  The nonlinear evolution of a vortex sheet driven by the Kelvin--Helmholtz
instability is characterized by the formation of a spiral possessing complex
stretching and intensity patterns. We show that the power energy spectrum of a
single two-dimensional vortex sheet tends to the usual fluid turbulent
spectrum, with an exponent of -3. Using numerical simulations and asymptotic
methods, we demonstrate the relation between this power law and the
singularities in the geometry and vorticity distribution of the sheet.
