Hydrodynamics of Moonpool-Type Floaters: A Theoretical and a CFD Formulation

Moonpool-type floaters were initially proposed for applications such as artificial islands or as protecting barriers around a small area enabling work at the inner surface to be carried out in relatively calm water. In recent years, a growing interest on such structures has been noted, especially in relation to their use as heaving wave energy converters or as oscillating water column (OWC) devices for the extraction of energy from waves. Furthermore, in the offshore marine industry, several types of vessels are frequently constructed with moonpools. The present paper deals with the hydrodynamics of bottomless cylindrical bodies having vertical symmetry axis and floating in a water of finite depth. Two computation methods were implemented and compared: a theoretical approach solving analytically the corresponding diffraction problem around the moonpool floater and a computational fluid dynamics (CFD) solver, which considers the viscous effects near the sharp edges of the body (vortex shedding) as non-negligible. Two different moonpool-type configurations were examined, and some interesting phenomena were discussed concerning the viscous effects and irregularities caused by the resonance of the confined fluid.

SOLUTION OF THE TWO-DIMENSIONAL WAVE DIFFRACTION PROBLEM ON FRACTAL BODIES BY THE PATTERN EQUATIONS METHOD

The solution of the two-dimensional wave diffraction problem for infinite cylinder of complex cross-section was considered by using the pattern equations method (PEM). A triangle and a Koch snowflake of first iteration were chosen as the geometry of the cross-sections of the cylinder. The numerical algorithms of the PEM for a single scatterer and for a group of bodies with the Dirichlet condition on their boundary are briefly presented, and the results of numerical calculations of the scattering characteristics for the above geometries are obtained using the PEM and the method of continued boundary conditions (MCBC). To check the convergence of the numerical algorithm in both methods, the optical theorem was used. The limits of applicability of the PEM for fractal scatterers are established. It is shown that for all convex bodies the algorithm of the PEM is sufficiently stable and allows obtaining calculation results with an accuracy acceptable in practice. In the case of a non-convex body, namely, a Koch snowflake, the algorithm of the PEM for a single scatterer turns out to be unstable and the acceptable accuracy can be obtained only if this geometry is considered as a group of bodies composed of convex geometries (for example, triangles).

Universal atom interferometer simulation of elastic scattering processes

In this article, we introduce a universal simulation framework covering all regimes of matter-wave light-pulse elastic scattering. Applied to atom interferometry as a study case, this simulator solves the atom-light diffraction problem in the elastic case, i.e., when the internal state of the atoms remains unchanged. Taking this perspective, the light-pulse beam splitting is interpreted as a space and time-dependent external potential. In a shift from the usual approach based on a system of momentum-space ordinary differential equations, our position-space treatment is flexible and scales favourably for realistic cases where the light fields have an arbitrary complex spatial behaviour rather than being mere plane waves. Moreover, the solver architecture we developed is effortlessly extended to the problem class of trapped and interacting geometries, which has no simple formulation in the usual framework of momentum-space ordinary differential equations. We check the validity of our model by revisiting several case studies relevant to the precision atom interferometry community. We retrieve analytical solutions when they exist and extend the analysis to more complex parameter ranges in a cross-regime fashion. The flexibility of the approach, the insight it gives, its numerical scalability and accuracy make it an exquisite tool to design, understand and quantitatively analyse metrology-oriented matter-wave interferometry experiments.

On the asymptotic properties of a canonical diffraction integral

We introduce and study a new canonical integral, denoted I + − ε , depending on two complex parameters α 1 and α 2 . It arises from the problem of wave diffraction by a quarter-plane and is heuristically constructed to capture the complex field near the tip and edges. We establish some region of analyticity of this integral in C 2 , and derive its rich asymptotic behaviour as | α 1 | and | α 2 | tend to infinity. We also study the decay properties of the function obtained from applying a specific double Cauchy integral operator to this integral. These results allow us to show that this integral shares all of the asymptotic properties expected from the key unknown function G +− arising when the quarter-plane diffraction problem is studied via a two-complex-variables Wiener–Hopf technique (see Assier & Abrahams, SIAM J. Appl. Math. , in press). As a result, the integral I + − ε can be used to mimic the unknown function G +− and to build an efficient ‘educated’ approximation to the quarter-plane problem.

Non-stationary diffraction problem of a plane oblique pressure wave on the shell in the form of a hyperbolic cylinder taking into account the dissipation effect

The plane non-stationary problem of the dynamics of a thin elastic shell in the form of a hyperbolic cylinder immersed in a liquid under the action of an oblique acoustic pressure wave is considered. To solve this problem, a system of equations is constructed in a related statement. In this case, hydroelasticity problems are reduced to equations of shell dynamics, the damping effect of the liquid (dissipation effect) is taken into account by introducing an integral operator of the convolution type in the time domain. The problem is solved approximately on the basis of the hypothesis of a thin layer taking into account the damping forces in the liquid. The integro-differential equations of shell motion are solved numerically based on the difference discretization of differential operators and the representation of the integral operator by the sum using the trapezoid rule. The kinematic and static parameters of the system are given.