In this work we apply a mathematical model developed by Teshukov (2007) to simulate turbulent powder snow avalanches. The two-parameter model describes the production of turbulent energy from shearing. This energy is associated with the formation of small and large vortices which provide avalanches with their distinctive billow and cleft-like structures. The model accurately predicts the concentration of translational kinetic energy at the avalanche front and likewise the formation of an almost stationary turbulent wake. The calculation of turbulent energy can be exploited to improve air-entrainment and turbulent drag models and therefore to improve engineering calculations of powder cloud height, speed and density, an important problem in snow avalanche mitigation. In present work we focus on the one-dimensional case. The governing equations are discretized with a finite volume second order Godunov-type scheme using HLLC Riemann solver. A good agreement between numerical solution of the new model and the photogrammetric measurements (height, length and frequency of billows, depths of clefts) is observed both at the front and tail of the avalanche for two different data sets.