Extreme water-wave profile recovery from pressure measurements at the seabed

Clamond, Didier; Henry, David

doi:10.1017/jfm.2020.729

Cited by 15 publications

(8 citation statements)

References 31 publications

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“…Chen and Walsh [1] later proved an analogous result with vorticity of Sobolev regularity and allowed for density stratification using strong unique continuation techniques. See also [2,16,3] for further results of this variety. Pressure recovery for (4.2) is simpler in that we require constant vorticity and have pressure data on an open set, rather than the boundary.…”

Section: Discussionmentioning

confidence: 99%

Rigidity of three-dimensional internal waves with constant vorticity

Chen¹,

Fan²,

Walsh³

et al. 2022

Preprint

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This paper studies the structural implications of constant vorticity for steady threedimensional internal water waves. It is known that in many physical regimes, water waves beneath vacuum that have constant vorticity are necessarily two dimensional. The situation is more subtle for internal waves that traveling along the interface between two immiscible fluids. When the layers have the same density, there is a large class of explicit steady waves with constant vorticity that are three-dimensional in that the velocity field and pressure depend on one horizontal variable while the interface is an arbitrary function of the other. We prove the following rigidity result: every three-dimensional traveling internal wave with bounded velocity for which the vorticities in the upper and lower layers are nonzero, constant, and parallel must belong to this family. If the densities in each layer are distinct, then in fact the flow is fully two dimensional.

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Section: Discussionmentioning

confidence: 99%

Rigidity of three-dimensional internal waves with constant vorticity

Chen¹,

Fan²,

Walsh³

et al. 2022

Preprint

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“…When , the flow is irrotational and one can use the powerful theory of holomorphic functions (Clamond 2013; Clamond & Constantin 2013; Clamond & Henry 2020). In the case where , one can still use this technique following Helmholtz representation (Aris 1962).…”

Section: Holomorphic Functionsmentioning

confidence: 99%

“…Exact tractable relations were derived in Clamond (2013) and Clamond & Constantin (2013), which permit a straightforward numerical procedure for deriving the free surface from the bottom pressure. A significant advantage of these approaches is that they work directly with nonlinear waves in the physical plane, allowing recovery of nonlinear wave profiles up to, and including, Stokes wave of greatest height (Clamond & Henry 2020). The robustness of this nonlinear wave surface reconstruction approach is further illustrated in this paper by expanding it to encompass flows with constant vorticity.…”

Section: Introductionmentioning

confidence: 99%

Recovery of steady rotational wave profiles from pressure measurements at the bed

2023

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We derive equations relating the pressure at a flat seabed and the free-surface profile for steady gravity waves with constant vorticity. The resulting set of nonlinear equations enables the recovery of the free surface from pressure measurements at the bed. Furthermore, the flow vorticity (unknown a priori) is determined solely from the bottom pressure as part of the recovery method. This approach is applicable even in the presence of stagnation points and its efficiency is illustrated via numerical examples.

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“…The recovery method studied in Clamond (2013), Clamond & Constantin (2013), Clamond & Henry (2020) and Clamond et al. (2023) has two shortcomings, however.…”

Section: Introductionmentioning

confidence: 99%

General procedure for free-surface recovery from bottom pressure measurements: application to rotational overhanging waves

Labarbe,

Clamond

2023

J. Fluid Mech.

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A novel boundary integral approach for the recovery of overhanging (or not) rotational water waves (with constant vorticity) from pressure measurements at the bottom is presented. The method is based on the Cauchy integral formula and on an Eulerian–Lagrangian formalism to accommodate overturning free surfaces. This approach eliminates the need to introduce a priori a special basis of functions, thus providing a general means of fitting the pressure data and, consequently, recovering the free surface. The effectiveness and accuracy of the method are demonstrated through numerical examples.

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Extreme water-wave profile recovery from pressure measurements at the seabed

Abstract: Abstract

Cited by 15 publications

References 31 publications

Rigidity of three-dimensional internal waves with constant vorticity

Rigidity of three-dimensional internal waves with constant vorticity

Recovery of steady rotational wave profiles from pressure measurements at the bed

General procedure for free-surface recovery from bottom pressure measurements: application to rotational overhanging waves

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