Low Reynolds number flow over cavities

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Abstract
Low Reynolds number flow over rectangular cavities is analyzed. The problem is posed to simulate towing tank experiments of Taneda [J. Phys. Soc. Jpn. 46, 1935 (1979)]. A very good agreement exists between numerical and experimental results. The dividing streamline separates from the cavity side wall below the upper corner. The separation point moves toward this corner when the aspect ratio decreases. Flow structure inside the cavity changes considerably with the aspect ratio. Only corner vortices exist in a cavity of aspect ratio W/h=4.0. A decrease of the aspect ratio leads to the enlargement and eventual merger of these vortices. The merger begins with the formation of a stagnation point separating two vortex centers inside the cavity. These vortex centers become progressively weaker and merge to form a single central vortex in a cavity of aspect ratio W/h=2.0. Further decrease of the aspect ratio results in the enlargement of the new corner vortices and their eventual merger. This process begins in a cavity of aspect ratio between 0.6 and 0.575 and is finished in a cavity of aspect ratio 0.5, where two central vortices have been identified. The further decrease of the aspect ratio leads to the sequential repetition of this process and creation of additional central vortices.