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Abstract Results from a large eddy simulation of a tornadic supercell developing in a horizontally homogeneous environment are presented which clearly illustrate a connection between low‐level mesoyclone development and the development of a streamwise vorticity current (SVC). Although the environment supports tornadic supercells, a strong low‐level mesocyclone (LLM) does not develop until a well‐defined SVC forms in the storm's forward flank. As the streamwise vorticity in the SVC flows southward and is tilted into the storm updraft creating updraft helicity, the LLM strengthens and lowers toward the surface. The SVC also focuses LLM development in a confined storm‐relative position favorable for converging/stretching preexisting vertical vorticity. Tornadogenesis occurs within ∼5 min of the establishment of a strong LLM. These results illustrate a possible mode of internal storm variability that may be an important factor in explaining why some supercells produce tornadoes while others do not in similar favorable environments.