The CROSS-FLO static dewatering sieve continuously removes solids from waste streams at ultra-high rates, clarifying high volumes of process and municipal wastewater at low cost. The sloped screening deck is fitted with stainless steel profile wire screen having slots oriented perpendicular to the flow of material, accelerating fluid through the screen. The deck is adjustable, providing effective control over product discharge and degree of clarification as well as dewatering rates. An extended acceleration/orientation ramp at the upper portion of the unit establishes a proper feed velocity to the profile wire deck, aligning individual fibers in the direction of flow prior to reaching the transverse slotted openings, allowing the widest openings and highest flow rates. The unit is designed to maximize the "Coanda" effect whereby each thin layer of fluid sliced by the profile wire screen clings to the wall of the preceding profile wire, resulting in the acceleration of fluid through the screen.