The presence of shear instability can lead to the generation of turbulence in a stably stratified fluid. Using linear hydrodynamic stability theory, a turbulent kinetic energy budget is computed for an unbounded viscous shear layer for which the hyperbolic tangent shear layer is used to define the mean flow. For neutrally stable flows, the turbulent production due to the action of the Reynolds stress on the mean shear flow is balanced by viscous dissipation and the conversion to potential energy through the buoyancy term. The calculations show that maximum production of turbulent energy occurs at the center of the shear layer and that some of this energy is then transported to the edges of the shear layer where viscous dissipation occurs and some of the energy is converted to potential energy near the center of the flow. As the horizontal wavenumber decreases, the viscous dissipation becomes more important than the buoyancy term in removing energy from the flow. As the Reynolds number increases, the production term is concentrated over a narrower region at the center of the shear layer. Streamlines for neutral and stable conditions are presented to show the flow patterns of the disturbances in thex–zplane. Some possible atmospheric and oceanic applications are suggested in the last section.