Seismic‐Generated Water Waves in Axisymmetric tanks

This paper provides a new two-grid discretization method for solving partial differential equation or integral equation eigenvalue problems. In 2001, Xu and Zhou introduced a scheme that reduces the solution of an eigenvalue problem on a finite element grid to that of one single linear problem on the same grid together with a similar eigenvalue problem on a much coarser grid. By solving a slightly different linear problem on the fine grid, the new algorithm in this paper significantly improves the theoretical error estimate which allows a much coarser mesh to achieve the same asymptotic convergence rate. Numerical examples are also provided to demonstrate the efficiency of the new method.

We propose a new method for the problems of computing free energy and surface pressure for various statistical mechanics models on a lattice $\Z^d$. Our method is based on representing the free energy and surface pressure in terms of certain marginal probabilities in a suitably modified sublattice of $\Z^d$. Then recent deterministic algorithms for computing marginal probabilities are used to obtain numerical estimates of the quantities of interest. The method works under the assumption of Strong Spatial Mixing (SSP), which is a form of a correlation decay. We illustrate our method for the hard-core and monomer-dimer models, and improve several earlier estimates. For example we show that the exponent of the monomer-dimer coverings of $\Z^3$ belongs to the interval $[0.78595,0.78599]$, improving best previously known estimate of (approximately) $[0.7850,0.7862]$ obtained in \cite{FriedlandPeled},\cite{FriedlandKropLundowMarkstrom}. Moreover, we show that given a target additive error $\epsilon>0$, the computational effort of our method for these two models is $(1/\epsilon)^{O(1)}$ \emph{both} for free energy and surface pressure. In contrast, prior methods, such as transfer matrix method, require $\exp\big((1/\epsilon)^{O(1)}\big)$ computation effort.

Seawall is a most commonly used structure in coastal areas to protect the landscape and coastal facilities. The studies of interactions between the tsunami-like solitary waves and the seawalls are relatively rare in the literature. In this study, a three-dimensional numerical model based on OpenFOAM® was developed to investigate the tsunami-like solitary waves propagating over a rectangular seawall. The Navier–Stokes equations for two-phase incompressible flow, combining with methods of [Formula: see text] for turbulence closure and Volume of Fluid (VOF) for tracking the free surface, were solved. Laboratory experiments were performed to measure some of the hydrodynamic feature associated with solitary waves. The model was then validated by the laboratory data, and good agreements were found for free surface, velocity and dynamic pressure around the seawall. Finally, a series of numerical experiments were conducted to analyze the evolution of both wave and flow fields, the overtopping discharge as well as wave pressure (force) around the seawall, special attention is given to the effects of seawall crest width. Our findings will help to improve the understanding in the occurrences of tsunami-induced damages in the vicinity of seawall such as wave impact and local scouring.

An extension of general identities for 3D water-wave diffraction with application to the Diffraction Transfer Matrix

A liquid sloshing experimental rig driven by a wave-maker is designed and built to study liquid sloshing problems in a rectangular liquid tank with perforated baffle. A series of experiments are conducted in this experimental rig to estimate the free surface fluctuation and pressure distribution by changing external excitation frequency of the shaking table. An in-house CFD code is also used in this study to simulate the liquid sloshing in three-dimensional (3D) rectangular tank with perforated baffle. Good agreements of free surface elevation and pressure between the numerical results and the experimental data are obtained and presented. Spectral analysis of the time history of free surface elevation is conducted by using the fast Fourier transformation.

The gravity-driven free surface flow problems for which both the solid and free surface boundaries are highly curved are very difficult to solve. A computational scheme using a variable domain and a fixed domain natural element method (NEM) is developed in the present study for the computation of the free surface profile, velocity and pressure distributions, and the flow rate of a 2D gravity fluid flow through a conduit and under a radial gate. The problem involves two highly curved unknown free surfaces and arbitrary curved-shaped boundaries. These features make the problem more complicated than flow under a sluice gate or over a weir. The fluid is assumed to be inviscid and incompressible and the results obtained are confirmed by conducting a hydraulic model test. The results are in agreement with other flow solutions for free surface profiles and pressure distributions.

Numerical simulation of mid-air collisions between droplets and particles: An examination of particle forces and kinetic energy dissipation

This paper describes a dynamic framework for an atmospheric general circulation spectral model in which a reference stratified atmospheric temperature and a reference surface pressure are introduced into the governing equations so as to improve the calculation of the pressure gradient force and gradients of surface pressure and temperature. The vertical profile of the reference atmospheric temperature approximately corresponds to that of the U.S. midlatitude standard atmosphere within the troposphere and stratosphere, and the reference surface pressure is a function of surface terrain geopotential and is close to the observed mean surface pressure. Prognostic variables for the temperature and surface pressure are replaced by their perturbations from the prescribed references. The numerical algorithms of the explicit time difference scheme for vorticity and the semi-implicit time difference scheme for divergence, perturbation temperature, and perturbation surface pressure equation are given in detail. The modified numerical framework is implemented in the Community Atmosphere Model version 3 (CAM3) developed at the National Center for Atmospheric Research (NCAR) to test its validation and impact on simulated climate. Both the original and the modified models are run with the same spectral resolution (T42), the same physical parameterizations, and the same boundary conditions corresponding to the observed monthly mean sea surface temperature and sea ice concentration from 1971 to 2000. This permits one to evaluate the performance of the new dynamic framework compared to the commonly used one. Results show that there is a general improvement for the simulated climate at regional and global scales, especially for temperature and wind.

The Euler Equations for Multiphase Compressible Flow in Conservation Form: Simulation of Shock–Bubble Interactions

Euler's equations describe the motion of inviscid fluid. In the case of shallow water, when a perturbative asymptotic expansion of Euler's equations is considered (to a certain order of smallness of the scale parameters), relations to certain integrable equations emerge. Some recent results concerning the use of integrable equation in modelling the motion of shallow water waves are reviewed in this contribution.

<p>For various experimental reasons, the measurement of water waves propagating in shallow water environments such as surf zones or coastal areas is a difficult task. Deploying surface measuring instruments can be inconvenient, dangerous, or simply expensive. Thus, such measurements are often performed using bottom mounted pressure sensors. Unfortunately, the problem of reconstructing surface elevation based on a single point pressure sensor is an ill-posed problem.</p><p>Indeed, the pressure data collected should be inverted to provide the related water elevation. However, the transfer function traditionally used to perform this inversion is subject to question. When considering very long waves, like tides and tsunamis, the pressure is hydrostatic as long as dispersive effects can be neglected and recovering surface elevation from the bottom pressure does not imply any particular difficulty. Yet, for steeper waves propagating in such depth conditions, nonlinearity might play a significant role (Didenkulova et al., 2021).</p><p>In coastal areas, the propagation of water waves is more complex, and often involves dispersion or nonlinearity. In such areas, one may find wind waves, which are strongly dispersive, even in the coastal zone. Using linear theory might be helpful, in such cases, but is also subject to questions (Touboul & Pelinovsky, 2018). Besides, other corrections related to their dispersive behaviour might play a significant role. Various phenomena, such as partially standing waves (Touboul & Pelinovsky, 2014), or the superimposition of current, might also play a significant role.</p><p>In this work, we investigate the performance of classical reconstruction techniques, but also more recent approaches (Oliveras et al., 2012, Clamond & Constantin, 2013, Bonneton et al., 2018), by confronting their prediction to field data collected in the central part of the Bay of Biscay using current meters mounted with pressure and acoustic surface tracking sensors . These data are obtained in various depth conditions, often in extreme conditions and provide pressure records, current velocity, and direct measurement of the water elevation. Thus, the use of methods presenting various degrees of sophistication allows us to analyze in details the respective roles played by the current, the dispersion, and the nonlinearity.</p><p>The joint French-Russian grant No. 19-55-15005 is acknowledged.</p><p>[1] E. Didenkulova, E. Pelinovsky & J. Touboul, Long-wave approximations in the description of bottom pressure, Wave Motion, vol. 100, No. 1, 102668 (2021)</p><p>[2] J. Touboul & E. Pelinovsky, "On the use of linear theory for measuring surface waves using bottom pressure distribution", Eur. J. Mech. B: Fluids, 67, 97–103, (2018).</p><p>[3] J. Touboul & E. Pelinovsky, "Bottom pressure distribution under a solitonic wave reflecting on a vertical wall", Eur. J. Mech., B. Fluids, 48, p. 13-18, (2014).</p><p>[4] K.L. Oliveras, V. Vasan, B. Deconinck, D. Henderson, Recovering the water wave profile from pressure measurement, SIAM J. Appl. Math. 72 (3) 897–918 (2012).</p><p>[5] P. Bonneton, D. Lannes, K. Martins., H. Michallet, A nonlinear weakly dispersive method for recovering the elevation of irrotational surface waves from pressure measurements, Coastal Engineering 138, 1–8 (2018).</p><p>[6] D. Clamond, A. Constantin, Recovery of steady periodic wave profiles from pressure measurements at the bed, J. Fluid Mech. 714, 463–475 (2013).</p>

Evaluating handwriting in children with developmental coordination disorder (DCD): Temporal, spatial, pressure and grip-force measures

Tiny insects with bristled wings perform the “rowing” motion: the wings accelerate rapidly from zero-velocity to certain reference velocity at 90° angle-of-attack, and the drag produced in this motion provides the weight-supporting force. A flat-plate wing will produce a large drag in such a motion, but it is unknown whether a bristled wing could do so. Here, we study this problem using numerical simulation and simple model wings. The acceleration is large: the wing translates only about half the wing chord length to reach the reference velocity. The following is shown. The bristled wing can produce a very large unsteady drag peak and large time-averaged drag as a flat-plate wing does; the time-averaged drag is about 2.5 times as large as the quasi-steady value. The force production mechanisms are different between the two wings: for the flat-plate wing, because of the large acceleration, the added-mass and the strong free vorticity in the flow produce a large pressure difference between the windward and leeward surfaces of the plate, resulting in large drag (surface frictional force has negligible contribution). Yet for the bristled wing, although the acceleration of the wing is large, a bristle needs to translate about 80 diameters to reach the reference velocity; thus, the effect of acceleration is very weak. Each bristle operates in a quasi-steady Stokes flow and the large drag of the bristled wing is due to the very large surface pressure and frictional forces on each bristle, generated by the strong viscous effect of the Stokes flow (the drag is equally contributed by the surface pressure and frictional forces).

Two problems of scattering of surface water waves involving a semi-infinite elastic plate and a pair of semi-infinite elastic plates, separated by a gap of finite width, floating horizontally on water of finite depth, are investigated in the present work for a two-dimensional time-harmonic case. Within the frame of linear water wave theory, the solutions of the two boundary value problems under consideration have been represented in the forms of eigenfunction expansions. Approximate values of the reflection and transmission coefficients are obtained by solving an over-determined system of linear algebraic equations in each problem. In both the problems, the method of least squares as well as the singular value decomposition have been employed and tables of numerical values of the reflection and transmission coefficients are presented for specific choices of the parameters for modelling the elastic plates. Our main aim is to check the energy balance relation in each problem which plays a very important role in the present approach of solutions of mixed boundary value problems involving Laplace equations. The main advantage of the present approach of solutions is that the results for the values of reflection and transmission coefficients obtained by using both the methods are found to satisfy the energy-balance relations associated with the respective scattering problems under consideration. The absolute values of the reflection and transmission coefficients are presented graphically against different values of the wave numbers.

The classical solutions of the first problem of Stokes for viscous fluids, as it was to be expected, are obtained as limiting cases of those of the simple Couette flow. Something similar is valid for the motions of the fluids induced by a constant shear stress on the boundary. As a direct consequence, new exact solutions are immediately obtained for other two classes of motions of the same fluids.