The dynamics of non-axisymmetric turbidity currents is considered here for a range of Reynolds numbers of O(10^4) when based on the initial height of the release. The study comprises a series of experiments and highly resolved simulations for which a finite volume of particle-laden solution is released into fresh water. A mixture of water and polystyrene particles of mean diameter dp=300 μm and mixture density ρc=1012 kg/m^3 is initially confined in a hollow cylinder at the centre of a large tank filled with fresh water. Cylinders with two different cross-sectional shapes, but equal cross-sectional areas, are examined: a circle and a rounded rectangle in which the sharp corners are smoothened. The time evolution of the front is recorded as well as the spatial distribution of the thickness of the final deposit via the use of a laser triangulation technique. The dynamics of the front and final deposit are significantly influenced by the initial geometry, displaying substantial azimuthal variation especially for the rectangular case where the current extends farther and deposits more particles along the initial minor axis of the rectangular cross-section. Several parameters are varied to assess the dependence on the settling velocity, initial height aspect ratio and volume fraction. Even though resuspension is not taken into account in our simulations, good agreement with experiments indicates that it does not play an important role in the front dynamics, in terms of velocity and extent of the current. However, wall shear stress measurements show that incipient motion of particles and particle transport along the bed are likely to occur in the body of the current and should be accounted to properly capture the final deposition profile of particles.