We present a numerical model for stochastic propagation of acoustic waves in fluctuating marine environment. This model predicts the de-coherence effects of the propagated acoustic signals (space decorrelation, and time-distortions of transmitted waveform) which degrade the performances of sonar processing and induce further limitations of the detection capabilities of sonar systems. We investigate the effects of random sound speed fluctuations on the performance of linear horizontal arrays from numerical runs of the stochastic propagation model. As an illustration, we present quantified results for the performance degradation of conventional beamforming for spatial processing, associated to a towed linear array, in presence of realistic random fluctuations of the medium: waves in a deep ocean environment. We observe trends in the behavior of the degradation of the array gain which are summarized within an approximate closed analytical formula. This formula will be helpful for quickly correcting the Array Gain term in the sonar equation and for evaluating in a more realistic way the detection range in a fluctuating oceanic environment.
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