  The scalar induced gravitational waves are produced from primordial curvature
perturbations in the second order of perturbations. We constrain the fractional
energy density of scalar induced gravitational waves from gravitational waves
observations. If there is no detection of the scalar induced gravitational
waves, the fractional energy density of scalar induced gravitational waves is
constrained by some upper limits. Depends on these upper limits, we can obtain
the constraints on the power spectrum of the primordial curvature
perturbations. For a power-law scalar power spectrum, the constraints on the
power spectrum are affected by adding the upper limit of scalar induced
gravitational waves from Square Kilometer Array (SKA). In the standard model,
the mean values of the scalar amplitude and the spectral index shift to lower
values when SKA is added to the combination of Cosmic Microwave Background
(CMB) and Baryon Acoustic Oscillation (BAO) datasets, namely
$\ln(10^{10}A_s)=3.038\pm0.013$ and $n_s=0.9589^{+0.0021}_{-0.0011}$ at $68\%$
confidence level. We also consider the effects of the existing ground-based
gravitational-wave detectors, the existing Pulsar Timing Arrays (PTAs) and
Five-hundred-meter Aperture Spherical radio Telescope (FAST), while the
constraints from CMB+BAO datasets are totally within their upper limits of
scalar induced gravitational waves. Furthermore, we characterize the scalar
fluctuation spectrum in terms of the spectral index $n_s$ and its first two
derivatives. We calculate corresponding power spectrum of scalar induced
gravitational waves theoretically and give the constraints on the running of
the spectral index and the running of the running of the spectral index.
