  We study the second order scalar and density perturbations generated by the
Gaussian curvature perturbations and primordial gravitational waves in the
radiation-dominated era. After presenting all the possible second-order source
terms, we obtain the explicit expressions of the kernel functions and the power
spectra of the second order scalar perturbations. It shows that the primordial
gravitational waves might affect the second order energy density perturbation
significantly. The effects of the primordial gravitational waves are studied in
terms of different kinds of primordial power spectra.
