The ubiquitous occurrence of submesoscale cyclonic spirals in the sea as inferred from space imagery is interpreted in terms of the inertial instability of a horizontally sheared current in the oceanic mixed layer. The instability is shown to weaken anticyclonic current shear while enhancing cyclonic shear, which, in turn, becomes unstable and creates a cyclonic vortex; concurrently, surface tracer particles concentrated along the evolving cyclonic shear are wound up into a spiral, mimicking the spiral slick patterns seen in the imagery. The entire process, investigated with a fully nonlinear nonhydrostatic 3D numerical model, is contrasted with the baroclinic frontal process considered previously. The differences point to a clear need for field observations of this significant phenomenon, which are presently almost totally lacking.