Passive sonar arrays are often used to find submerged vessels by measuring their radiated signal. Acoustic vector-sensor (AVS) arrays, which are normally towed by the ship at the ends of long cables, have been proven to be very effective for target direction of arrival (DOA) estimation. The flow noise, arising from the flow of water over the vector-sensor or its housing when the array is towed, is often a major source of interference to the towed array as it is usually directly coupled to the array sensing elements. In this paper, we obtain a closed-form expression for the spatial correlations of all the components of an AVS array in a flow-noise field. We apply the noise correlation model to DOA estimation using a uniform linear AVS array beamforming. The flow-noise impact on the beamforming capabilities is evaluated via numerical simulations.