Numerical investigation of turbulence of surface gravity waves

In this paper, we numerically study the wave turbulence of surface gravity waves in the framework of Euler equations of the free surface. The purpose is to understand the variation of the scaling of the spectra with wavenumber $k$ and energy flux $P$ at different nonlinearity levels under different forcing/free-decay conditions. For all conditions (free decay and narrow-band and broad-band forcing) that we consider, we find that the spectral forms approach the wave turbulence theory (WTT) solution $S_\eta \sim k^{-5/2}$ and $S_\eta \sim P^{1/3}$ at high nonlinearity levels. With a decrease of nonlinearity level, the spectra for all cases become steeper, with the narrow-band forcing case exhibiting the most rapid deviation from WTT. We investigate bound waves and the finite-size effect as possible mechanisms causing the spectral variations. Through a tri-coherence analysis, we find that the finite-size effect is present in all cases, which is responsible for the overall steepening of the spectra and the reduced capacity of energy flux at lower nonlinearity levels. The fraction of bound waves in the domain generally decreases with the decrease of nonlinearity level, except for the narrow-band case, which exhibits a transition at a critical nonlinearity level below which a rapid increase is observed. This increase serves as the main reason for the fastest deviation from WTT with the decrease of nonlinearity in the narrow-band forcing case.

OC6 Phase Ia: CFD Simulations of the Free-Decay Motion of the DeepCwind Semisubmersible

Currently, the design of floating offshore wind systems is primarily based on mid-fidelity models with empirical drag forces. The tuning of the model coefficients requires data from either experiments or high-fidelity simulations. As part of the OC6 (Offshore Code Comparison Collaboration, Continued, with Correlation, and unCertainty (OC6) is a project under the International Energy Agency Wind Task 30 framework) project, the present investigation explores the latter option. A verification and validation study of computational fluid dynamics (CFD) models of the DeepCwind semisubmersible undergoing free-decay motion is performed. Several institutions provided CFD results for validation against the OC6 experimental campaign. The objective is to evaluate whether the CFD setups of the participants can provide valid estimates of the hydrodynamic damping coefficients needed by mid-fidelity models. The linear and quadratic damping coefficients and the equivalent damping ratio are chosen as metrics for validation. Large numerical uncertainties are estimated for the linear and quadratic damping coefficients; however, the equivalent damping ratios are more consistently predicted with lower uncertainty. Some difference is observed between the experimental and CFD surge-decay motion, which is caused by mechanical damping not considered in the simulations that likely originated from the mooring setup, including a Coulomb-friction-type force. Overall, the simulations and the experiment show reasonable agreement, thus demonstrating the feasibility of using CFD simulations to tune mid-fidelity models.

Molecule-molecule and atom-molecule collisions with ultracold RbCs molecules

Understanding ultracold collisions involving molecules is of fundamental importance for current experiments, where inelastic collisions typically limit the lifetime of molecular ensembles in optical traps. Here we present a broad study of optically trapped ultracold RbCs molecules in collisions with one another, in reactive collisions with Rb atoms, and in nonreactive collisions with Cs atoms. For experiments with RbCs alone, we show that by modulating the intensity of the optical trap, such that the molecules spend 75\% of each modulation cycle in the dark, we partially suppress collisional loss of the molecules. This is evidence for optical excitation of molecule pairs mediated via sticky collisions. We find that the suppression is less effective for molecules not prepared in the spin-stretched hyperfine ground state. This may be due either to longer lifetimes for complexes or to laser-free decay pathways. For atom-molecule mixtures, RbCs+Rb and RbCs+Cs, we demonstrate that the rate of collisional loss of molecules scales linearly with the density of atoms. This indicates that, in both cases, the loss of molecules is rate-limited by two-body atom-molecule processes. For both mixtures, we measure loss rates that are below the thermally averaged universal limit.

Kinematic dynamos in triaxial ellipsoids

Planetary magnetic fields are generated by motions of electrically conducting fluids in their interiors. The dynamo problem has thus received much attention in spherical geometries, even though planetary bodies are non-spherical. To go beyond the spherical assumption, we develop an algorithm that exploits a fully spectral description of the magnetic field in triaxial ellipsoids to solve the induction equation with local boundary conditions (i.e. pseudo-vacuum or perfectly conducting boundaries). We use the method to compute the free-decay magnetic modes and to solve the kinematic dynamo problem for prescribed flows. The new method is thoroughly compared with analytical solutions and standard finite-element computations, which are also used to model an insulating exterior. We obtain dynamo magnetic fields at low magnetic Reynolds numbers in ellipsoids, which could be used as simple benchmarks for future dynamo studies in such geometries. We finally discuss how the magnetic boundary conditions can modify the dynamo onset, showing that a perfectly conducting boundary can strongly weaken dynamo action, whereas pseudo-vacuum and insulating boundaries often give similar results.

Effect of Bilge Radius and Bilge Keel Height on Roll Damping Performance of Floating Structures

A round bilge with a bilge keel structure is a key element which can alleviate roll motions of ships and floating structures by transferring the roll momentum of a floating body into the kinetic energy of water. This study presents a practical guide to properly designing a bilge radius and bilge keel height of a barge-shaped and tanker-shaped FPSOs. A parametric study to figure out the effect of bilge radius and bilge keel height on the roll damping performance is conducted through a series of numerical roll free decay simulations based on Computational Fluid Dynamics (CFD). The bilge radius is normalized by the half breadth of ship, and the bilge keel height is normalized by the maximum bilge keel height which is limited by the molded lines of a side shell and bottom shell. In addition, it is investigated to identify how the roll damping performance of a rectangular section differs from the result of a typical round bilge section with maximum available bilge keel height.

Dynamic Responses of the State-of-the-Art Floating System Integrating a Wind Turbine With a Steel Fish Farming Cage: Model Tests vs. Numerical Simulations

This work is dedicated to comparing the experimental and numerical results of the dynamic responses of a novel floating system integrating a floating offshore wind turbine with a steel fish farming cage (FOWT-SFFC) under wind and wave loadings. The patents of this floating system have been successfully licensed recently in China and USA. The experimental study is carried out in the Ocean Basin of Tsinghua Shenzhen International Graduate School, with a Froude scaling of 1:30. A small commercial wind turbine is used to produce the scaled wind loads on FOWT-SFFC in terms of the similarity of thrust force. In this paper, the setup of model tests is described first. Second, a numerical model of prototype FOWT-SFFC is built in the software OrcaFlex. Then, this numerical model is calibrated and updated by the results of free decay tests and static offset tests in the basin. The numerical model also adopts three sets of drag coefficients. Finally, the experimental results of FOWT-SFFC under a variety of load cases are presented and compared with the numerical simulation results. They include seakeeping tests for hydrodynamic motion response amplitude operators (RAOs) and dynamic responses corresponding to normal operating and survival conditions. The numerical simulation results show that, though they are in good agreement with model test data especially on time records of dynamic responses, they are sensitive to the selection of drag coefficients particularly on extreme values and low-frequency spectral contents. Appropriate drag coefficients are suggested to be used in the numerical model for a specific environmental condition. Drag coefficients benchmarked from the free decay tests may not be suitable for moderate and harsh wave conditions.

A Numerical Study of the Hydrodynamics of an Offshore Fish Farm Using REEF3D

In this paper, the CFD framework REEF3D is utilized to investigate the hydrodynamics of a large offshore fish farm in waves. The solver consists of a rigid body dynamics solver for the frame structure coupled to a fluid solver including the shielding effects of the nets. The solver and the grid independence are validated using a 2D numerical wave tank, a free decay test, and a study of the wave loads on a rigid net panel. Then, the effects of regular wave parameters, the thickness of the vertical outer columns of the structure, and varies aspect ratios on the loads, response and maximum mooring tensions are investigated. It is concluded that the response is sensitive to the wave period rather than the wave height and that the net system accounts for about 30% of the total drag but does not influence the structural response to a larger extend. The effect of the aspect ratio on the hydrodynamics is more distinct than that of the frame thickness especially. Thus, the first step towards a systemic evaluation of the importance of different structural parts of an offshore fish cage for the expected responses is presented in this paper.

Hydrodynamic Response of Buoy Form Spar With Heave Plate Near Free Surface

Hydrodynamic response of spar with appendages such as heave plate has been investigated in the past, mostly attached at the bottom of the spar. The effect of geometry and appendages on the hydrodynamic response of spar has been investigated in this article. A curved neck form with a heave plate near the free surface is proposed as an energy dissipation device for both heave and pitch responses. Numerical simulation using Computational Fluid Dynamics (CFD) is used for capturing the flow around the curved neck with heave plate and corresponding damping characteristics. CFD free decay simulations have been carried out to obtain heave and pitch damping and were noted to be higher than the conventional spar with heave plate at the bottom. Comparison of the proposed geometry and heave plate at the free surface with a conventional heave plate at the bottom of the spar has been made, and significant changes to the response and hydrodynamic characteristics have been noted. It is observed that the buoy form spar combined with the heave plate located near the surface (within 10% of the draft) helps dissipate energy and thus reduce the heave response.