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We consider the scenario of an unsteady viscous flow between two coaxial finite disks, one stationary and the other rotating with an axial velocity changing impulsively from zero to a constant value. The three-dimensional (3D) incompressible Navier–Stokes equations are analytically solved by postulating the polynomial profiles for the axial and circumferential velocity components and by employing the open-end condition of zero pressure difference and an integral approach. It is shown that the time-dependent squeezing of the fluid between the disks and the edge effects of the finite open-ended disks in the flow domain are determined by the compressing Reynolds number and the rotating Reynolds number for the case of laminar flow at low Reynolds numbers and small aspect ratios. The general explicit formulae are derived for the velocity and pressure distributions as a function of the compressing and rotating Reynolds numbers in this unsteady flow process (and the steady-state solutions are then obtainable as the compressing Reynolds number vanishes). A simple theoretical relationship between the radial and axial pressure gradients is deduced to hinge the radial and circumferential velocity components together. The values of the compression and rotation Reynolds numbers suitable to this theory are also suggested for the problem of rotating disk flows at low Reynolds numbers. The validity of the theoretical predictions for the circumferential, radial, and axial velocity components is partially verified through comparison with previous steady experimental and numerical results. These analytical results have the immediate engineering applications of fluid flows with varying gap widths, including wet brakes, wet clutches, hydrostatic bearings, face seals, and rotating heat exchangers.

A numerical model based on the double-averaged (spatial and ensemble averaged) method has been developed to simulate vegetated free surface flows. The classical $$k - \varepsilon$$ model is modified by including additional turbulence generation and dissipation terms. These new terms consider the large-scale turbulence generated by shear flows near the flow-vegetation interface and the small-scale wake turbulence generated by the flow separation behind vegetation stems. A new damping function is introduced in the turbulence closure model to suppress the wake turbulence inside the vegetation domain if the shear-generated turbulence is dominant. A series of dense emergent and submerged vegetated flows experiments have been conducted and the velocities have been measured by ADV (Acoustic Doppler Velocimetry) and PIV (Particle Image Velocimetry) at different locations. The experimental results show that the turbulence characteristics near each stem in a group of cylinders are similar to that of a single cylinder, even when the vegetation is dense. The measured data are then used to calibrate the new turbulence closure model. The numerical model is further validated against other published laboratory data of both dense and sparse emergent, submerged and floating vegetated flows. The comparisons show that the new model provides consistently better predictions for mean velocity and turbulence kinetic energy than those by using the existing models.

In this study, based on 55 years’ worth of high-resolution simulated wave data using numerical modeling off the southern coasts of China, intra-annual and decadal variations of the wave climate and wave energy were evaluated. The results show that it is important to consider a sufficiently long time period for wave energy assessment to take into account the changing climate. The high-resolution wave dataset enabled the quantitative analysis in both nearshore and offshore, and the quantitative analysis was performed in two phases: First, using two different approaches. i.e., “Climate-dependent Sustainability Index” and “Wave Exploitability Index”, the wave power and its short and long-term changes were considered to prioritize the candidate stations for further assessment. Then, a modified “Multi-Criteria Approach” consisting of both sea state and Wave Energy Converters (WECs) was applied to determine the most suitable combination of WEC and location in the domain, which is Wave Dragon in the eastern parts of the domain with the energy production of around 92, 000 MWh for a single device. The results provide the quantitative analysis for different scenarios of development plans in the study area on the selection of appropriate location and technology.

For a fluid system with an interface between two-layer liquids and a free surface, there exist two series of natural frequencies. Under vertical excitations, the interface and the free surface can be excited separately or simultaneously. Laboratory experiments were conducted to excite the first- and second-mode Faraday waves on the free surface, which forced the in-phase motion of the interface. The experimental data were used to validate the extended numerical model NEWTANK. The secondary surface instability in the form of period tripling breaking occurred on the free surface when second-mode surface resonant response was large. Further numerical investigations were conducted to study the resonance of interface and in addition to the primary Faraday instability, the secondary interface instability occurred due to Rayleigh–Taylor (RT) instability. The analysis revealed that this was due to the contribution from the combined effects of vertical fluid acceleration and external excitation, which made the upper layer liquid essentially ‘heavier’ than the lower layer at certain instances, even when the amplitude of acceleration of the external excitation was lower than that of gravity at all times. A dimensionless parameter ‘normalised effective gravitational acceleration’ (NEGA) was proposed to quantify the occurrence criterion of RT instability in a dynamic fluid system. Furthermore, simultaneous resonances at both the interface and the free surface were studied and reverse flows could be formed across the interface as the upper Faraday waves and lower Faraday waves moved in opposite directions, which generated the secondary interface instability of Kelvin–Helmholtz (KH) type. When KH instability took place, more energy was transferred to higher frequency modes as time evolved.

This paper presents ISOPE’s 2020 comparative study on the interaction between focused waves and a fixed cylinder. The paper discusses the qualitative and quantitative comparisons between 20 different numerical solvers from various universities across the world for a fixed cylinder. The moving cylinder cases are reported in a companion paper as part B (Agarwal, Saincher, et al., 2021). The numerical solvers presented in this paper are the recent state of the art in the field, mostly developed in-house by various academic institutes. The majority of the participants used hybrid modeling (i.e., a combination of potential flow and Navier–Stokes solvers). The qualitative comparisons based on the wave probe and pressure probe time histories and spectral components between laminar, turbulent, and potential flow solvers are presented in this paper. Furthermore, the quantitative error analyses based on the overall relative error in peak and phase shifts in the wave probe and pressure probe of all the 20 different solvers are reported. The quantitative errors with respect to different spectral component energy levels (i.e., in primary, sub-, and superharmonic regions) capturing capability are reported. Thus, the paper discusses the maximum, minimum, and median relative errors present in recent solvers as regards application to industrial problems rather than attempting to find the best solver. Furthermore, recommendations are drawn based on the analysis.

This study examines the mass and Lagrangian transport, kinematic and dynamic characteristics of shallow-water breaking waves, focusing on the wave breaking, and jet impingement processes. A multiphase Navier–Stokes flow model has been developed to track the origin and trajectory for the jet and the splash-up using both a geometric piece-wise linear interface calculation volume-of-fluid (PLIC-VOF) and the Lagrangian particle tracking approaches. The model is first validated both quantitatively and qualitatively against the experimental data for the plunging jet and the splash-up during wave breaking, in which a good agreement is obtained. The mass transport and the origin of the jet and splash-up are studied using the new multi-component PLIC-VOF approach, and the different regions in the interior of the wave are tracked in an Eulerian way. Both horizontal and vertical drifts for the interior and surface particles are shown using the Lagrangian particles. The location and origin of the plunging jet can be clearly seen from the simulations. Various wave steepness and beach slopes have been investigated for different types of breakers. Furthermore, the detailed jet impingement, velocity, pressure, vorticity, and turbulence fields during wave breaking are discussed and presented, providing more detailed flow fields to gain further insight into the plunging jet and splash-up in shallow-water breaking waves.

Salt marshes are coastal wetlands that provide many ecosystem services. They protect coasts from erosion, storm surge, and small tsunami by dissipating wave energy. Plant flexibility has been reported to reduce drag force on and wave attenuation of marsh plants. In this study, we proposed a new drag coefficient formula to account plant flexibility so that the classical theory based on rigid cylinders can be extended to predict wave decay by flexible plants. To validate this new formula, the field survey was conducted in the North Hangzhou Bay, China. The wave attenuation was measured in a Spartina alterniflora marsh under a combined macro-tidal and storm surge condition, during which strong bending motions of the plants were observed. The new formula provided better predictions of wave decay than that by the traditional drag formula when compared to the field data measured in both the present study and the earlier studies.

The swirling motion of the interface of two-layer liquids in a tank with a square base is investigated experimentally in this study. The tank was fixed on a platform and the horizontal circular-orbital excitations were applied. Both resonant and off-resonant responses were studied and the profiles of the interface between two liquids along two adjacent vertical walls of the tank were recorded and processed by using the image processing method. When the frequency of the excitation was equal to the lowest natural frequency of the interface between two liquids, the resonant response of the interface was triggered as swirling waves with strong nonlinearity. Instead of being a circular shape, the parametric curve was more of a triangular shape. The modal analysis revealed that this is caused by the additional contributions from the nonlinear modes of sloshing waves with multiple times of the natural frequency. For off-resonant cases, the nonlinear contribution is weaker and the parametric curve is, thus, close to a circular shape.

In order to investigate the relationship between water surface velocity and breach hydrograph, a series of dam breach experiments with a generalised landslide dam were conducted in an open channel of 50 m × 4 m × 2 m. The large‐scale particle image velocimetry (LSPIV) technique was applied to measure the time history of water surface velocity during the dam breach process, and the hydrography was obtained by integrating the surface velocity along the water depth. The influence of different vertical velocity profile approximation and suspended sediment concentration on the peak breach discharge were analysed and discussed. The results showed that the water depth over the breach crest can be described as a function of water surface velocity using d¯t=k22u¯surf2/k1g. A simple formula based on surface velocity and breach width for the estimation of breach discharge was further proposed and verified.