We have developed a time-dependent three-dimensional model of isotropic, adiabatic, and compressible magnetohydrodynamic plasma to understand nonlinear cascades of density fluctuations in local interstellar medium. Our simulations, describing evolution of initial supersonic, super Alfv\'enic plasma modes, indicate that nonlinear interactions lead to damping of plasma motion. During the process, turbulent cascades are governed predominantly by the Alfv\'enic modes and velocity field fluctuations evolve towards a state charachterized by near incompressibility. Consequently, density field is advected passively by the velocity field. Our findings thus demonstrate that the observed density fluctuations in the interstellar medium are the structures passively convected by the background velocity field.