Simple laminar flow models of the magnetosheath plasma lead to predictions of large-scale reconnection structures on the dayside magnetopause. There is observational evidence from the ionosphere that such structures exist. However, in situ observations of the magnetosheath plasma near the magnetopause indicate that the fluid is highly disordered, with the magnetic field orientation in particular being extremely noisy. This raises the question of how coherent large-scale reconnection structures can be created and persist. This paper shows that, if the apparent noise in the magnetosheath field has the characteristics of fractal turbulence, large-scale structures can persist even when the apparent noise levels in the draped magnetic field are very large. Furthermore, the common observation of reconnection transients is naturally explained by this model.