Gravity Driven Flow Past the Bottom with Small Waviness

  • R. Wojnar
  • W. BielskiEmail author
Conference paper
Part of the Trends in Mathematics book series (TM)


We propose an introductory study of gravity driven Stokesian flow past the wavy bottom, based on Adler’s et al. papers. In examples the waviness is described by a sinus function and its amplitude is small, up to O(ε2). A correction to Hagen-Poiseuille’s type free-flow solution is found. A contribution of capillary surface tension is discussed.


Stokes’ equation Asymptotic and Fourier’s expansions Roughness Obstacles 

Mathematics Subject Classification (2010)

Primary 35C20 35J05; Secondary 41A58 42B05 85A30 86A05 



The authors gratefully acknowledge many helpful suggestions from Professor Vladimir V. Mityushev.

This work was partially supported within statutory activities No 3841/E-41/S/2017 of the Ministry of Science and Higher Education of Poland.


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institute of Fundamental Technological Research PASWarszawaPoland
  2. 2.Institute of GeophysicsPolish Academy of SciencesWarsawPoland

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