Tidal Energy Research Articles

Seasonal variation and fundamental characteristics of baroclinic tides in the Arabian Gulf

In the Arabian Gulf, baroclinic tides significantly impact physical and biological phenomena, shaping the region’s marine ecosystem. This study provides the first high-resolution investigation of the baroclinic tides using the three-dimensional, nonhydrostatic MIT general circulation model (MITgcm). The simulation outputs were validated against data from Oregon State University’s Tidal Inversion Software (OTIS), tidal stations, and mooring observations, showing high agreement and confirming the model’s accuracy. We further examined the characteristics of baroclinic and barotropic tides, identifying four key regions with high-intensity baroclinic tides based on energy budget analysis: 1) the narrow Strait of Hormuz; 2) the strait’s entrance along the trough, including the islands Farur, Siri, Abumusa, and Greater Tunb; 3) the central axial trough area with sea-bottom ridges; and 4) the northern area following a secondary ridge. Most baroclinic tides dissipate quickly due to interactions with complex bottom topography and do not propagate far from their sources. Significant seasonal variation shows that in winter, only the Strait of Hormuz and the area around the four islands showed significant baroclinic tidal energy, likely due to well-mixed upper layer seawater that hinders thermocline disturbances. The strong correlation between the simulation results and satellite images of internal waves suggests that intense baroclinic tides generate internal solitary waves in the Gulf.

Experimental Investigation of the Yaw Misalignment Effect on the Power Performance and System Loading of a Flapping‐Foil Hydrokinetic Turbine

ABSTRACTHydrokinetic turbines (HTs) extract power by utilizing hydrodynamic forces from flow energy. The surplus load not used for power generation acts as a system load and must be considered when designing the turbine. Additionally, due to the variability of the flow direction during tidal power generation, the effect of the yaw misalignment angle on the power generation performance and system loading is an important design consideration. This study investigates the characteristics of an experimental model of an HT that uses two flapping foils, at different yaw misalignment angles through circulating water tunnel experiments. Experimental results show that with a yaw angle change of 10°, the power performance decreases by approximately 10% and the load increases by about 30% compared to an aligned configuration. Notably, the load in the flow‐perpendicular direction was significant, with periodic changes due to repetitive up‐and‐down motions. Consequently, the hydrodynamic force characteristics of the HT differ from those of conventional rotary turbines, necessitating the development of a design method that fits these characteristics for the actual installation of flapping‐foil HTs at tidal current power generation sites.

Ocean current turbine power take-off design using fluid dynamics and towing tank experiments

This study investigates the performance and power generation capabilities of a small-scale hydrokinetic turbine by comparing numerical simulations with experimental measurements. The key difference between the two models comes from the initial numerical analysis which focused only on the permanent magnet DC motor (PMDC) motor’s parameters and did not account for the gear-head reduction that leads to discrepancies in current and torque predictions, especially at lower input voltages. In practice, friction losses within the gear-head increased the required current and torque, highlighting inefficiencies in the motor gear-head system. A modified experimental setup incorporated a magnetic coupling to address leakage issues and enhance system reliability. While the magnetic coupling resulted in a slight reduction in speed, current, and torque, it improved the overall integrity of the system which is essential for marine applications. The comparison between experimental results and Blade Element Momentum (BEM) simulations showed good agreement at lower speeds, but the simulations under-predicted power at higher speeds, likely due to the model’s limitations in capturing complex hydrodynamic phenomena. This shows the need for comprehensive analysis, integrating both numerical and experimental approaches to optimize turbine performance. Future research will focus on refining experimental methodologies and further improving turbine design and efficiency for hydrokinetic energy systems.

Life cycle environmental impact assessment of the “Sindhuja-I” wave energy converter

The life cycle assessment (LCA) is an inevitable part of ocean wave energy systems. This paper presents an LCA of the Sindhuja-I ocean wave energy converter (WEC). The WEC is a point absorber type WEC tested at the Tuticorin port in India. This study utilized the ISO 14044 standard and SimaPro LCA software to assess the environmental impact of the WEC in comparison to a coal power plant, offshore wind, and tidal energy devices. The functional unit considered is the generation of 1 kWh of electricity. The WEC has a global warming potential of 174 gCO2-eq/kWh, showcasing an impressive 81.9% reduction in emissions compared to coal power plants. Stainless steel contributes significantly to emissions, accounting for 93.7%, 94.6%, 99.4%, and 94.1% of total CO2, NOx, SO2, and PM2.5 emissions, respectively. The paper emphasizes the potential environmental benefits of recycling WEC materials at the end of their lifespan. Furthermore, the study suggests that the longevity of a point absorber device can positively impact its overall environmental footprint, given its minimal moving parts and low maintenance requirements. The WEC has a promising environmental footprint of ocean wave energy conversion, particularly compared to traditional fossil fuel-based power generation.

Design and Research of Dual-Mode Power Generation Device Based on Improved Oscillating Buoy

In response to the national “dual-carbon” strategic goals, a dual-mode ocean energy generation device was researched. First, improvements were made to the power generation system and mechanical structure of an oscillating buoy with a radius of 2.5 m, designing a power generation device that utilizes both wave energy and tidal energy. Subsequently, wave generation was carried out using the Realizable k-ε turbulence model, and the buoy’s strength was analyzed using the Ansys Fluent simulation platform with finite element analysis, with simulation results indicating a rational design. Then, the Froude–Krylov hypothesis method and the oscillating buoy body decomposition method were used to calculate the combined force in the vertical direction of the buoy, and combined with other forces, the maximum wave force on the buoy was determined. It was verified that the buoyancy of the buoy met the requirements of the hydraulic system. Finally, the hydraulic power generation system model was simulated and analyzed using AMEsim, yielding a power generation of 55.2284 kW. Using a formula, the maximum power generation of a single buoy was calculated to be approximately 15.5 kW, and the ideal maximum power generation of the entire device was able to reach 101.7284 kW.

An Overview of Tidal Power in China

Abstract. Tidal energy is a renewable, clean and non-polluting renewable energy source with huge reserves, which is of great significance to alleviate the energy tension in coastal areas. The eastern coast of China is dotted with many economically developed cities such as Shanghai, Shenzhen, Hong Kong, etc. The energy consumption of these cities is very high and growing at a very high rate year by year. Although China has constructed the "West-East Electricity Transmission" project to alleviate the problem of electricity tension in the eastern coastal cities, it cannot fundamentally reduce the dependence on traditional fossil energy. Therefore, on the basis of extensive data collation, this paper further explores the possibility of utilizing tidal energy for power generation in China by studying China's tidal energy reserves, and analyzes the difficulties in developing tidal energy in China as well as puts forward suggestions for the future development of tidal energy.

Characteristic Analysis of Vertical Tidal Profile Parameters at Tidal Current Energy Site

Many mathematical models have been proposed to estimate vertical tidal current profiles. However, as previous studies have shown that tidal current energy sites have different characteristics in their vertical tidal current profiles, it is necessary to estimate the profiles from field-measured data for practical purposes. In this study, we measured layered tidal currents over two months using an acoustic Doppler current profiler (ADCP) to analyze the characteristics of vertical tidal current profiles at the Jangjuk Strait, a candidate site for tidal current energy. As a result, the power law parameter α and bed roughness β were estimated as 4.51–12.41 and 0.38–0.42, respectively. Additionally, the maximum roughness length representing seabed roughness in the logarithmic profile was estimated as 0.221 m, and the estimated friction velocity was 0.038–0.194 m/s. Furthermore, a high correlation was observed between the depth-averaged tidal current velocity and friction velocities at all sites during flood and ebb tide conditions. A high correlation was also found between the bed roughness, roughness length, and power law exponent at relatively deeper sites. Tidal current energy sites display distinct characteristics compared to other sea areas. Therefore, it is essential to account for field conditions when conducting numerical modeling and design.

Study on measurement uncertainty of energy conversion efficiency of tidal energy converters

Accurate assessment of the measurement uncertainty in the energy conversion efficiency of tidal energy converters is pivotal for a comprehensive analysis of experimental results. This paper presents a sophisticated measurement uncertainty assessment model which is based on energy conversion efficiency experiments of tidal energy converters. The model conducts a careful assessment of the input quantities using both Type A and Type B standard measurement uncertainties and provides an extended understanding of the experimental result uncertainties. The findings reveal that: (1) Even with human factors excluded, the experimental results show a dispersion ranging from 1.5 % to 4.2 % under the optimal experimental conditions; (2) Compared with the Type B standard measurement uncertainty evaluation method, the experimental results based on the Type A standard measurement uncertainty evaluation are more discrete, but the experimental results are more realistic; (3) Through the data analysis of the experimental results, the flow rate becomes a primary factor influencing the measurement uncertainty of experimental results. This paper provides a theoretical reference for scientific analysis of energy capture efficiency of tidal energy converters and for improving the credibility of experimental results.

Planet-star interactions with precise transit timing. IV. Probing the regime of dynamical tides for GK host stars

Giant exoplanets on 1--3 day orbits, known as ultra-hot Jupiters, induce detectable tides in their host stars. The energy of those tides dissipates at a rate related to the properties of the stellar interior. At the same time, a planet loses its orbital angular momentum and spirals into the host star. The decrease in the orbital period is empirically accessible with precise transit timing and can be used to probe planet-star tidal interactions. Statistical studies show that stars of GK spectral types, with masses below 1.1 $M_ odot $, are depleted in hot Jupiters. This finding is evidence of tidal orbital decay during the main-sequence lifetime. Theoretical considerations show that in some configurations the tidal energy dissipation can be boosted by non-linear effects in dynamical tides, which are wave-like responses to tidal forcing. To probe the regime of these dynamical tides in GK stars, we searched for orbital period shortening for six selected hot Jupiters in systems with 0.8--1 $M_ odot $ host stars: HATS-18, HIP 65A, TrES-3, WASP-19, WASP-43, and WASP-173A. For the hot Jupiters in our sample, we analysed transit timing datasets based on mid-transit points homogeneously determined from observations performed with the Transiting Exoplanet Survey Satellite and high-quality data available in the literature. For the TrES-3 system, we also used new transit light curves we acquired with ground-based telescopes. We searched mid-transit times for shortening of orbital periods by statistically testing quadratic transit ephemerides. Theoretical predictions on the dissipation rate for dynamical tides were calculated under the regimes of internal gravity waves (IGWs) undergoing wave breaking (WB) in stellar centres and weak non-linear (WNL) wave-wave interactions in radiative layers. Stellar parameters of the host stars, such as mass and age, which were used in those computations, were homogeneously redetermined using evolutionary models with the Bayesian inference. We found that transit times follow the refined linear ephemerides for all ultra-hot Jupiters of our sample. The non-detection of orbital decay allowed us to place lower constraints on the tidal dissipation rates in those planet-star systems. In three systems, HATS-18, WASP-19, and WASP-43, we reject a scenario with total dissipation of IGWs. We conclude that their giant planets are not massive enough to induce WB. Our observational constraints for HIP 65A, TrES-3, and WASP-173A are too weak to probe the WB regime. Calculations show that WB is not expected in the former two, leaving the WASP-173A system as a promising target for further transit timing observations. The WNL dissipation was tested in the WASP-19 and WASP-43 systems, showing that the theoretical dissipation rates are overestimated by at least one order of magnitude. For the remaining systems, decades or even centuries of transit timing measurements are needed to probe the WNL regime entirely. Among them, TrES-3 and WASP-173A have the predicted WNL dissipation rates that coincide with the values obtained from gyrochronology. Tidal dissipation in the GK stars of our sample is not boosted by WB in their radiative cores, preventing their giant planets from rapid orbital decay. Weakly non-linear tidal dissipation could drive orbital shrinkage and stellar spin-up on gigayear timescales. Although our first results suggest that theory might overestimate the dissipation rate and some fine-tuning would be needed for at least a fraction of planet-star configurations, some predictions coincide intriguingly with the gyrochronological estimates. We identify the WASP-173A system as a promising candidate for exploring this problem in the shortest possible time of the coming decades.

A Comprehensive Review of Remaining Useful Life Estimation Approaches for Rotating Machinery

This review paper comprehensively analyzes the prognosis of rotating machines (RMs), focusing on mechanical-flaw and remaining-useful-life (RUL) estimation in industrial and renewable energy applications. It introduces common mechanical faults in rotating machinery, their causes, and their potential impacts on RM performance and longevity, particularly in wind, wave, and tidal energy systems, where reliability is crucial. The study outlines the primary procedures for RUL estimation, including data acquisition, health indicator (HI) construction, failure threshold (FT) determination, RUL estimation approaches, and evaluation metrics, through a detailed review of published work from the past six years. A detailed investigation of HI design using mechanical-signal-based, model-based, and artificial intelligence (AI)-based techniques is presented, emphasizing their relevance to condition monitoring and fault detection in offshore and hybrid renewable energy systems. The paper thoroughly explores the use of physics-based, data-driven, and hybrid models for prognosis. Additionally, the review delves into the application of advanced methods such as transfer learning and physics-informed neural networks for RUL estimation. The advantages and disadvantages of each method are discussed in detail, providing a foundation for optimizing condition-monitoring strategies. Finally, the paper identifies open challenges in prognostics of RMs and concludes with critical suggestions for future research to enhance the reliability of these technologies.

Impact of Leading-Edge Tubercles on Airfoil Aerodynamic Performance and Flow Patterns at Different Reynolds Numbers

In recent years, leading-edge tubercles have gained significant attention as an innovative biomimetic flow control technique. This paper explores their impact on the aerodynamic performance and flow patterns of an airfoil through wind tunnel experiments, utilizing force measurements and tuft visualization at Reynolds numbers between 2.7 × 105 and 6.3 × 105. The baseline airfoil exhibits a hysteresis loop near the stall angle, with sharp changes in lift coefficient during variations in the angle of attack (AOA). In contrast, the airfoil with leading-edge tubercles demonstrates a smoother stall process and enhanced post-stall performance, though its pre-stall performance is slightly reduced. The study identifies four distinct flow regimes on the modified airfoil, corresponding to different segments of the lift coefficient curve. As the AOA increases, the flow transitions through stages of full attachment, trailing-edge separation, and local leading-edge separation across some or all valley sections. Additionally, the study suggests that normalizing aerodynamic performance based on the valley section chord length is more effective, supporting the idea that leading-edge tubercles function like a series of delta wings in front of a straight-leading-edge wing. These insights provide valuable guidance for the design of blades with leading-edge tubercles in applications such as wind and tidal turbines.

The Role of Marine Energy Production in The Development of Urban Infrastructure with Tidal Power Plants

Marine structures, designed and built to develop urban infrastructure, play a very important role in improving access to marine resources, protecting beaches, and facilitating urban and marine communications. These structures can be influential in different parts of urban development. This article, marine energy production facilities with a focus on tidal power plants, which include types of tidal power plants, how they work, the effect of power plants on urban development, design and construction, advantages and challenges, and their comparison. Together with each other. Also, the contribution of each of the tidal power plants in marine energy production facilities is shown to provide a better understanding of the users of this article. These types of structures in addition to economic development and infrastructure improvement Transportation also help to protect the environment and the sustainable use of natural resources, which is why familiarizing and investigating these types of structures and the role they play in the development of urban infrastructure is of particular importance and needs Further investigations using numerical modelling and laboratory methods will be necessary to achieve accurate and reliable engineering results

A radius and minimum velocity Jensen model for far wake distribution prediction of tidal stream turbine

The rational layout of tidal stream turbines (TSTs) is beneficial for making full use of tidal stream energy. It is essential to consider the wake radius and velocity distribution for determining the spacing between the TSTs. The wake is primarily affected by the turbulence intensity. The attenuation of turbulence results in the non-linear expansion of the wake. Additionally, the high turbulence in the near wake region inhibits the velocity deficit, which is more evident under high ambient turbulence intensity. Therefore, a radius and minimum velocity Jensen (RMV-Jensen) model is proposed to predict the wake radius and the wake velocity distribution downstream of a TST. The RMV-Jensen model consists of a radius block (R-Block) and a minimum velocity block (MV-Block). The R-Block is a piecewise exponential function based on the turbulence attenuation in the wake region, accurately describing the change of the wake expansion coefficient. The MV-Block is a wake minimum velocity model, and the inhibitory effect of turbulence on velocity deficit is considered for the first time. The RMV-Jensen model is applied to predict the wake distribution in the Zhoushan sea area. The prediction accuracy of the RMV-Jensen model is improved by 10%–20% compared to that of the classical Jensen model, according to the experimental results.

Near wake evolution of a tidal stream turbine due to asymmetric sheared turbulent inflow with different integral length scales

Tidal stream turbines deployed at highly energetic open water sites are subjected to sheared inflow in the rotor plane. The inflow shear is expected to cause asymmetric loading on the rotor blades and affect the downstream wake. In the current study, two different turbulent inflow conditions, static-high shear and dynamic shear, were generated via an active-grid turbulence generator. A 1:20 scaled three-bladed horizontal axis tidal turbine model was tested in those conditions. The results were compared to a quasi-laminar case with no imposed turbulence or shear. The results show that the high shear reduces the average performance, with a drop of up to 16% in the optimal power coefficient. Besides, the shear profiles increase torque fluctuations and induce significant differences in wake hydrodynamics between the high-speed (upper) and low-speed (lower) regions. The large integral length scales further enhance the load fluctuations perceived by the rotor but have a negligible effect on the mean wake field quantities. The wake recovery was found to be ∼2 to 4 times faster in the upper half region than in the lower region in the near wake. The lower half region featured a faster breakdown of tip vortex structure and a rapid drop of swirl number, a phenomenon conjectured to be a consequence of the strong turbulence intensities and Reynolds stresses in the lower half region. The sheared turbulent inflow also results in a very intensive energy redistribution process towards large-scale, low-frequency motions, which is important to the downstream turbines.

Structural dynamic characteristics of vertical axis wind and tidal current turbines

Vertical axis turbines have received great attention in both offshore wind and tidal current energy communities considering their advantages of economic design and unidirectional operation. However, their commercialization process is rather slow compared with the development of horizontal axis turbines due to technical challenges resulting from higher loads from unsteady aero/hydrodynamic forces, centrifugal forces and gravity of the structures. These are mainly because, while the inherent unsteady tangential pulls and fatigue loads intensify the structural vibration, aggravating structural safety and fatigue life, the relationship between the geometric parameters and the structural responses of blades remains unclear. Therefore, in order to clarify this issue, in this study, we focus on the modal and transient analysis of vertical axis turbines using multi-body dynamics, geometrically exact beam theory and detached eddy simulation. We find that the natural frequency of the rotor is directly related to the ratio of blade length and arm length. The effect of arms cannot be ignored in the structural analysis of the turbine. Moreover, an increase of blade length intensifies the deformation and vibration of the turbine’s structure, making the turbine more prone to fatigue failure. This article is expected to extend the existing knowledge of wind and tidal current turbines and provide a reference for choosing proper design parameters and developing suitable-capacity vertical axis turbines.

A novel generative approach to the parametric design and multi-objective optimization of horizontal axis tidal turbines

As the demand for ocean energy continues to grow, the development of efficient design and optimization methods for tidal current turbines is crucial. Traditional approaches, often based on parameterized models, face challenges in fully capturing the intricate geometric features of turbine blades, limiting the optimization space and affecting convergence efficiency. In response, this study introduces a novel design methodology for horizontal axis tidal turbines (HATTs) using a variational autoencoder generative adversarial network (VAEGAN) model. This approach uses unsupervised learning from a custom dataset to generate new HATT designs, with the VAEGAN model encoding distinct geometric features of turbine blades within a compact latent space, enabling more efficient design space exploration and facilitating the discovery of innovative shapes. Furthermore, in the multi-objective optimization process targeting both hydrodynamic performance and structural strength, the reduced dimensionality of the design variables accelerates convergence while maintaining a broad and meaningful design space. The proposed methodology demonstrates the VAEGAN model's ability to generate diverse and effective turbine blade designs, highlighting its potential as a powerful tool in advancing HATT technology.

A Case Study on the Risk Assessment for O&M of a 1 MW Tidal Current Energy Converter

Tidal power is a technology that generates electricity by utilizing tidal current energy, and in recent years, with the advancement of technology, it has reached the stage of real sea performance test. However, in the case of Korea, there is a lack of construction experience and equipment, and work in fast flows such as the Uldolmok region involves various risk factors. In order to establish measures to reduce these risk factors, Korea’s Occupational Safety and Health Act recommends performing a risk assessment to identify and manage risk factors that may occur during work in advance. Risk assessment is a process aimed at identifying and evaluating potential risk factors that may arise during work, with the goal of minimizing losses caused by accidents. Therefore, in this study, a risk assessment was conducted to identify risk factors that may occur during offshore O&M work of the 1 MW tidal current energy converter and to ensure the safety of workers and the environment. A total of 60 risk factors were identified, including marine and weather conditions, equipment and personnel, and work environments, and a qualitative risk assessment was conducted three times based on the judgment of several field experts.

Investigating the Performance of Glass Fibre-Reinforced Polymer (GFRP) in the Marine Environment for Tidal Energy: Velocity, Particle Size, Impact Angle and Exposure Time Effects

Tidal energy, with its potential to provide a consistent energy output and reduce carbon emissions, has garnered significant interest. This study, which evaluates the performance of tidal turbine blades in seawater conditions and with sand particles, presents a novel approach. A slurry rig was developed to examine composite materials, and a glass fibre-reinforcement polymeric material was tested over a range of particle sizes, velocities, and impact angles. In addition, this paper used a new test protocol with 14 days (336 h) and 91 days (2184 h) of pre-exposure time of materials before testing. The results, which show significant changes in the erosive mechanisms of GFRP in short- and long-term pre-exposure time as a function of these variables, have profound implications for the design and performance of tidal turbine blades. The study also utilised scanning electron microscopy (SEM), depth profiling analysis, and erosion mapping techniques to compare the erosion behaviours of GFRP. These tools can be used to optimise such materials in tidal turbine conditions.

Climate Change Implications on Middle Eastern Geography and Stability – A Case Studies of GCC- with a Focus on the Kingdom of Saudi Arabia

The environment constitutes the natural setting where humans reside, secure food sources, and utilize natural resources to fulfill their material and life necessities. Unlike other creatures, humans have not adapted to nature and the surrounding environment; instead, they have manipulated it to their advantage, disrupting the ecological balance. The primary catalyst for this disruption was the Industrial Revolution, which significantly increased pollution rates, harmful emissions, and the extraction of raw materials, thereby intensifying the exploitation of natural resources. The gravest concern is that the damage inflicted upon nature may reach a point of no return, with catastrophic and enduring consequences, such as global warming, ice melting, rising sea levels, and escalation in greenhouse gases, along with severe repercussions of these events, including an increase in mortality rates due to natural disasters. Effective responses necessitate actions at various levels, including cultural and educational initiatives and international measures, particularly in legislation. Such laws must enforce stringent controls on emissions from industrial and automotive sources. Individuals are called upon to conserve electricity and water, and adopting renewable energy sources, such as solar, hydro, wind, and tidal energy, that do not rely on fuel combustion is encouraged. Planting trees, which absorb carbon dioxide as a primary contributor to global warming, is among the most critical measures we can undertake. The Gulf Cooperation Council (GCC) is essential in combating climate change in this arena, and the Kingdom of Saudi Arabia is leading in this. This paper elaborates on the impact of climate change in Middle Eastern countries using a brief case study of the Saudi Green Initiatives. The paper also presents the policy recommendations to the concerned stakeholders of the GCC and the government of Saidi Arabia.

Shear behavior at the interface of rough surfaces and cohesive soils under axial loading

Foundation elements with rough (textured) surfaces mobilize larger interface shear resistance than ones with conventional smooth or random rough surfaces when sheared against soils under monotonic loading. The overall performance of foundation elements such as piles supporting offshore wind turbines, suction caissons supporting tidal energy converters, soil nails, and soil anchors installed in cohesive soils could be enhanced through utilizing rough (textured) surfaces to resist applied static and/or cyclic loading. This paper describes the shear behavior of smooth and rough (textured) surfaces in kaolinite clay and kaolinite clay-sand mixture soils under static and cyclic axial loading. The experimental investigation presented herein consists of a series of interface shear tests performed on 3D printed rough (textured) surfaces and a 3D printed smooth reference surface utilizing the Cyclic Interface Shear Test system. The paper includes a description of the interface testing system components, cohesive soil specimens’ preparation procedure, smooth and rough (textured) surfaces details, testing procedure, and results of static and cyclic tests. Test results indicate that kaolinite clay-sand mixture soil mobilized larger static and post-cyclic interface shear resistance and volume contraction relative to kaolinite clay soil when sheared against the smooth reference surface. When tested against rough (textured) surfaces with variable asperity height, larger shear resistance was mobilized and larger soil dilation greater than that mobilized by the reference untextured surface in both soils. The results also indicate rough (textured) surfaces exhibited a prevalent frictional anisotropy increases with asperity angle and height in cohesive soils, the surfaces mobilized larger shear resistance and volume change in one direction (i.e., against the asperity right-angled side) than the other direction (i.e., along the asperity inclined side).