mesoscale vortex that develops in eastern Colorado under southerly to southeasterly flow. Diurnal effects (e.g., surface heating/cooling) have been excluded from these simulations, but are discussed in Part II of this study. Simulations are first performed with a southerly ambient wind (i.e., parallel to the Continental Divide). If the Froude number of the flow based on the height of the Palmer Divide (an east-west ridge to the south of Denver) is small, then a vortex forms over the Denver region. This circulation then propagates northward at just over half the upstream flow velocity, leaving essentially stagnant air in the lee of the Palmer Divide. It is shown that Coriolis turning has a negligible effect on the flow when the ambient wind is from the south. However, when the ambient wind is at an angle to the Continental Divide, northerly winds can develop along the foothills due to Coriolis turning of the flow as it approaches the Divide. Idealized experiments of low Froude number flow past a bell-shaped hill are also performed to explore the connection between lee vortices and the stagnation aloft predicted by linear theory. In one experiment, a low Froude number (Fr = 0.3) flow is approached from a Fr approximately 1 flow, where linear theory gives useful predictions, by applying a reverse pressure gradient to decelerate the flow. During this deceleration, the flow reverses aloft at the point predicted by linear theory. Wave breaking then follows and the region of flow reversal descends to the surface. This experiment suggests that the intense, concentrated vorticity that develops in the lee of obstacles at low Froude numbers is due to the tilting of horizontal vorticity as gravity waves overturn and break.