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NACRA 17 is a small foiling catamaran used in Olympic sailing. Sailing in the NACRA 17 is truly unsteady, especially in the foiling conditions. Dynamic velocity prediction has gained a lot of attention in recent years due to the unsteady nature of foiling sailboats. Different approaches have been applied to predict the motions of foiling or skimming boats in unsteady conditions. Typically, the aerodynamic forces are computed by the quasi-steady theory assumption. Static coefficients are used, and the applied velocities are corrected with boat motions. The hydrodynamic forces of a fully foiling boat can be computed in a similar fashion, but this method fails to include the effect of changes in the free surface as well as added mass. This paper proposes an approach where dynamic coefficients of the NACRA 17 hydrofoils are determined based on unsteady Computational Fluid Dynamics (CFD) simulations with a free surface. In the simulations the foil is moved in prescribed motions in one degree of freedom (DOF) at a time and dynamic coefficients are extracted for different frequencies of motion. All coefficients are combined in a coupled system of equations, and the equations can be solved in 6 DOFs in the time domain. Test scenarios with time-varying conditions are simulated and compared with full dynamic CFD simulations. The initial investigation of the approach shows promising results, but more investigations are needed to validate the approach and to identify possible limitations.

In order to predict nonlinear wave loading on marine structures, a fully nonlinear higher-order finite difference based potential flow solver with all boundary conditions treated by an immersed boundary method has been developed in this paper. The solver adopts high-order finite difference schemes for the spatial derivatives and a 4th order Runge–Kutta method for time stepping. Test cases of forced oscillation of a cylinder in an infinite fluid domain are first studied, which reveal the advantage of the acceleration potential method in terms of wave load computation. Then a wave generation problem using a piston type wave maker is tested. Special attention is paid to the intersection point between the free surface and the body surface, and a scheme which best meets the accuracy and stability requirements is suggested from several proposals. A novel hyperviscosity filter, which works for both uniform and non-uniform grids, is introduced to stabilize the time-domain solution of the wave maker problem. Finally, a forced heaving cylinder on the free surface is considered, and the nonlinear wave loads on the cylinder are analyzed and compared to benchmark results.

Ocean wave energy has the potential of contributing significantly to the industrial energy production and export, both as a standalone solution by using wave energy converters (WECs) in wave energy parks, and in combination with offshore wind energy. For comparison the power intensity of wind is 0.4 - 0.6 kW/m2, solar is 0.1 - 0.2 kW/m2 and wave power intensity is about 2 - 3 kW/m2 [1, 2]. The wave energy converter Crestwing is an attenuator type of WEC with proven technology and simple feasibility originated from the shipbuilding industry [3]. Although it seems to be a feasible technology it still has many avenues for optimizing efficiency and minimizing costs to drive down levelized cost of electricity. Effective energy harvesting is only conceivable by interpretation of underlying physics and optimization of key parameters of a WEC such as hull shape. For these goals we use state-of-the-art CFD simulation tools based on fifth-order Stokes wave theory, overset mesh technique and dynamic fluid body interaction. At the symposium we will present verification and validation of the CFD model relying on existing model tests and use the CFD results to highlight the key components of theCrestwing WEC [4, 5].

Floating offshore structures often exhibit low-frequency oscillatory motions in the horizontal plane, with amplitudes in the same order as their characteristic dimensions and larger than the corresponding wave-frequency responses, making the traditional formulations in an inertial coordinate system inconsistent and less applicable. To address this issue, we extend and explore an alternative formulation completely based on a non-inertial body-fixed coordinate system. Unlike the traditional seakeeping models, this formulation consistently allows for large-amplitude horizontal motions. A numerical model based on a higher-order boundary element is applied to solve the resulting boundary-value problems in the time domain. A recently developed new set of explicit time-integration methods, which do not necessitate the use of upwind schemes for spatial derivatives, are adopted to deal with the convective-type free-surface conditions. To suppress the weak saw-tooth instabilities on the free surface in time marching, we also present novel low-pass filters based on optimized weighted least squares, which are in principle applicable for both structured and unstructured meshes. The presented schemes for the convection equation and the low-pass filter are also relevant for other engineering fields dealing with similar mathematical problems. For ship seakeeping and added resistance analyses, we show that the present computational model does not need to use soft-springs for surge and sway, in contrast to the traditional models. For a floating monopile, the importance of consistently taking into account the effects of large horizontal motions is demonstrated considering the bichromatic incident waves. The present model is considered as a complete second-order wave-load model, as all the second-order wave loads, including the sum-frequency and difference-frequency components, are solved simultaneously.

Poisson equation lies in the heart of the numerical solutions of incompressible Navier–Stokes equations (NSEs) based on the popular projection methods, which decouple the pressure and velocities fields. This paper presents enhanced numerical solutions of the 2D incompressible NSEs inspired by a newly-developed Generalized Harmonic Polynomial Cell (GHPC) method for the Poisson equation, which has a fourth-order spatial accuracy. To achieve that, the original GHPC method is adapted to accommodate immersed boundaries, necessary when a staggered grid for velocities and pressure is applied. The finite difference method (FDM) is used in the spatial discretization of the diffusion and advection terms. Numerical analyses of lid-driven cavity flow, a Taylor–Green vortex, and flow around a smooth circular cylinder all show encouraging results, confirming the accuracy and efficiency of the new solver. Through comparison with an NSEs solver which applies second-order FDM for the Poisson equation, we demonstrate that the accuracy of the pressure solution can be greatly improved by applying the more accurate GHPC method for the Poisson equation, even though the accuracy of the velocities solutions are limited by the numerical schemes for advection–diffusion equations. The accuracy in the pressure solution can also be translated into CPU time saving to achieve a predefined accuracy. The present immersed-boundary GHPC Poisson equation solver can easily be ‘plugged’ into other existing NSEs solvers utilizing staggered grids.

NACRA 17 is a small foiling catamaran used in Olympic sailing. Sailing in the NACRA 17 is truly unsteady, especially in the foiling conditions. Dynamic velocity prediction has gained a lot of attention in recent years due to the unsteady nature of foiling sailboats. Different approaches have been applied to predict the motions of foiling or skimming boats in unsteady conditions. Typically, the aerodynamic forces are computed by the quasi-steady theory assumption. Static coefficients are used and the applied velocities are corrected with boat motions. The hydrodynamic forces of a fully foiling boat can be computed in a similar fashion, but this method fails to include the effect of changes in the free surface as well as added mass. This paper proposes an approach where dynamic coefficients of the NACRA 17 hydrofoils are determined based on unsteady Computational Fluid Dynamics (CFD) simulations with a free surface. In the simulations the foil is moved in prescribed motions in one degree of freedom (DOF) at a time and dynamic coefficients are extracted for different frequencies of motion. All coefficients are combined in a coupled system of equations, and the equations can be solved in 6 DOFs in the time domain. A number of test scenarios with time varying conditions are simulated and compared with full dynamic CFD simulations. The initial investigation of the approach shows promising results, but more investigations are needed to validate the approach and to identify possible limitations.

Hyper-singular integral equations are often applied in the frequency-domain wave diffraction/radiation analyses of marine structures with thin plates or shell sub-structures. Their numerical solutions require the higher-order derivatives of the free-surface Green function featuring hyper-singularity, and hence the corresponding evaluation is very challenging. To circumvent the associated numerical difficulties, this paper will propose alternative formulations for the higher-order derivatives of both free-surface and Rankine-source parts of the Green function. For the free-surface term G F , the higher-order derivatives are analytically expressed by a combination of G F itself and its first-order horizontal radial derivative. Further, we derive an asymptotic representation, enabling us to deal exactly with a removable singularity in this representation. The superiority of the proposed formulation is demonstrated by comparing with a conventional direct differentiation. For the Rankine-source term, analytical expressions for the velocities induced by a uniform dipole distribution over a flat panel (involving second derivatives of the Rankine source term) are presented, which is directly relevant to numerical implementation based on constant panel methods. As illustrative examples, linear hydrodynamic coefficients of submerged circular impermeable and perforated plates are calculated for verification purposes. The proposed formulas are simple and easy to implement in the hyper-singular integral equations.

The extraction of road centreline from a remote sensing image is an important part of obtaining and updating basic geographic information data. In view of the shortcomings of traditional road centreline extraction algorithm, such as the presence of burrs, lengthy time consumption and ineffective extraction of the centreline around intersections, we propose an algorithm based on an improved beamlet transform combined with K-means clustering to extract the road centreline of high-resolution remote sensing images. The proposed method includes the following steps. Firstly, K-means clustering is used to identify the road area. Secondly, the improved beamlet transform algorithm is utilised to extract the road centreline. Reducing the beamlet base and simplifying the beamlet dictionary reduces the algorithm complexity. By adding energy threshold and direction constraint, each binary block is guaranteed to contain only one optimal base that avoids the overlapping and missing of the beamlet base. Lastly, a connection algorithm is designed to connect the breaks of some road centrelines. Experimental results show that the proposed algorithm can accurately extract the road centreline, effectively form high-resolution remote sensing images and had good anti-noise ability. Compared with traditional beamlet transform, the proposed beamlet transform achieves better results.

A novel two-dimensional numerical wave tank based on the two-phase Navier–Stokes equations (NSEs) is presented. The popular projection method is applied to decouple the pressure and velocity fields, while the solutions are uniquely enhanced by a newly-developed immersed-boundary generalized harmonic polynomial cell (IB-GHPC) method for the pressure Poisson equation, which lies at the heart of the projection method. The GHPC method, originally proposed for the constant-coefficient Poisson equation, has been employed in solving the single-phase NSEs with success, though it cannot be directly applied for two-phase flows. In this paper, we show that the GHPC method can still be used in solving two-phase flow problems by introducing a pressure-correction method. By considering wave generation and propagation, the accuracy and convergence rate of the present numerical model is demonstrated. The solver is further validated against model tests for wave propagation over a submerged breakwater, and a perforated plate in oscillatory flows and incident waves. Excellent agreement with benchmark results confirms the accuracy and the validity of the new numerical wave tank towards more general wave–structure-interaction problems. The free-surface effect on the wave loads of a perforated plate is further investigated through applications of the present numerical model.

Root system architecture (RSA) is a key factor in the efficiency of nutrient capture and water uptake in plants. Understanding the genetic control of RSA will be useful in minimizing fertilizer and water usage in agricultural cropping systems. Using a hydroponic screen and a gel-based imaging system, we identified a rice (Oryza sativa) gene, VAP-RELATED SUPPRESSOR OF TOO MANY MOUTHS1 (OsVST1), which plays a key role in controlling RSA. This gene encodes a homolog of the VAP-RELATED SUPPRESSORS OF TOO MANY MOUTHS (VST) proteins in Arabidopsis (Arabidopsis thaliana), which promote signaling in stomata by mediating plasma membrane–endoplasmic reticulum contacts. OsVST1 mutants have shorter primary roots, decreased root meristem size, and a more compact RSA. We show that the Arabidopsis VST triple mutants have similar phenotypes, with reduced primary root growth and smaller root meristems. Expression of OsVST1 largely complements the short root length and reduced plant height in the Arabidopsis triple mutant, supporting conservation of function between rice and Arabidopsis VST proteins. In a field trial, mutations in OsVST1 did not adversely affect grain yield, suggesting that modulation of this gene could be used as a way to optimize RSA without an inherent yield penalty.

It is essential for a Navier–Stokes equations solver based on a projection method to be able to solve the resulting Poisson equation accurately and efficiently. In this paper, we present numerical solutions of the 2D Navier–Stokes equations using the fourth-order generalized harmonic polynomial cell (GHPC) method as the Poisson equation solver. Particular focus is on the local and global accuracy of the GHPC method on non-uniform grids. Our study reveals that the GHPC method enables the use of more stretched grids than the original HPC method. Compared with a second-order central finite difference method (FDM), global accuracy analysis also demonstrates the advantage of applying the GHPC method on stretched non-uniform grids. An immersed-boundary method is used to deal with general geometries involving the fluid–structure interaction problems. The Taylor–Green vortex and flow around a smooth circular cylinder and square are studied for the purpose of verification and validation. Good agreement with reference results in the literature confirms the accuracy and efficiency of the new 2D Navier–Stokes equation solver based on the present immersed-boundary GHPC method utilizing non-uniform grids. The present Navier–Stokes equations solver uses second-order central FDM and Quadratic Upstream Interpolation for Convective Kinematics scheme for the discretization of the diffusion term and advection term, respectively, which may be replaced by other higher-order schemes to further improve the accuracy.

Accurate estimation of the actual nominal wake behind the ship in waves is important for propeller designers when improving efficiency and minimizing cavitation. The present CFD study investigates the nominal wake fields of the Kriso Container Ship (KCS) in regular waves with wavelength equal to the ship length in five different headings. The ship is sailing at design speed and the wave steepness is 1/60. The results show that when sailing in the studied waves, the nominal wake fraction fluctuate up to 39% of the mean nominal wake fraction. The mean nominal wake fraction is higher than in calm water for all headings besides head sea waves. The maximum mean nominal wake fraction is found to occur in stern quartering sea waves, with a 16% higher mean nominal wake fraction than in calm water. It is also found that the transient bilge vortex and shadow from the skeg have a significant influence on the nominal wake field. Finally the study shows that the modified advance angle on the r/R=0.7 circle in the propeller plane varies 3.5 degrees more in port stern quartering than in calm water, increasing the risk of cavitation., Applied Ocean Research, 119

The importance of CFD is increasing in marine hydrodynamics in studying seakeeping and added resistance of ships. While extensive numerical studies have been reported for various ships in head seas in the literature, much fewer CFD studies are found for oblique waves, which in practice is very important in, for instance, estimating required power and manoeuvrability of ships in realistic sea states. In this paper, the added resistance and motion responses for the KCS container ship in regular waves are studied and validated systematically for five wave headings and six wavelengths using CFD. The ship is free to heave, pitch, and roll. Implementations to the commercial CFD code are made to fix the yaw and surge motions. Extensive verification of the CFD model finds the estimated spatial and temporal discretization errors to be less than 5%. Results of the verified CFD model are compared with up to three sets of experimental data sets, Potential Flow (PF) and existing CFD results from the literature. In general, the present CFD results show significantly better agreement with the experiments than previously published CFD results. The agreement between the present CFD model and experiments is better for the headings, where the uncertainties of the experiments are smallest. Present CFD results confirm previous published numerical findings that the experimental roll motion is excessive for the 45 heading.

Nonlinear sloshing in an upright circular container near the lowest natural frequency is analyzed by using a fully nonlinear overset-mesh-based harmonic polynomial cell method, two weakly nonlinear Narimanov–Moiseev-type multimodal models and a linear multimodal method. Modal responses are extracted from the fully nonlinear results based on a simple but accurate least-square procedure using the time series of free-surface wave elevations, which provides new ways to delve into the underlying modal responses and energy transfer between modes, as well as to verify the validity of ordering assumptions in the weakly nonlinear models. Wavelet analyses are also performed for the wave elevations and generalized coordinates of the modes to better understand the time-frequency information of the higher harmonics of the sloshing responses and energy transfer in a nonlinear process. Planar harmonic sloshing state, swirling harmonic sloshing state, and periodically modulated sloshing state are analyzed. It is found that the energy is more dispersed among different modes in the periodically modulated sloshing state, which means higher natural modes are consequential. In general, energies are found to transfer from lower to higher natural modes and between symmetric and antisymmetric natural modes. The results also show that the O ( ε 1 / 3 ) and O ( ε 2 / 3 ) responses are dominated by only first and second harmonics, respectively, while the O ( ε ) response contains non-negligible first and third harmonic contribution. At last, the influence of initial disturbance is examined, demonstrating that different initial disturbances may lead to the different rotation direction of the swirling waves and the sloshing-wave responses in the transient stage, while the main characteristics of the sloshing waves are robust and independent of initial conditions.

In this paper, a generalized weak-scatterer (GWS) approximation is proposed for solving nonlinear wave–structure interaction problems. In contrast to the original weak-scatterer (OWS) theory, where the approximated free surface boundary conditions (FSBCs) are Taylor-expanded in the vertical direction from the incident wave surface, we apply Taylor series expansion in an arbitrary direction which, in particular, is tangential to the boundary of the floating structure close to the waterline. This leads to generalized kinematic and dynamic FSBCs for the radiated and scattered waves, along with corresponding expressions of the wave loads. Accordingly, an Arbitrary Lagrangian–Eulerian (ALE) approach is adopted to track the free-surface properties. The new GWS method is more consistent than the OWS model in that the wave markers do not separate from the body surface at the waterline for structures with flare. An Immersed- Boundary Adaptive Harmonic Polynomial Cell (IB-AHPC) method is implemented to solve the corresponding boundary value problems (BVPs) for both the velocity potential and the Lagrangian acceleration potential at each time step. The new formulation introduces additional convective terms in the FSBCs, making them similar to the seakeeping problems for ships with forward speed, and this requires special treatment to avoid instability in the time-domain simulations. Based on a matrix-based eigenvalue stability analysis, we illustrate that stable solutions can be achieved by introducing an upwind-biased scheme to discretize the convective terms in the kinematic FSBC. The proposed model is verified by three wave diffraction problems in regular waves, including a submerged circular cylinder, a rounded-corner rectangular ship section, and a trapezoidal section with a large flare angle.

Floating offshore structures often exhibit low-frequency oscillatory motions in the horizontal plane, with amplitudes in the same order as their characteristic dimensions and larger than the corresponding wave-frequency responses, making the traditional formulations in an inertial coordinate system inconsistent and less applicable. To address this issue, we extend and explore an alternative formulation completely based on a non-inertial body-fixed coordinate system. Unlike the traditional seakeeping models, this formulation consistently allows for large-amplitude horizontal motions. A numerical model based on a higher-order boundary element is applied to solve the resulting boundary-value problems in the time domain. A new set of explicit time-integration methods, which do not necessitate the use of upwind schemes for spatial derivatives, are adopted to deal with the convective-type free-surface conditions. To suppress the weak saw-tooth instabilities on the free surface in time marching, novel low-pass filters based on optimized weighted-least-squares are also developed, which are applicable for both structured and unstructured meshes.For ship seakeeping and added resistance analyses, we show that the present computational model does not need to use soft-springs for surge and sway, in contrast to the traditional models. The present model is considered as a complete 2nd order wave-load model, as all the 2nd order wave loads, including the sum-frequency and difference-frequency components, are solved simultaneously. Some more details on the model can be found in two recent paper by Zheng et al. (2020) and Shao et al. (2022).At the end of the lecture, two examples, including a floating monopile and the OC5 floating offshore wind turbine, both exposed to irregular waves, will be studied using the new solver for demonstration purposes.

Evaluation of wave loads on a ship translating in water waves is of practical importance in ship hydrodynamics, because it is paramount to the design of ship hull structures and provides essential inputs for ship maneuvering analysis. The linear radiation and diffraction of water waves by a translating ship is studied in this paper. A time-domain Rankine panel method is developed in a non-inertial body-fixed coordinate system, which is able to consider large-amplitude horizontal motions consistently. The double-body flow is used as the basic steady flow model. To ensure numerical stability, an implicit Euler scheme is adopted for time marching, and horizontal derivatives on the free surface are calculated using an upwind-biased finite difference scheme. Numerical examples in comparison with experimental measurements are exhibited to demonstrate the validity of the developed solver.

The original weak-scatterer (OWS) hypothesis, pioneered by Pawlowski [1], assumes a vertical displacement of the scattered wave elevation from the underlying incident wave, which leads to an inconsistency when the surface-piercing structure has flares near the waterline. Thus, the predicted waterline position using the superposition of the incident and scattered waves will separate from the surface of the structure, particularly for incident waves with large amplitudes and structures with large flare angles. With this in mind, we have re-derived the free-surface boundary conditions based on a generalized weak-scatterer (GWS) approximation to avoid this inconsistency. The basic idea of GWS is that the fully nonlinear (FN) freesurface conditions are linearized about the incident wave surface, but using a Taylor expansion along an arbitrary direction which can be manually prescribed in practice according to the geometry of the structure. In this way, we can precisely capture the waterline position on the structure at each time step of the solution. Accordingly, expressions for the wave loads acting on the structure based on direct pressure integration are also derived based on the same assumption.

Coupled piston-mode fluid response and the heave motion of two identical barges in side-by-side configuration is studied under finite-depth and shallow-water waves using a two-dimensional fully nonlinear numerical wave tank. To understand possible critical responses of the gap flow and the floating barge, regular-wave conditions which are able to excite up to 5th-order nonlinear gap resonance and also the resonant heave motion of the barge are considered. In shallow-water waves, high-frequency oscillations, featured by secondary peaks in the time histories, are observed for both wave elevation in the gap and the heave motion of the barge. The shallow-water wave-induced 4th- or 5th-order gap resonance can be equally crucial as the 1st- and 2nd-order resonances due to finite-depth waves. At higher-order gap resonance, the higher-harmonic heave motion of the barge is negligibly small, in contrast to the gap-flow response. Compared with fixed barges, the free-heave motion of an upstream barge tends to increase the wave elevation in the gap in most of the resonant conditions, except at 1st-order gap resonance where the gap response is greatly reduced. When the resonant heave motion of a floating barge, either located upstream or downstream, is excited, significant barge motion is observed. However, the relative motion between the gap flow and the floating barge is seen to be very small, ascribed by small phase difference between the two. The present study suggests that the effects of heave motion and water-depth should be carefully considered in the design of side-by-side marine operations, and hiding the small bunkering ships behind the large receiving ships is regarded as a preferred arrangement during the bunkering operations in offshore and coastal environments., Ocean Engineering, 266 (Part 3), ISSN:0029-8018

In the quest for a numerical method for surface waves and wave-induced effects applicable when linear or weakly nonlinear methods are insufficient, a three-dimensional numerical wave tank assuming fully-nonlinear potential-flow theory is proposed. When viscous-flow effects, breaking waves or other violent flow-phenomena are not of primary importance, potential-flow methods may have similar capability in capturing the involved physics as Navier-Stokes solvers while being potentially more accurate in handling wave-propagation mechanism and more computationally efficient. If made sufficiently accurate, efficient and numerically robust, fully-nonlinear potential flow models can therefore represent a powerful tool in the study of ocean waves and their interaction with marine structures, which is the main motivation behind the present work. The governing Laplace equation for the velocity potential is solved using the harmonic polynomial cell method, which is a field method giving high-order accuracy provided that the cells used to describe the water domain have no stretching or distortion. This can only be achieved in a grid with cubic cells, which leads to poor numerical efficiency unless measures are introduced to refine the grid locally. Here, to improve the efficiency using strictly cubic cells, an adaptive grid refinement technique is introduced. It is shown that this has the ability to improve the computational speed with a factor of up to 20 without sacrificing accuracy. Numerical results are shown to be in good agreement with highly accurate nonlinear reference solutions for regular and irregular waves of various steepness up to the limit of theoretical wave breaking. For long-crested irregular waves, significant discrepancies with a second-order theory for the crest-height distribution are identified, while the second-order theory appears to provide a better description of the crest height for the single short-crested irregular sea state simulated. Having demonstrated that the proposed numerical method accurately models nonlinear wave phenomena up to the limit of wave breaking, future work should seek to implement wave-body interaction capabilities. The adaptive grid refinement technique, which refines the grid dynamically depending on the position of boundaries of interest, is developed with this application in mind. Except from providing a robust way of dealing with wave-body intersection points, extending the method to account for wave-body interactions should therefore involve limited difficulty.

Wave focusing is one of the main mechanisms that can generate freak waves in deep water. The strongly nonlinear High-Level Irrotational Green–Naghdi (HLIGN) equations and the Harmonic Polynomial Cell (HPC) method are used here to simulate the focused waves. Numerical simulations are performed in intermediate water depth as well as in deep water. In intermediate water, the HLIGN free surface and wave kinematics are then compared with the well-accepted laboratory data and the results of the HPC method. The effect of water depth on focused waves is also carried out. It is demonstrated that both the HLIGN equations and the HPC method can accurately simulate the surface elevation and particle velocity of focused waves compared with the experiments. The velocity distribution is distinct for the focused waves with the same crest elevations but in different water depths. The HLIGN equations are considered to be an accurate and efficient wave model to investigate focused waves in the intermediate and deep water cases.

The development practice of polymer flooding shows that the injection profile easily inverses during the process of single slug polymer flooding. The low effective or ineffective circulation of abu...

It is essential for a Navier-Stokes equations solver based on a projection method to be able to solve the resulting Poisson equation accurately and efficiently. In this paper, we present a new 2D Navier-Stokes equation solver based on a recently proposed fourth-order method, namely the generalized harmonic polynomial cell (GHPC) method, as the Poisson equation solver. The GHPC method is a generalization of the 2D HPC method originally developed for the Laplace equation. In the recent development of the HPC method, loss of accuracy on highly stretched or distorted grids has been reported when solving the Laplace equation, while the performance of the GHPC method on non-uniform grids is still not explored and discussed in the literature. Therefore, the local accuracy of the GHPC method is investigated in detail in the present study, which reveals that the GHPC method allows for the use of much larger grid aspect ratio than that for the original HPC method. Global accuracy of the GHPC method on stretched non-uniform girds is also thoroughly analyzed by considering cases with analytical solutions. Obvious advantages of using the GHPC method in terms of accuracy are demonstrated by comparing with a second-order central Finite Difference Method (FDM). The present Navier-Stokes equations solver uses second-order FDMs for the discretization of the diffusion and advection terms, which may be replaced by other higher-order schemes to further improve the accuracy. Meanwhile, an immersed boundary method [1] is used to study the fluid-structure-interaction problems. The Taylor-Green vortex and flow around a smooth circular cylinder are studied to confirm the accuracy and efficiency of the new 2D Navier-Stokes equation solver. The predictions show good agreements with the experimental and numerical results in the literature.

Crown root (CR) is the main component of the fibrous root system in cereal crops, but the molecular mechanism underlying CR development is still unclear. Here, we isolated the crown root defect 1 (crd1) mutant from ethyl methane sulfonate-mutated mutant library, which significantly inhibited CR development. The CRD1 was identified through genome resequencing and complementation analysis, which encodes an Xpo1 domain protein: the rice ortholog of Arabidopsis HASTY (HST) and human exportin-5 (XPO5). CRD1 is ubiquitously expressed, with the highest expression levels in the CR primordium at the stem base. CRD1 is a nucleocytoplasmic protein. The crd1 mutant contains significantly reduced miRNA levels in the cytoplasm and nucleus, suggesting that CRD1 is essential for maintaining normal miRNA levels in plant cells. The altered CR phenotype of crd1 was simulated by target mimicry of miR156, suggesting that this defect is due to the disruption of miR156 regulatory pathways. Our analysis of CRD1, the HST ortholog identified in monocots, expands our understanding of the molecular mechanisms underlying miRNA level and CR development.

A numerical wave tank based on the Harmonic Polynomial Cell (HPC) method is created to study the generation, propagation and interaction of solitary waves. The HPC method has been proven to be of high accuracy and efficiency in modeling of water waves, wave–wave and wave–structure interaction within the context of potential flow. An important feature of the present HPC method is that the free surface and solid boundaries are immersed in a stationary Cartesian grid. Solitary waves with σ , i.e. amplitude to water depth ratio, up to 0.6 are generated by different methods. We demonstrate that the results based on the first-, third- and ninth-order method are less satisfactory than the fully-nonlinear method in generating solitary waves with σ > 0 . 4 . Additionally, both the head-on and overtaking collision between two solitary waves are studied. In the investigation of the phase shifts after the head-on collision, our window model successfully explain the main reason why Su and Mirie (1980)’s third-order approximation of the uniform phase shifts is inconsistent with Chen and Yeh (2014)’s experimental results and Craig et al. (2006)’s fully nonlinear numerical results. For the overtaking collision of solitary waves, the collision process and the phase shifts are numerically analyzed. Our present result also confirms Craig et al. (2006)’s category of the overtaking collision.

Nonlinear piston-mode fluid resonance in the gap formed by two identical fixed barges in close proximity is investigated using a two-dimensional (2D) fully nonlinear numerical wave tank. To delve into the effect of water depth on higher-order resonances in the gap, consistent models are employed to describe the incident waves and wave-structure interactions for finite and shallow water depths. In contrast to previous studies, strong fourth- and fifth-order nonlinear gap resonances are observed under the action of shallow-water waves, resulting in significant higher-harmonic responses that are comparable to the corresponding first and second harmonics. For a given wave height, those waves are found to be more critical than the finite-depth waves, which are capable of evoking second- or third-order gap resonance. Highly oscillatory behavior is observed at the trough under the action of shallow-water waves. This is ascribed to the higher-harmonic diffraction effects, breaking the “perfect cancellation” between the incident-wave harmonics, which should, otherwise, produce smooth and flatter wave trough. Unlike what a linear diffraction theory will predict, the gap response does not behave completely in a quasi-static manner under long cnoidal waves, and the higher harmonics generally show larger phase differences to the corresponding incident-wave components until the resonance occurs. The present study suggests that the water-depth effect and higher harmonics should be consistently accounted for in the design and analysis of side-by-side marine operations in coastal environments involving piston-mode gap responses.

RNA modifications constitute an essential layer of gene regulation in living organisms. As the most prevalent internal modification on eukaryotic mRNAs, N

Among various types of floating offshore wind turbines (FOWTs), the tension leg platform (TLP) floating wind turbines have relatively small motions due to stiff tendons. Similar to TLP applications in the offshore industry, tendon failure may lead to deteriorated stability and large transient responses, which should be considered as part of accidental limit state (ALS) checks at the design stage of the TLP FOWTs. This paper takes the WindStar TLP system as a representative and investigates the transient effects of one-tendon failure on the system responses. A coupled numerical model is first established using the aero-hydro-servo-elastic simulation tool FAST. Subsequent numerical simulations of tendon failure are carried out to consider different tendon breakage and turbine shutdown scenarios in both operational and parked conditions. Response statistics of key design parameters including platform motion, nacelle acceleration, and tendon tension are analyzed. The results indicate that several transient responses of the FOWT under operational conditions may be even higher than the extreme values under 50-year conditions. Our analyses also reveal that the shutdown strategies, if not applied appropriately, may have limited effects in reducing the responses of the FOWT, thus in certain scenarios threaten the safety of the tendon closest to the broken tendon if no other actions are taken. For the considered TLP FOWT, the ALS design requirements dominate over the ultimate limit state requirements. These findings can be relevant to the ALS design of TLP FOWTs.

In the field of offshore renewable energy, impermeable plates are used as underwater lenses to amplify the wave amplitude, and perforated plates can harness wave energy as a power takeoff device. Within the framework of the linear potential-flow theory, the water wave scattering by impermeable and perforated horizontal plates is investigated in the present study, and both circular and elliptical plates are considered. The hypersingular integral equation is constructed to model the interaction between water waves and plates of small thickness. For wave scattering by impermeable plates with the focus on wave amplification, wave interference effects due to multiple plates can be utilized to achieve large wave amplification. For perforated plates used for harnessing wave energy, deploying an array of elliptical plates is promising if the deployment line coincides with the major axis and the incident wave propagates along the minor axis. The study gives insight into harnessing energy from water waves by horizontal plates.

The interaction between the first-order cnoidal wave and a concentric structure with dual-arc porous breakwaters is studied semi-analytically based on eigenfunction expansion. Both arcs of the breakwater are considered as thin shell structures and rigidly mounted on a flat sea bottom. The fluid domain is divided into an unbounded and two bounded sub-domains, within which the solutions are described by eigenfunctions. Matched conditions along the boundaries between different regions are applied, leading to a semi-analytical solution of the considered problem. The method is applied to study a special case of cnoidal wave diffraction with a solid cylinder and the results of wave loads and wave runups agree excellently with reference results in the literature. For a double-layer arc-shaped vertical porous breakwater standing in shallow-water waves where cnoidal wave theory is applicable, our results show that the approach using linear Airy waves may significantly underestimate the wave loads on the breakwater. It is also shown that the dual-arc breakwater has a better protective performance than a single-arc breakwater. Parametric studies on porosity, annular spacing, opening angle, water depth and incident wave angle are also presented.

We present a 2D high-order and easily accessible immersed-boundary adaptive harmonic polynomial cell (IB-AHPC) method to solve fully nonlinear wave-structure interaction problems in marine hydrodynamics using potential-flow theory. To reduce the total number of cells without losing accuracy, adaptive quad-tree cell refinements are employed close to the free-surface and structure boundaries. The present method is simpler to implement than the existing IB-HPC alternatives, in that it uses standard square cells both in the fluid domain and at the boundaries, thus without having to use the more complex and expensive overlapping grids or irregular cells. The spurious force oscillations on moving structures, which is a known issue for immersed boundary methods (IBMs), are eliminated in this study by solving a separate boundary value problem (BVP) for a Lagrangian acceleration potential. We also demonstrate that solving a similar BVP for the corresponding Eulerian acceleration potential is far less satisfactory due to the involved second derivatives of the velocity potential in the body-boundary condition, which are very difficult to calculate accurately in an IBM-based approach. In addition, we present, perhaps for the first time since the HPC method was developed, a linear matrix-based stability analysis for the time-domain IB-AHPC method. The stability analysis is also used in this study as a general guide to design robust and stable numerical algorithms, in particular related to the treatment of boundary conditions close to the intersection between a Dirichlet and a Neumann boundary, which is essential in time-domain wave-structure interaction analyses using IBMs. We confirm theoretically through the stability analysis that square cells have the best stability properties. The present method has been verified and validated satisfactorily by various cases in marine hydrodynamics, including a moving structure in an infinite fluid, fully nonlinear wave generation and propagation, and fully nonlinear diffraction and radiation of a ship cross section.

As the worldwide oil and gas market continues to grow and environmental concerns with respect to in-port offloading of gas have increased, there has been a boom of interest in new liquefied natural gas LNG terminals in the past years. Loading - offloading operations at LNG and bulk terminals are generally protected by a breakwater to ensure high operability. For these terminals, caisson breakwaters are generally a preferred solution in water depth larger than 15 m due to its advantages compared to rubble mound breakwaters. The caisson installation is generally planned to be carried out in the period where sea conditions are relatively calm. However, many of these terminal locations are exposed to swell conditions, making the installation particularly challenging and subject to large downtime. There is no clear guidance on the caisson installation process rather than contractors’ experiences from different projects/sites. Therefore, studies are required in order to provide general guidance on the range of acceptable wave conditions for the installation operations and to have a better understanding of the influence of the caisson geometry. This paper presents a numerical study to determine the limiting wave conditions for caisson installing operations at larger water depth of 30–35 m for a confidential project along the African coast. Three caisson sizes/geometries are considered in order to assess and compare the wave-structure hydrodynamic interaction. The linear frequency-domain hydrodynamic analysis is performed for various seastates to determine the limiting wave conditions. Viscous effects due to flow separation at the sharp edges of the caisson are considered by using a stochastic linearization approach, where empirical drag coefficients are used as inputs. Parametric studies on caisson size and mooring stiffness are also presented, which can be used as a basis for future optimization. The uncertainty in the applied empirical viscous drag coefficients taken from the literature is examined by using a range of different drag coefficients. Further, the use of clearance-independent hydrodynamic coefficients (e.g. added mass and damping) may be questionable when the caisson is very close to the seabed, due to a possible strong interaction between caisson bottom and seabed. This effect is also checked quantitatively by a simplified approach. The findings of the study are presented in the form of curves and generalized to be used by designers and contractors for general guidance in future projects.