Abstract.
A modified Lundgren’s model (the LABSRL model) accounting for the effect of surface tension is applied for the description of stationary bathtub vortices in a viscous liquid with a free surface. Laminar liquid flow through the circular bottom orifice is considered in a horizontally unbounded domain with the liquid being assumed to be undisturbed at infinity and approaching to a constant depth. An approximate analytical solution of the LABSRL model is obtained for small-dent vortices. Good agreement is achieved between the constructed analytical and numerical solutions for the same set of parameters.
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Stepanyants, Y.A., Yeoh, G.H. Burgers–Rott vortices with surface tension. Z. angew. Math. Phys. 59, 1057–1068 (2008). https://doi.org/10.1007/s00033-008-7071-9
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DOI: https://doi.org/10.1007/s00033-008-7071-9