Turbine systems for extracting energy from water traveling relative to the turbine system can include a rotor assembly for extracting the energy, a turbine shroud having a turbine shroud inner volume within which at least a portion of the rotor assembly is disposed, and an ejector shroud having a ejector shroud inner volume within which at least a portion of the turbine shroud is disposed. The turbine shroud and the ejector shroud can each have a terminus comprising a plurality of turbine shroud mixer elements or ejector shroud mixer elements, respectively. One or more of the mixer elements and ejector shrouds comprise a mixer/ejector pump which increases the energy extraction potential of the turbine system. One or more of the turbine shroud mixer elements, ejector shroud mixer elements, and ejector shroud and turbine shroud inlets can be asymmetric about a plane passing through the axis of rotation of the rotor assembly. Methods, systems, apparatus and articles of manufacture relating to these features and others are also disclosed.