An $$L^2$$ approach to viscous flow in the half space with free elastic surface

We consider a linearized fluid-structure interaction problem, namely the flow of an incompressible viscous fluid in the half space $${\mathbb {R}}^n_+$$ R + n such that on the lower boundary a function h satisfying an undamped Kirchhoff-type plate equation is coupled to the flow field. Originally, h describes the height of an underlying nonlinear free surface problem. Since the plate equation contains no damping term, this article uses $$L^2$$ L 2 -theory yielding the existence of strong solutions on finite time intervals in the framework of homogeneous Bessel potential spaces. The proof is based on $$L^2$$ L 2 -Fourier analysis and also deals with inhomogeneous boundary data of the velocity field on the “free boundary” $$x_n=0$$ x n = 0 .

Unsteady Wave-Making Resistance of an Accelerating Ship

To measure the resistance of a ship in a towing tank, the target speed of the ship model is achieved by towing the model from the rest at a given acceleration imposed by the carriage. The fluctuations in resistance are generated because of the impulse effects during rapid acceleration. Such acceleration effects in deep water have been studied by previous works [1–3]. In shallow water, the unsteady effects are expected to be stronger, making the fluctuating resistance persisting longer. In order to predict the unsteady waves and to estimate the unsteady oscillating components in the wave resistance, a numerical method based on 3D unsteady potential-flow theory was developed. An implicit finite-difference algorithm coupled with an iterative boundary integral-equation solution procedure was used to deal with the unsteady linear and nonlinear free-surface condition. The results showed that both the acceleration intensity and water depth have a significant effect on the oscillation amplitude of the unsteady wave resistance as well as other force components. Findings of these computations and comparative evaluation of experimental observation are made where relevant. The findings in the present work can be applied to provide guidance for using the appropriate settings, e.g., magnitude and duration of carriage acceleration, when conducting ship-model resistance tests.

Mitigation of liquid sloshing in a rectangular tank due to slotted porous screen

Liquid sloshing inside a tank with a slotted porous screen at the center is studied based on numerical and experimental methods. Slotted screens with three different porosities (0.0964, 0.1968 and 0.3022) for two submergence depths of 1 and 2 cm have been considered. One of the main advantages of the slotted screens is that the resonance frequency of the sloshing tank can be altered and the sloshing-induced motion/load can be suppressed by energy dissipation across the porous screen. The complexities of slotted screens equipped in a sloshing tank are accompanied by wave breaking, jet formation and liquid fragmentations which are commonly seen phenomena across the porous screen. These violent free surface behaviors in a tank are studied based on numerical simulations using the incompressible turbulent model and compared with the experiments. For the numerical sloshing tank with porous screen, free surface elevation and pressure at the tank wall are in good agreement with the experimental results. The adopted numerical technique will be able to capture the nonlinear free surface wave profile, air entrapment and jet formation across the screen in agreement with the experiments. For the fully submerged screen, the lowest resonance period shifted slightly to higher values. The sloshing tank equipped with porous screen of 0.1968 for the fully submerged screen predicted lower values of the amplification factor and pressure at the tank wall compared to other cases.

Second Order Wave Propagating Along VLFS

This paper addresses the nonlinear deflection wave which propagates along a Very Large Floating Structure (VLFS). The whole VLFS is modeled as a one-dimensional beam afloat on the water surface in a vertical two-dimensional plane. It is assumed that the deflection of the wave propagating along the VLFS has a finite amplitude. The nonlinear wave propagating along the VLFS is investigated by extending the propagation theory of the linear wave along the VLFS. The kinetic and kinematic conditions at the boundary surface between the water and VLFS are considered rigorously up to the 2nd order. The 2nd order wave is obtained as a wave associated with the 1st order wave. The characteristics of the nonlinear wave along the VLFS are elucidated by the mathematical solution. The nonlinear wave along the VLFS has characteristics slightly different from the nonlinear free surface wave, known as Stokes wave. The positive peak of the wave along the VLFS is higher than the negative peak due to the nonlinearity in some frequency range while it is the opposite in the other frequency range. The amplitude of the 2nd order wave increases divergently at the frequency range between the two frequency regimes.

The Method of Fundamental Solutions for Three-Dimensional Nonlinear Free Surface Flows Using the Iterative Scheme

In this article, we present a meshless method based on the method of fundamental solutions (MFS) capable of solving free surface flow in three dimensions. Since the basis function of the MFS satisfies the governing equation, the advantage of the MFS is that only the problem boundary needs to be placed in the collocation points. For solving the three-dimensional free surface with nonlinear boundary conditions, the relaxation method in conjunction with the MFS is used, in which the three-dimensional free surface is iterated as a movable boundary until the nonlinear boundary conditions are satisfied. The proposed method is verified and application examples are conducted. Comparing results with those from other methods shows that the method is robust and provides high accuracy and reliability. The effectiveness and ease of use for solving nonlinear free surface flows in three dimensions are also revealed.

Assessment of the Finite VolumE Sea Ice Ocean Model (FESOM2.0), Part I: Description of selected key model elements and comparison to its predecessor version

The evaluation and model element description of the second version of the unstructured-mesh Finite-volumE Sea ice–Ocean circulation Model (FESOM2.0) is presented. The model sensitivity to arbitrary Lagrangian Eulerian (ALE) linear and nonlinear free surface formulation, Gent McWilliams eddy parameterisation, isoneutral Redi diffusion and different vertical mixing schemes is documented. The hydrographic biases, large scale circulation, numerical performance and scalability of FESOM2.0 are compared with its predecessor FESOM1.4. FESOM2.0 shows biases with a magnitude comparable to FESOM1.4 and it simulates a more realistic AMOC. Compared to its predecessor FESOM2.0 provides clearly defined fluxes and a three times higher throughput in terms of simulated years per day (SYPD). It is thus the first mature global unstructured-mesh ocean model with computational efficiency comparable to state-of-the-art structured-mesh ocean models. Other key elements of the model and new development will be described in following-up papers.