  For velocity and magnetic fields, the turbulent pressure and, more generally,
the squared fields such as the components of the turbulent stress tensor, play
important roles in astrophysics. For both one and three dimensions, we derive
the equations relating the energy spectra of the fields to the spectra of their
squares. We solve the resulting integrals numerically and show that for
turbulent energy spectra of Kolmogorov type, the spectral slope of the stress
spectrum is also of Kolmogorov type. For shallower turbulence spectra, the
slope of the stress spectrum quickly approaches that of white noise, regardless
of how blue the spectrum of the field is. For fully helical fields, the stress
spectrum is elevated by about a factor of two in the subinertial range, while
that in the inertial range remains unchanged. We discuss possible implications
for understanding the spectrum of primordial gravitational waves from causally
generated magnetic fields during cosmological phase transitions in the early
universe. We also discuss potential diagnostic applications to the interstellar
medium, where polarization and scintillation measurements characterize the
square of the magnetic field.
