This study introduces a nonlinear wave-wave coupling model to understand the nature of the turbulence generation at the ion scale observed in the interaction of high-intensity laser with plasma. For this nonlinear coupling of waves, the fast magnetosonic wave and the extraordinary mode laser are taken into account, along with the nonlinear ponderomotive force. The model dynamical equations have been developed for the extraordinary mode laser and the fast magnetosonic wave. Laboratory simulations have been employed to solve the obtained model equations utilizing the finite difference and pseudo-spectral methods. The simulation results show the initiation of the nonlinear progression of the laser beam at an early time and its turbulent nature at a later time. The background density perturbation, along with the cavity and hump caused by the ponderomotive force, has also been studied. The simulation results demonstrate that the propagation angle of the fast magnetosonic wave affects the magnitudes of the localization of the laser beam (pump wave) and the perturbed background density. The turbulent power spectra (ensemble-averaged) have also been studied for the different propagation angles of the fast magnetosonic wave. The turbulent spectra demonstrate that the plasma turbulence is MHD-type at small-scale lengths and ion-dominated at larger-scale lengths. This study also observed that the simulation results have some resemblance with the experimental results reported by Chatterjee et al.12 in the intense laser-plasma interaction experiment at a laboratory astrophysical scale.