Acoustic dyadic sensor measures pressure, particle velocity and the velocity gradient at a single point in space. Using these information is very useful for improving detection and estimation of sonar. The auto-correlation of the velocity gradient, the cross-correlation between the pressure and the velocity gradient, and that between the particle velocity and the velocity gradient in 3-D spherical isotropic noise field are investigated. Noise covariance matrix is derived, and a simple simulation method of isotropic noise field is analyzed. The numerical simulation results utilizing this method are in good agreement with the theoretical values, which indicate the theory results and the given methods are effective.