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# Free surface shear flow model for bow vortices phenomena

Citation Link: https://doi.org/10.15480/882.896

Publikationstyp

Technical Report

Publikationsdatum

1986

Sprache

English

Author

Free surface shear flow model for bow vortices phenomena

Institut fur Schiffbau, Hamburg showed that when a horizontal circular cylinder is towed semisubmerged at a uniform speed, there exists a free surface shear

layer ahead of the cylinder. The deceleration of the fluid particles in the free surface boundary layer gives rise to vortices before the body and a free surface separation point which separates the vortex zone Dear the body from rest of the flow. These observations provided an explanation to the origin of the phenomenon of bowwave-breaking which occurs as vortical motion ahead of

the ships with usually blunt bows and extends all around the hull commonly called as necklace vortex.

In the present study an attempt is made to formulate a shear flow-model for the free surface flow ahead of the cylinder in the framework of boundary layer theory in order to provide a theoretical analysis to the experimental

observations. The vorticity generated due to viscous forces at the boundary is assumed to be concentra ted in a thin free surface boundary layer while the flow underneath this layer is assumed to be potential. Karman-Pohlhausen method

is used to solve the two dimensional boundary layer equations in curvilinear coordinates. The boundary layer profile is assumed to be a cubic satisfying stress and velocity conditions at the boundary. The velocity defect in that boundary layer is assumed to be relatively small in order to simplify the problem. The free surface configuration which needed to be prescribed for the computations is substituted from that of constant pressure surface of the double body flow without satisfying any kinematic condition.

Institut fur Schiffbau, Hamburg showed that when a horizontal circular cylinder is towed semisubmerged at a uniform speed, there exists a free surface shear

layer ahead of the cylinder. The deceleration of the fluid particles in the free surface boundary layer gives rise to vortices before the body and a free surface separation point which separates the vortex zone Dear the body from rest of the flow. These observations provided an explanation to the origin of the phenomenon of bowwave-breaking which occurs as vortical motion ahead of

the ships with usually blunt bows and extends all around the hull commonly called as necklace vortex.

In the present study an attempt is made to formulate a shear flow-model for the free surface flow ahead of the cylinder in the framework of boundary layer theory in order to provide a theoretical analysis to the experimental

observations. The vorticity generated due to viscous forces at the boundary is assumed to be concentra ted in a thin free surface boundary layer while the flow underneath this layer is assumed to be potential. Karman-Pohlhausen method

is used to solve the two dimensional boundary layer equations in curvilinear coordinates. The boundary layer profile is assumed to be a cubic satisfying stress and velocity conditions at the boundary. The velocity defect in that boundary layer is assumed to be relatively small in order to simplify the problem. The free surface configuration which needed to be prescribed for the computations is substituted from that of constant pressure surface of the double body flow without satisfying any kinematic condition.

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