Spiral eddies were first seen in the sunglitter on the Apollo Mission 30 ye
ars ago; they have since been recorded on synthetic aperture radar (SAR) im
ages and in the infrared. We present a small sample of images. The spirals
are broadly distributed over the world's oceans, 10-25 km in size and overw
helmingly cyclonic. Under light winds favourable to visualization, linear s
urface features with high surfactant density and low surface roughness are
of common occurrence. The linear features are wound into spirals in vortice
s associated with horizontal shear instability, modified by rotation, in re
gions where the shear is comparable with the Coriolis frequency. Two models
for concentrating shear are presented: a softened version of the classical
sharp Margules front, and the time-dependent Lagrangian model of Hoskins &
Bretherton. Horizontal shear instabilities and both frontal models favour
cyclonic shear and cyclonic spirals, but for different reasons.