Underwater acoustic detection of ultra-high-energy neutrinos was proposed already in 1950s: when a neutrino interacts with a nucleus in water, the resulting particle cascade produces a pressure pulse that has a bipolar temporal structure and propagates within a flat disk-like volume. A telescope that consists of thousands of acoustic sensors deployed in the deep sea can monitor hundreds of cubic kilometres of water looking for these signals and discriminating them from acoustic noise. To study the feasibility of the technique it is critical to have a calibrator able to mimic the neutrino “signature” that can be operated from a vessel. Due to the axial-symmetry of the signal, their very directive short bipolar shape and the constraints of operating at sea, the development of such a calibrator is very challenging. Once the possibility of using the acoustic parametric technique for this aim was validated with the first compact array calibrator prototype, in this paper we describe the new design for such a calibrator composed of an array of piezo ceramic tube transducers emitting in axial direction.