A turbine apparatus is immersed in an ambient stream of a flowing fluid, such as water, so as to encapture a portion of the flowing fluid and extract power therefrom, before returning it back into the ambient stream, which may be a tidal flow of ocean water, or a relative flow of water behind a boat. The apparatus includes a converging intake duct with an inlet opening that faces forward into the ambient stream flow, a spiral volute casing that redirects the fluid into a spiral flow, a rotor arranged coaxially on the spiral axis, and an exhaust duct that diverges and curves from an exhaust inlet coaxial with the spiral axis to an exhaust outlet that opens rearwardly into the ambient flow. The rotor has a peripheral rotor inlet around the circumference of a first stage thereof and an axial rotor outlet at one axial end thereof, and is arranged with its rotor axis coinciding with the spiral axis oriented transverse to the ambient stream flow. The rotor redirects the fluid from the spiral tangential and radial direction at the rotor inlet to the axial direction at the rotor outlet, while extracting power therefrom. Fluid flow channels are designed to achieve smooth acceleration, redirection, power transfer, and deceleration of the fluid preferably without turbulence and cavitation, and preferably using streamlines to develop the surface contours of complex channel components.