Snow avalanches possess two types of kinetic energy: the kinetic energy associated with the mean velocity in the downhill direction and the kinetic energy associated with individual particle velocities that vary from the mean. The mean kinetic energy is directional; the kinetic energy associated with the velocity fluctuations is non-directional in the sense that it is connected to random particle movements. However, the rigid, basal boundary directs the random fluctuation energy into the avalanche. Thus, the random energy flux is converted to free mechanical energy which lifts and dilates the avalanche flow mass, changing the flow density and increasing the normal (dispersive) pressure and, as a consequence, changing the flow resistance. In this paper we derive macroscopic relations that link the production of the random kinetic energy to the perpendicular acceleration of the avalanche's center of mass. We show that a single burst of fluctuation energy will produce pressures that oscillate around the hydrostatic pressure. Because we do not include a damping process, the oscillations of the center of mass remain, even if the production of random kinetic energy stops. We formulate relationships that can be used within the framework of depth-averaged mass and momentum equations that are often used to simulate snow avalanches in realistic terrain.