70 research outputs found
Remarks on bernoulli constants, gauge conditions and phase velocities in the context of water waves
This short note is about the gauge condition for the velocity potential, the
definitions of the Bernoulli constant and of the velocity speeds in the context
of water waves. These definitions are often implicit and thus the source of
confusion in the literature. Thi
New exact relations for steady irrotational two-dimensional gravity and capillary surface waves
Steady two-dimensional surface capillary-gravity waves in irrotational motion
are considered on constant depth. By exploiting the holomorphic properties in
the physical plane and introducing some transformations of the boundary
conditions at the free surface, new exact relations and equations for the free
surface only are derived. In particular, a physical plane counterpart of the
Babenko equation is obtained
Efficient resolution of the Colebrook equation
A robust, fast and accurate method for solving the Colebrook-like equations
is presented. The algorithm is efficient for the whole range of parameters
involved in the Colebrook equation. The computations are not more demanding
than simplified approximations, but they are much more accurate. The algorithm
is also faster and more robust than the Colebrook solution expressed in term of
the Lambert W-function. Matlab and FORTRAN codes are provided
Multi-symplectic structure of fully-nonlinear weakly-dispersive internal gravity waves
In this short communication we present the multi-symplectic structure for the
two-layer Serre-Green-Naghdi equations describing the evolution of large
amplitude internal gravity long waves. We consider only a two-layer
stratification with rigid bottom and lid for simplicity, generalisations to
several layers being straightforward. This multi-symplectic formulation allows
the application of various multi-symplectic integrators (such as Euler or
Preissman box schemes) that preserve exactly the multi-symplecticity at the
discrete level.Comment: 15 pages, 1 figure, 15 references. Other author's papers can be
downloaded at http://www.denys-dutykh.com
Explicit Dirichlet-neumann Operator For Water Waves
An explicit expression for the Dirichlet-Neumann operator for surface water
waves is presented. For non-overturning waves, but without assuming small
amplitudes, the formula is first derived in two dimensions, subsequently
extrapolated in higher dimensions and with a moving bottom. Although described
here for water waves, this elementary approach could be adapted to many other
problems having similar mathematical formulations
Note on the velocity and related fields of steady irrotational two-dimensional surface gravity waves
International audienceThe velocity and other fields of steady two-dimensional surface gravity waves in irrotational motion are investigated numerically. Only symmetric waves with one crest per wavelength are considered, i.e. Stokes waves of finite amplitude, but not the highest waves, nor subharmonic and superharmonic bifurcations of Stokes waves. The numerical results are analysed, and several conjectures are made about the velocity and acceleration fields
A plethora of generalised solitary gravity-capillary water waves
The present study describes, first, an efficient algorithm for computing
capillary-gravity solitary waves solutions of the irrotational Euler equations
with a free surface and, second, provides numerical evidences of the existence
of an infinite number of generalised solitary waves (solitary waves with
undamped oscillatory wings). Using conformal mapping, the unknown fluid domain,
which is to be determined, is mapped into a uniform strip of the complex plane.
In the transformed domain, a Babenko-like equation is then derived and solved
numerically.Comment: 20 pages, 7 figures, 45 references. Other author's papers can be
downloaded at http://www.denys-dutykh.com
On the multi-symplectic structure of the Serre-Green-Naghdi equations
In this short note, we present a multi-symplectic structure of the
Serre-Green-Naghdi (SGN) equations modelling nonlinear long surface waves in
shallow water. This multi-symplectic structure allow the use of efficient
finite difference or pseudo-spectral numerical schemes preserving exactly the
multi-symplectic form at the discrete level.Comment: 10 pages, 1 figure, 30 references. Other author's papers can be
downloaded at http://www.denys-dutykh.com
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