scholarly journals A note on the Stokes phenomenon in flow under an elastic sheet

2020 ◽  
Vol 378 (2179) ◽  
pp. 20190530
Author(s):  
Christopher J. Lustri ◽  
Lyndon Koens ◽  
Ravindra Pethiyagoda
Keyword(s):  
Free Surface ◽  
Surface Waves ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Capillary Waves ◽  
Stokes Phenomenon ◽  
Elastic Sheet ◽  
Free Surface Waves ◽  
Wide Range ◽  
Fluid Behaviour

The Stokes phenomenon is a class of asymptotic behaviour that was first discovered by Stokes in his study of the Airy function. It has since been shown that the Stokes phenomenon plays a significant role in the behaviour of surface waves on flows past submerged obstacles. A detailed review of recent research in this area is presented, which outlines the role that the Stokes phenomenon plays in a wide range of free surface flow geometries. The problem of inviscid, irrotational, incompressible flow past a submerged step under a thin elastic sheet is then considered. It is shown that the method for computing this wave behaviour is extremely similar to previous work on computing the behaviour of capillary waves. Exponential asymptotics are used to show that free-surface waves appear on the surface of the flow, caused by singular fluid behaviour in the neighbourhood of the base and top of the step. The amplitude of these waves is computed and compared to numerical simulations, showing excellent agreements between the asymptotic theory and computational solutions. This article is part of the theme issue ‘Stokes at 200 (part 2)’.

scholarly journals A topological study of gravity free-surface waves generated by bluff bodies using the method of steepest descents

2016 ◽  
Vol 472 (2191) ◽  
pp. 20150833 ◽  
Author(s):  
Philippe H. Trinh
Keyword(s):  
Free Surface ◽  
Riemann Surface ◽  
Surface Waves ◽  
Water Waves ◽  
Wave Equations ◽  
Free Surface Flow ◽  
Surface Flow ◽  
The Body ◽  
Bluff Bodies ◽  
Free Surface Waves

The standard analytical approach for studying steady gravity free-surface waves generated by a moving body often relies upon a linearization of the physical geometry, where the body is considered asymptotically small in one or several of its dimensions. In this paper, a methodology that avoids any such geometrical simplification is presented for the case of steady-state flows at low speeds. The approach is made possible through a reduction of the water-wave equations to a complex-valued integral equation that can be studied using the method of steepest descents. The main result is a theory that establishes a correspondence between different bluff-bodied free-surface flow configurations, with the topology of the Riemann surface formed by the steepest descent paths. Then, when a geometrical feature of the body is modified, a corresponding change to the Riemann surface is observed, and the resultant effects to the water waves can be derived. This visual procedure is demonstrated for the case of two-dimensional free-surface flow past a surface-piercing ship and over an angled step in a channel.

Measurement of free-surface flow velocity using controlled surface waves

2005 ◽  
Vol 16 (1) ◽  
pp. 47-55 ◽  
Author(s):  
Marian Muste ◽  
Jörg Schöne ◽  
Jean-Dominique Creutin
Keyword(s):  
Free Surface ◽  
Surface Waves ◽  
Flow Velocity ◽  
Free Surface Flow ◽  
Surface Flow

scholarly journals The pattern of surface waves in a shallow free surface flow

2013 ◽  
Vol 118 (3) ◽  
pp. 1864-1876 ◽  
Author(s):  
K. V. Horoshenkov ◽  
A. Nichols ◽  
S. J. Tait ◽  
G. A. Maximov
Keyword(s):  
Free Surface ◽  
Surface Waves ◽  
Free Surface Flow ◽  
Surface Flow

scholarly journals Fluid Structure Interaction of Buoyant Bodies with Free Surface Flows: Computational Modelling and Experimental Validation

Water ◽  
2019 ◽  
Vol 11 (5) ◽  
pp. 1048 ◽  
Author(s):  
Andrea Luigi Facci ◽  
Giacomo Falcucci ◽  
Antonio Agresta ◽  
Chiara Biscarini ◽  
Elio Jannelli ◽  
...  
Keyword(s):  
Free Surface ◽  
Numerical Model ◽  
Fluid Structure Interaction ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Water Impact ◽  
Ocean Engineering ◽  
Fluid Structure ◽  
Structure Interaction ◽  
Wide Range

In this paper we present a computational model for the fluid structure interaction of a buoyant rigid body immersed in a free surface flow. The presence of a free surface and its interaction with buoyant bodies make the problem very challenging. In fact, with light (compared to the fluid) or very flexible structures, fluid forces generate large displacements or accelerations of the solid and this enhances the artificial added mass effect. Such a problem is relevant in particular in naval and ocean engineering and for wave energy harvesting, where a correct prediction of the hydrodynamic loading exerted by the fluid on buoyant structures is crucial. To this aim, we develop and validate a tightly coupled algorithm that is able to deal with large structural displacement and impulsive acceleration typical, for instance, of water entry problems. The free surface flow is modeled through the volume of fluid model, the finite volume method is utilized is to discretize the flow and solid motion is described by the Newton-Euler equations. Fluid structure interaction is modeled through a Dirichlet-Newmann partitioned approach and tight coupling is achieved by utilizing a fixed-point iterative procedure. As most experimental data available in literature are limited to the first instants after the water impact, for larger hydrodynamic forces, we specifically designed a set of dedicated experiments on the water impact of a buoyant cylinder, to validate the proposed methodology in a more general framework. Finally, to demonstrate that the proposed numerical model could be used for a wide range of engineering problems related to FSI in multiphase flows, we tested the proposed numerical model for the simulation of a floating body.

Nonlinear resonance of free surface waves in a current over a sinusoidal bottom: a numerical study

1994 ◽  
Vol 279 ◽  
pp. 377-405 ◽  
Author(s):  
Paolo Sammarco ◽  
Chiang C. Mei ◽  
Karsten Trulsen
Keyword(s):  
Free Surface ◽  
Numerical Study ◽  
Fixed Bed ◽  
Nonlinear Resonance ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Free Surface Waves ◽  
Linearized Theory ◽  
The Mean ◽  
Mean Current

We examine the free surface flow over a fixed bed covered by rigid sinusoidal dunes. The mean current velocity is near the critical value at which the linearized theory predicts unbounded response. By allowing transients we examine the instability of the steady and nonlinear solution of Mei (1969) and the possibility of chaos when the current has a small oscillatory component.

Inviscid free-surface flow over a periodic wall

1991 ◽  
Vol 226 ◽  
pp. 189-203 ◽  
Author(s):  
V. Bontozoglou ◽  
S. Kalliadasis ◽  
A. J. Karabelas
Keyword(s):  
Free Surface ◽  
Free Surface Flow ◽  
Free Surface Flows ◽  
Surface Flow ◽  
Surface Shape ◽  
Flow Parameters ◽  
Material Deposition ◽  
Straightforward Method ◽  
Wide Range ◽  
Free Surface Shape

A numerical method is described, based on the hodograph formulation, for analysing in viscid, free-surface flows over a periodic wall. An efficient implementation of the wall boundary condition results in a straightforward method, accurate for a wide range of bottom undulation heights and flow parameters. It is demonstrated that a series of resonances is possible between the bottom undulations and the free surface. The steady, free-surface profiles are accurately calculated for a wide range of current velocities and are shown to be significantly dimpled by higher harmonics. A study of the flow field indicates that the free-surface shape strongly affects the velocities close to the wall, leading to distributions which change dramatically with current velocity. Some implications of the new results on the phenomena of wall dissolution or material deposition, Bragg scattering of surface waves and sediment transport in rivers, are discussed.

NUMERICAL SIMULATION OF WAVE POWER DEVICES USING A TWO-FLUID FREE SURFACE SOLVER

2005 ◽  
Vol 19 (28n29) ◽  
pp. 1479-1482 ◽  
Author(s):  
LING QIAN ◽  
CLIVE MINGHAM ◽  
DEREK CAUSON ◽  
DAVID INGRAM ◽  
MATT FOLLEY ◽  
...  
Keyword(s):  
Free Surface ◽  
Free Surface Flow ◽  
Variable Density ◽  
Surface Flow ◽  
Flow Problems ◽  
Cut Cell ◽  
Wide Range ◽  
Complex Fluid ◽  
Cartesian Cut ◽  
Two Fluid

A generic two-fluid (water/air) numerical model has been developed and applied for the simulation of the complex fluid flow around a wave driven rotating vane near a shoreline in the context of a novel wave energy device OWSC (Oscillating wave surge converter). The underlying scheme is based on the solution of the incompressible Euler equations for a variable density fluid system for automatically capturing the interface between water and air and the Cartesian cut cell method for tracking moving solid boundaries on a background stationary Cartesian grid. The results from the present study indicate that the method is an effective tool for modeling a wide range of free surface flow problems.

scholarly journals Laminar free-surface flow into a vertical cylinder

1975 ◽  
Vol 3 (1) ◽  
pp. 51-68 ◽  
Author(s):  
Thomas G. Smith ◽  
J.O. Wilkes
Keyword(s):  
Free Surface ◽  
Vertical Cylinder ◽  
Free Surface Flow ◽  
Surface Flow
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