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Potential flow over a submerged rectangular obstacle: Consequences for initiation of boulder motion

Part of: Incompressible inviscid fluids Incompressible viscous fluids Geometric function theory Coupling of solid mechanics with other effects

Published online by Cambridge University Press:  05 September 2019

J. G. HERTERICH Open the ORCID record for J. G. HERTERICH [Opens in a new window]  and
F. DIAS Open the ORCID record for F. DIAS [Opens in a new window]
J. G. HERTERICH
Affiliation:
School of Mathematics and Statistics, University College Dublin, Belfield, Dublin 4, Ireland emails: james.herterich@ucd.ie; frederic.dias@ucd.ie Earth Institute, University College Dublin, Belfield, Dublin 4, Ireland
F. DIAS
Affiliation:
School of Mathematics and Statistics, University College Dublin, Belfield, Dublin 4, Ireland emails: james.herterich@ucd.ie; frederic.dias@ucd.ie CMLA, ENS Paris–Saclay, CNRS, Université Paris–Saclay, 94235 Cachan, France Earth Institute, University College Dublin, Belfield, Dublin 4, Ireland
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Abstract

Steady two-dimensional fluid flow over an obstacle is solved using complex variable methods. We consider the cases of rectangular obstacles, such as large boulders, submerged in a potential flow. These may arise in geophysics, marine and civil engineering. Our models are applicable to initiation of motion that may result in subsequent transport. The local flow depends on the obstacle shape, slowing down in confining corners and speeding up in expanding corners. The flow generates hydrodynamic forces, drag and lift, and their associated moments, which differ around each face. Our model replaces the need for ill-defined drag and lift coefficients with geometry-dependent functions. We predict smaller flow velocities to initiate motion. We show how a joint-bound boulder can be transported against gravity, and analyse the influence of a wake region behind an isolated boulder.

Keywords

Complex variable methodsconformal mappingincompressible inviscid fluidsgeophysicsfluid–solid interaction

MSC classification

Primary: 86-08: Computational methods 74F10: Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
Secondary: 30C20: Conformal mappings of special domains 76B99: None of the above, but in this section 76D10: Boundary-layer theory, separation and reattachment, higher-order effects
Type
Papers
Information
European Journal of Applied Mathematics , Volume 31 , Issue 4 , August 2020 , pp. 646 - 681
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Copyright
© Cambridge University Press 2019

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