Afterwards,   Spiegel's work focused on models of the solar cycle and radiative processes in hot stars. He authored or co-authored more than 100 papers involving collaborations with over 60 individuals; these papers have been cited well in excess of 3000 times.
In the 1960s his research focused on turbulence and on chaos theory, returning to mathematical aspects of that subject from 1975 to 1985. In the late 1980s he concentrated on mathematical pattern theory in fluids and other systems.