Sound waves in the ocean are affected by the space and time variabilities of the propagation medium. These fluctuations, mainly caused by internal waves such as tides and gyres, can lead to a loss of phase information in measured wave-fronts, and make hardly predictable the true location of a source. As a consequence, the performance of classical direction of arrival (DOA) estimation algorithms are significantly degraded. An important literature addresses this issue by considering either the phase as non-informative or the environment as a noise with no physical information. In this work, we propose to introduce a phase prior inspired by random fluctuation theories. This prior is combined with a sparsity assumption on the number of expected DOAs and exploited within a Bayesian framework. The contributions of such an approach are twofold: by the use of suitable prior information (small number of DOAs and phase distortion), it allows an estimation of DOAs from a single snapshot , while simultaneously providing a posterior estimation of the mean fluctuations of the propagation medium. Bayesian inference can be performed in different ways. Among the different possible procedures, we chose here to resort to a Bethe approximation and a message-passing approach recently considered in compressive sensing setups. The resulting algorithm places in the continuation of our previous works. The main improvement lies in the proba-bilistic model used to describe the phase distortion. Here we use a Multivariate Von Mises distribution, more suitable to directional statistics and still fitting the simplified theory of phase fluctuation. Numerical experiments with synthetic datasets show that the proposed algorithm , dubbed as VITAMIN for ``Von mIses swepT Approximate Message passINg'', presents interesting performance compared to other state-of-the-art algorithms. In particular, in the considered experiments, VITAMIN behaves well regarding its robustness to additive noise and phase fluctuations.