Two models of a geostrophically rotating turbidity current are examined to compare predictions for ignition with the catastrophic state. Both models describe the current as a tube of sediment‐laden water traversing along and down a uniform slope. The first (four‐equation) model neglects the energy required to lift the sediment from the seabed into suspension. The second (five‐equation) model rectifies this shortcoming by introducing a turbulent kinetic energy equation and coupling the bottom stress to turbulence in the plume. These models can be used to predict the ignition, path and sediment deposition of a geostrophically rotating turbidity current. The criteria for ignition in the four‐equation model can be described by a surface in three‐dimensional phase space (for a non‐entraining current). This surface lies near the geostrophic equilibrium state. For a turbidity current occurring in the Greenland Sea, velocities above 0·053 m s^–1^ or volumetric concentrations of sediment above 2·7 × 10^–5^ lead to ignition. In general, if the tube is started pointing downslope, then ignition is more likely than if it is initially directed alongslope. However, there exists a set of initial conditions in which the current ignites if started along or downslope, but deposits if started at an intermediate angle. The five‐equation model requires a larger initial velocity (greater than 1·6 m s^–1^) to ignite than does the four‐equation model. Ignition is determined qualitatively by the geostrophic state and the initial normal Froude number. Solutions show a tendency to travel further alongslope during ignition, reflecting the restriction that the energy budget places on the sediment load. A qualitative difference to phase space in the five‐equation model is the existence of a region in which the tube has insufficient energy to support the sediment. Turbulence dies rapidly in this region, and so the sediment is deposited almost immediately.