Wave Flow Research Articles

Roll waves on laminar sheet flow of Newtonian fluid with negligible surface tension

We conduct direct numerical simulations (DNS) to study the temporal and spatial developments of the roll waves on a laminar sheet flow of Newtonian fluid. The DNS unveil the physics of the wavefront and show the limitation of the widely used shallow-layer approximations. The most prominent wave, the front runner, is determined by the DNS for the first time in studying the spatial development of the laminar sheet flow with negligible surface tension. Depending on the Froude and Reynolds numbers, the front runner can be a multi-peaked undular bore or a single-peaked non-breaking or breaking wave. The simulation has uncovered an extended region behind the wavefront, where the bed-friction stress is much higher than the corresponding friction in the undisturbed uniform flow. It also produces an uplift velocity needed in the description of wave breaking. For comparison, we also examine the nonlinear development of the instability using two-equation and four-equation shallow-layer models. The two-equation shallow-layer model has produced the bulk of the wave profile but is deficient because it fails to predict the uplift velocity and the substantial increase in bed friction in the frontal region. The four-equation shallow-layer model correctly predicts the bed friction but cannot produce the breaking wave. The simulations also determine the celerity and amplitude of the front runner to follow a linear relationship, qualitatively similar to the roll waves in a turbulent flow.

Internal gravity waves in flow past a bluff body under different levels of stratification

The flow field of a bluff body, a circular disk, that moves horizontally in a stratified environment is studied using large-eddy simulations. Five levels of stratification (body Froude numbers of ${{Fr}} = 0.5, 1, 1.5, 2$ and $5$ ) are simulated at Reynolds number of ${{Re}} = 5000$ and Prandtl number of $Pr =1$ . A higher ${{Re}} = 50\,000$ database at ${{Fr}} = 2, 10$ and $Pr =1$ is also examined for comparison. The wavelengths and amplitudes of steady lee waves are compared with a linear-theory analysis. Excellent agreement is found over the entire range of ${{Fr}}$ if an ‘equivalent body’ that includes the separation region is employed for the linear theory. For asymptotically large distances, the velocity amplitude varies theoretically as ${{Fr}}^{-1}$ but a correction owing to the dependence of the separation zone on ${{Fr}}$ is needed. The wake waves propagate in a narrow band of angles with the vertical, and have a wavelength that increases with increasing ${{Fr}}$ . The envelope of wake waves, demarcated using buoyancy variance, exhibits self-similar behaviour. The higher ${{Re}}$ results are consistent with the buoyancy effects exhibited at the lower ${{Re}}$ . The wake wave energy is larger at ${{Re}} = 50\,000$ . Nevertheless, independent of ${{Fr}}$ and ${{Re}}$ , the ratio of the wake wave potential energy to the wake turbulent energy increases to approximately 0.6–0.7 in the non-equilibrium stage showing their energetic importance besides suggesting universality in this statistic. There is a crossover of energetic dominance of lee waves at ${{Fr}} <2$ to wake-wave dominance at ${{Fr}} \approx 5$ .

Optimized Casing Treatment to Improve Stall Margin Under Circumferential Pressure Distortion in a High-Speed Axial Flow Fan

Abstract An optimized axial slot casing treatment (OPCT) was designed that experimentally improves the stall margin by 7.31% with an efficiency gain of 1.94% at a design speed of 100% in a high-speed axial flow fan. Subsequently, the OPCT was tested under the distorted inflow with a 9% composite distortion index; it can still improve the stall margin by 6.19% with an efficiency gain of 1.63% at the 100% design speed. The unsteady measurement results indicate that the location of the shock wave obviously moves forward toward the leading edge of the blade tip as the rotor blade rotates out of the distorted region and induces the stall in advance. When the OPCT is applied, the strength of the interaction between the shock wave and tip leakage flow can be suppressed, and the location of the shock wave at the distorted region is pushed backward. Thus, the trigger of the stall inception generated in the downstream of the distortion region is postponed. Meanwhile, a new phenomenon was discovered that the OPCT does not alter the instability mode of the fan, and the fan eventually surges, which is consistent with the B parameter value of 2.942. However, under the distorted inflow, the B parameter can be reduced from 2.942 to 0.863, thereby the instability mode of the fan is changed from surge to stall. It can guide the instability prediction when the boundary condition (distortion or casing treatment) of the fan is changed.

Numerical investigation of spindle position effects on steam ejector performance with a nonequilibrium condensation model

AbstractThis research studied the performance of a spindle‐controlled steam ejector using models such as ideal gas and wet steam under various operating conditions based on computational fluid dynamics (CFD). A wet steam model incorporating nonequilibrium condensation was employed to simulate the complex flow phenomena within the ejector. The structure of the flow, entrainment ratio (Er), and shock wave characteristics of the steam ejector were examined in two different models. Results indicate that the spindle position has a substantial impact on steam ejector performance. For the ideal gas and wet steam models, the optimal spindle position (SP‐5) at a .1 MPa motive pressure achieves the highest entrainment ratios (Er) of 1.01 and 1.042, respectively. However, an ejector with a fixed geometry achieves Er values of only .517 and .549 for the ideal gas and wet steam models, under identical working conditions. This represents a substantial improvement of 89.8% over the fixed‐geometry ejector. The wet steam model consistently predicts 2%–4% higher Er values compared with the ideal gas model across all spindle positions. The study also reveals that increasing the motive pressure from .1 to .3 MPa reduces Er by up to 45.8% at the optimal spindle position, with the shock train length extending to 35% of the mixing chamber at .3 MPa. These findings offer insights for improving the design and optimization of variable‐geometry steam ejectors, potentially increasing efficiency in industrial applications.

Ship Forebody Optimization Based on Rankine Source Method

Abstract The shape of the ship’s forebody has a greater impact on the ship’s resistance, and a reasonable optimization of the forebody can play a role in reducing the propulsion power and optimizing the resistance performance. Under the premise of Rankine source method of potential flow wave theory as the theoretical basis, SHIPFLOW software is used as the calculation tool, and CAESES software is used as the optimization tool to study the optimal design of the ship with minimum wave resistance. In the optimization process, a real ship is taken as the object, and the optimal solution of the rising wave resistance coefficient is calculated with the rising wave resistance coefficient as the objective function and the ship speed and displacement as the constraints. The real ship is selected as the mother ship, the parameters of the hull shape are taken as the design variables, and the shape of the forebody is optimized by the Lackenby shift method, so as to obtain a ship shape with less wave resistance at the same speed and within the displacement limit. The results show that the improved ship shape has obvious effect of reducing the wave resistance, which verifies the effectiveness and feasibility of this method for ship shape optimization

Characterisation of turbulence at sites with coexisting waves and currents: An analysis by empirical mode decomposition

This paper presents a novel side information assisted Empirical Mode Decomposition (EMD) method for separating wave orbital velocity from a combined wave-tidal current velocity data, measured by three different Acoustic Doppler Current Profilers (ADCPs) deployed in the Pentland Firth, Orkney Waters, UK. The effectiveness of this technique is confirmed through two methods: (1) the spectra of the wave-removed velocity align with the Kolmogorov −5/3 power law, and (2) the extracted wave orbital velocities were used to derive significant wave heights, which were validated against wave heights measured by the same ADCPs and through numerical modelling carried out with a coupled wave-current tool (TOMAWAC-TELEMAC 3D).The decomposed data was further used to calculate three-dimensional turbulence intensities (TI) for combined wave-current, wave-only, and current-only conditions, across different flow speeds and wave heights. The results demonstrate the robustness of the decomposition method in various scenarios and quantify the individual TI contributions from waves, currents, and their combined effects. This work provides valuable insights into the dynamics of areas where waves and currents coexist.

Novel CMR-assessed right ventricular-pulmonary artery coupling index independently associates with exercise capacity and clinical risk in pulmonary arterial hypertension

Abstract Background We defined a novel noninvasive right ventricle (RV)–pulmonary artery (PA) coupling index as the ratio of cardiovascular magnetic resonance (CMR)-assessed RV direct flow (RVDF) and PA pulse wave velocity (PWV), and investigated its associations with exercise capacity and clinical risk in pulmonary arterial hypertension (PAH). Method 43 PAH patients (mean age 46±12 years, M:F 7:36) and 60 healthy volunteers (mean age 46±13 years, M:F 11:48) underwent CMR and cardiopulmonary exercise test (CPET) within one week. From cine CMR, RV ejection fraction (EF) and RV end-diastolic volume (RVEDV) were calculated using volumetric analysis; and tricuspid annular plane systolic excursion (TAPSE), feature tracking. PAPWV was the ratio of early systolic DPA flow and DPA area measured from instantaneous phase and magnitude through plane 2D flow CMR images across the pulmonary trunk, respectively. RVDF was the 4D flow CMR-assessed blood volume entering and exiting the RV in one cardiac cycle, indexed to RVEDV. RV-PA coupling was RVDF/PAPWV. Based on CPET-assessed peak oxygen consumption (PVO2), all 103 participants were stratified into two groups: PVO2>15 ml/kg/min; and PVO2≤15 ml/kg/min. Based on the REVEAL (Registry to Evaluate Early and Long-term PAH Disease Management) 2.0 score, the 43 PAH patients were stratified into low risk (score ≤6) and intermediate to high risk (score >6) groups. Results RVDF/PAPWV was significantly lower in PAH vs. controls (7.9 vs. 20.4 %/(m/s), P<0.001); and in PAH patients with intermediate to high risk vs. low risk (4.6 vs. 9.4 %/(m/s), P=0.001). On multivariable analyses, RVDF/PAPWV was an independent predictor of PVO2≤15 ml/kg/min (=0.302, P=0.001) among all participants, and of REVEAL 2.0 score >6 (=0.621, P=0.009) among PAH patients. Compared to RVEF and TAPSE, RVDF/PAPWV had numerically higher discrimination (p values non-significant based on Delong test) for PVO2≤15 ml/kg/min (AUC=0.914 vs. 0.872, 0.843); and among PAH patients, REVEAL 2.0 score >6 (AUC=0.851 vs. 0.723 and 0.728) (Figure). Conclusion CMR-derived noninvasive RVDF/PAPWV independently associates with exercise capacity and PAH clinical risk, supporting its utility as an imaging marker of disease progression and therapeutic response.

Wave–Tide–Surge Interaction Modulates Storm Waves in the Bohai Sea

Typhoons, extratropical cyclones, and cold fronts cause strong winds leading to storm surges and waves in the Bohai Sea. A wave–flow coupled numerical model is established for storm events observed in 2022 caused by three weather systems, to investigate how storm waves are modulated by wave–tide–surge interaction (WTSI). Wave response is basically controlled by water level change in coastal areas, where bottom friction or breaking dominates the energy dissipation, and determined by the current field in deep water by altering whitecapping. Wave height increases/decreases are induced by positive/negative water level or obtuse/acute wave–current interaction angle, leading to six types of field patterns for significant wave height (Hs) responses. For the three storm events, Hs basically changed within ±5% in central deep water, while the maximum increase/decrease reached 160%/−60% in the coastal area of Laizhou Bay/Liaodong Bay. Based on maximum Hs and its occurrence time, WTSI modulation is manifested as the superposition effect of wave–tide and wave–surge interactions in both space and time scales, and occurrence time depends more on tide than surge for all three storms. The enhancement/abatement of WTSI modulation happens for consistent/opposite changing trends of wave–tide and wave–surge interaction, with the ultimate result showing the side with a higher effect.

Numerical Analysis and Experimental Validation of Trimaran and Pentamaran Resistance at Various Separation Distances

Trimaran and pentamaran are multihull types with an odd number of hulls, namely three and five hulls, generally consisting of one center hull and two or four side hulls smaller than the center hull, which can reduce ship resistance. The trimaran and pentamaran have a more complex phenomenon than the monohull, because of the interaction between the main hull and the side hull, which causes interference caused by changes in flow velocity, pressure changes, and wave interactions generated by each hull. The objective of this study is to analyze the resistance of trimaran and pentamaran NPL-4b models with transom-symmetrical hull and separation distances, specifically S/L ratios of 0.2, 0.3, and 0.4. Since a more limited base of experience exists for multihull ships, experimental or numerical modeling techniques are essential for designers. Numeric investigations were conducted using Numeca software, and experiments were performed in a towing tank. Both methods follow ITTC procedures. Furthermore, the numerical analysis with CFD simulation modifies the Navier-Stokes equation using the turbulence model k-ꞷ SST to generate the RANS equation so that unsteady fluid flow problems can be calculated. It can be implemented in predicting resistance in Froude numbers (Fr) 0.2 to 0.6 at the systematic series of trimaran and pentamaran hull shapes at the model scale. The simulation results were compared to experimental data to validate the resistance of the ships. Overall, good resistance was produced by the trimaran and pentamaran in the C configuration at an S/L ratio of 0.4 with a total resistance coefficient CT of 6.60 x 10-3 and 7.37 x 10-3, respectively. The two results are in good agreement, both methods have a discrepancy of 3.70 %. Fluctuations influence the resistance in the wetted surface area (WSA), wave interactions between hulls, ship velocity, and wave propagation in the aft hull.

Numerical investigation of dual‐source gas explosion dynamics in h‐type tunnels under varied enclosed situations

AbstractTo further investigate the propagation characteristics of shock waves and flame waves in H‐type tunnel gas explosions, numerical simulation studies were conducted on a dual‐source gas explosion model using Fluent software. Three distinct operational conditions were designed and modeled, leading to the following outcomes. The shock wave flow field parameters from dual sources (with equal source energy) are symmetrically distributed in the H‐type tunnel, with high pressure and low flow velocity in the connecting roadway between the two shock waves. Under different conditions, the pressure is generally higher in closed tunnels (fully closed greater than semi‐closed) and lower in open tunnels. The largest overpressure in non‐explosion areas occurs at the closed ends and in the connecting roadway, while the areas bearing the greatest impulse are the shock wave reflection zones and pressure coupling regions. In closed conditions, the flame wave first moves forward and then propagates backward after the explosion, influenced by reflected waves and pressure differences between the ends and the tunnel. In open conditions, the pressure in the flame zone is lower than at both ends, inhibiting the forward propagation of the flame wave.

Rainfall Enhancement Downwind of Hills Due to Stationary Waves on the Melting Level and the Extreme Rainfall of December 2015 in the Lake District of Northwest England

This paper investigates how stationary gravity waves generated by flow over orography enhance rainfall, with particular attention to the role of induced waves in the melting level. The findings reveal a new mechanism by which gravity wave flow focuses precipitation, amplifying rainfall intensity downwind of hills. This mechanism, which depends on the differential velocities of rain and snow, offers fresh insights into how orographic effects can intensify rainfall. A two-dimensional diagnostic model based on linear gravity wave theory is used to investigate the record-breaking rainfall of December 2015 in the Lake District of northwest England. The pattern of ascent is shown to have a qualitatively good fit to that of the Met Office’s operational high-resolution UKV model averaged over 24 h, suggesting that orographically excited stationary waves were the principal cause of the rain. Precipitation trajectories imply that a persistent downstream elevated wave caused by the Isle of Man supported a spray of seeding ice particles directed towards the Lake District, and that these grew whilst suspended in strong upslope flow before being focused by the undulating melting-level into intense shafts of rain.

Numerical simulation on the influence of artificial island on reef hydrodynamics

The construction of artificial island can greatly change the reef hydrodynamics, leading to increased water level and wave height as well as changes in flow field distribution. These alterations can affect sediment transport on the reef, and increase the risk of overtopping and structure instability. A numerical model based on the Reynolds Averaged Navier-Stokes (RANS) equations and k-ε turbulence closure model was developed to investigate the influence of artificial island on reef hydrodynamics. The numerical model was validated against the experimental results of wave height, mean water level, and wave breaking morphology. Detailed flow field, wave height, and wave set-up in front of artificial island were further analyzed based on the validated model. After building the reef-top structure, the wave breaking and offshore currents at reef edge were amplified. The flow stratification and increase of the wave set-up were also found on the reef flat. Furthermore, we found the relationship between maximum flow velocities on the reef flat and incoming wave conditions could be characterized by two non-dimensional parameters: |u¯|max/g(η¯+hr), (η¯+hr)/Hi.

Numerical Study of Shock Wave Interaction with V-Shaped Heavy/Light Interface

This paper investigates numerically the shock wave interaction with a V-shaped heavy/light interface. For numerical simulations, we choose six distinct vertex angles (θ=40∘,60∘,90∘,120∘,150∘, and 170∘), five distinct shock wave strengths (Ms=1.12,1.22,1.30,1.60, and 2.0), and three different Atwood numbers (At=−0.32,−0.77, and −0.87). A two-dimensional space of compressible two-component Euler equations are solved using a third-order modal discontinuous Galerkin approach for the simulations. The present findings demonstrate that the vertex angle has a crucial influence on the shock wave interaction with the V-shaped heavy/light interface. The vertex angle significantly affects the flow field, interface deformation, wave patterns, spike generation, and vorticity production. As the vertex angle decreases, the vorticity production becomes more dominant. A thorough analysis of the vertex angle effect identifies the factors that propel the creation of vorticity during the interaction phase. Notably, smaller vertex angles lead to stronger vorticity generation due to a steeper density gradient, while larger angles result in weaker, more dispersed vorticity and a less complex interaction. Moreover, kinetic energy and enstrophy both dramatically rise with decreasing vortex angles. A detailed analysis is also carried out to analyze the vertex angle effects on the temporal variations of interface features. Finally, the impacts of different Mach and Atwood numbers on the V-shaped interface are briefly presented.

Response of a patchy intertidal mudflat‐marsh transition zone to a typhoon

AbstractWhile tidal marshes are valued for their ability to reduce the impact of storm waves on shores, there is still more limited understanding of how storm waves impact the integrity of tidal marshes, particularly in mudflat‐marsh transition zones with patchy vegetation cover. This study aims to investigate changes in hydrodynamics, sediment bed elevation, and patchy vegetation cover along the sea‐to‐land elevation gradient in response to super typhoon IN‐FA, making landfall in 2021 in a mudflat‐marsh transition zone of the Yangtze Estuary (China). Utilizing in‐situ measurements and drone surveys, our results show: (1) A landward decrease in storm‐induced wave energy, flow velocities, turbulence, and erosion across a 200‐m mudflat‐marsh transition zone; (2) Elevation‐dependent spatial reconfiguration of marsh vegetation patches in response to the storm; (3) Different marsh response below and above an elevation threshold where a shift between marsh gain and marsh loss occurred. The observed landward decrease in storm‐induced marsh loss is attributed to a trade‐off between reduced disturbances due to landward increasing friction from the sediment bed and vegetation, and the landward increasing capacity of the vegetation to cope with disturbances. Our findings provide new insights relevant to the response of marsh systems to storms, and highlight the importance of the gradual and adequately wide sea‐to‐land gradient in delivering marsh resistance to extreme events.

Theory for plunger-type wavemakers to generate second-order Stokes waves and Smoothed Particle Hydrodynamics verification

Plunger-type wavemakers are used in ocean engineering laboratories globally. However, the wave-making theories remain incomplete due to the complex geometries of the plungers. This work derives the motion equations for an arbitrary-geometry plunger to generate second-order Stokes waves, along with the generic constraints on wave parameters. Taking wedge-shaped and cylinder-shaped plungers as examples, the motion equations and constraints are detailed. Subsequently, a smoothed particle hydrodynamics (SPH) model for the plunger-induced waves is established and validated by accurately reproducing published experimental results. Finally, the SPH model is applied to simulate the wave generation by the two plungers. The computed wave profiles, water pressures, and flow velocities are compared with their analytical solutions in terms of spatial distribution and time history. Additionally, the wave field stability and the wave generation process are evaluated. The results demonstrate that second-order Stokes waves with target waveforms can be precisely generated using an arbitrary-geometry plunger-type wavemaker within a short transition distance and time, thereby verifying the reliability of the proposed wavemaker theory.

Enabling large-scale and high-precision fluid simulations on near-term quantum computers

Quantum computational fluid dynamics (QCFD) offers a promising alternative to classical computational fluid dynamics (CFD) by leveraging quantum algorithms for higher efficiency. This paper introduces a comprehensive QCFD method, including an iterative method “Iterative-QLS” that suppresses error in quantum linear solver, and a subspace method to scale the solution to a larger size. We implement our method on a superconducting quantum computer, demonstrating successful simulations of steady Poiseuille flow and unsteady acoustic wave propagation. The Poiseuille flow simulation achieved a relative error of less than 0.2%, and the unsteady acoustic wave simulation solved a 5043-dimensional matrix. We emphasize the utilization of the quantum–classical hybrid approach in applications of near-term quantum computers. By adapting to quantum hardware constraints and offering scalable solutions for large-scale CFD problems, our method paves the way for practical applications of near-term quantum computers in computational science.

Design and Study of Wave Flow Field in Bipolar Plates for Proton Exchange Membrane Fuel Cells

Proton exchange membrane fuel cell (PEMFC) is an efficient energy conversion device that converts hydrogen and oxygen directly into electricity through a chemical reaction. In PEMFC, the bipolar plate plays a crucial role, responsible for the collection and transfer of current and the distribution of reactant gases. The wave flow channel bipolar plate is a new design designed to improve the performance of the battery, including enhancing the mass transfer efficiency and reducing the pressure drop. By comparing the advantages and disadvantages of other flow channels, this paper analyzes the conclusion that the wave flow field is more prominent in the comprehensive aspect. It is observed that the wave flow field can effectively increase the length of the flow path and improve the distribution of reactant gas by comparing the traditional flow path with the wavy flow path.

Flow Evolution and Vertical Accelerations in Wave‐Swash Interactions

AbstractWe report on a laboratory study of wave‐swash interactions, which occur in the very nearshore environment of a beach when the shallow swash flow of a breaking wave interacts with a subsequent wave. Wave‐swash interactions have been observed in the field, hypothesized to be important for nearshore transport processes, and categorized into different qualitative types, but quantitative descriptions of their dynamics have remained elusive. Using consecutive solitary waves with different wave heights and separations, we generate a wide variety of wave‐swash interactions with large flow velocities and vertical accelerations. We find that wave‐swash interactions can be quantitatively characterized in terms of two dimensionless parameters. The first of them corresponds to the wave height ratio for consecutive waves, and the second is a dimensionless measure of the time separation between consecutive wave crests. Using measurements of bed pressure and free‐surface displacement, we estimate the total vertical accelerations and focus on the peak upward‐directed acceleration. We find that wave‐swash interactions can generate vertical accelerations that can easily exceed gravity, despite occurring in very shallow water depths. The large vertical accelerations are upward‐directed and are quickly followed by onshore‐directed horizontal velocities. Together, our findings suggest that wave‐swash interactions are capable of inducing large material suspension events of sediment or solutes in sediment pores, and transporting them onshore. While the data are from a single location making it difficult to generalize the findings across the swash zone, the results clearly demonstrate the importance of large vertical accelerations in wave‐swash interactions.

Spectral stability of travelling waves in a thin-layer two-fluid Couette flow

We consider linear stability of travelling waves in a thin-film model for two-fluid Couette flow when a thin layer of the more viscous fluid resides next to the stationary wall. We prove that in a neighbourhood of a bifurcation point, characterized by a positive integer k b , the principal branch ( k b = 1 ) is spectrally stable while all other branches ( k b > 1 ) are spectrally unstable. For larger amplitude travelling waves, we establish a number of conditional theorems where the conditions were checked with help of computer assist for a set of parameter values. Using these theorems, we rigorously confirm earlier numerical evidence (D. Papageorgiou & S. Tanveer, Proc. R. Soc. A , (doi: 10.1098/rspa.2019.0367 )) on stability and instability of travelling waves over a range of parameters.

Structural stability of transonic shocks for the full compressible Euler system in a two-dimensional general nozzle with an external force

In this paper, we investigate the transonic shock solutions to the full compressible Euler system in a general two-dimensional nozzle with an external force. In their book, Courant and Friedrichs [Supersonic Flow and Shock Waves (Interscience Publishers, Inc., New York, 1948)] described the transonic shock phenomena in a de Laval nozzle: given the appropriate receiver pressure, if the upcoming flow is still supersonic after passing through the throat of the nozzle, then a shock front intervenes at some place in the diverging part of the nozzle, and the gas is compressed and slowed down to subsonic speed. We first establish the existence and uniqueness of one-dimensional transonic shock solutions to the steady full Euler system with an external force by prescribing suitable pressure at the exit of the nozzle when the upstream flow is a uniform supersonic flow. With the help of external forces, both existence and uniqueness are established by solving a nonlinear free boundary value problem in a weighted Hölder space.