The nonlinear interaction of two, mutually perpendicular crossed ultrasonic beams, overlapping in the presence of turbulence, generates a scattered sum frequency component that radiates outside the interaction region. In the absence of turbulence, virtually no scattered sum frequency component exists (outside the interaction region). A theoretical investigation is reported that relates the shape of the ensembled averaged scattered sum frequency intensity spectrum, I+ (ω,θ*) (which exhibits a Doppler shift, frequency broadening, skewness, and kurtosis), to the scattering angle θ*, incident and scattered wave vectors (where K+=ks−[k1+k2]), and statistical properties of the turbulent velocity field v. The n spectral moments 〈(K+⋅v)n〉∝∫I+(ω,θ*) (ω−〈ω〉)n dω (obtained from experiment) are used to evaluate turbulent velocity correlations like 〈vxvy〉, where n=2. The scattering geometry involves rotating the axis of the transmitting crossed beams (which are always perpendicular to each other) in the plane containi...