Wave-Dependence of Friction Velocity, Roughness Length, and Drag Coefficient over Coastal and Open Water Surfaces by Using Three Databases

The parameterization of friction velocity, roughness length, and the drag coefficient over coastal zones and open water surfaces enables us to better understand the physical processes of air-water interaction. In context of measurements from the Humidity Exchange over the Sea Main Experiment （HEXMAX）, we recently proposed wave-parameter dependent approaches to sea surface friction velocity and the aerodynamic roughness by using the dimensional analysis method. To extend the application of these approaches to a range of natural surface conditions, the present study is to assess this approach by using both coastal shallow （RASEX） and open water surface measurements （Lake Ontario and Grand Banks ERS-1 SAR） where wind speeds were greater than 6.44 m s-1. Friction velocities, the surface aerodynamic roughness, and the neutral drag coefficient estimated by these approaches under moderate wind conditions were compared with the measurements mentioned above. Results showed that the coefficients in these approaches for coastal shallow water surface differ from those for open water surfaces, and that the aerodynamic roughness length in terms of wave age or significant wave height should be treated differently for coastal shallow and open water surfaces.

Frictionless Surface Gravity Waves

A physical explanation is given for the observations that ocean surface gravity waves can travel up to half way around the world from generation in a wind storm to dissipation on shore. Inherent in these waves is an orbital fluid particle motion, known from laboratory experiments, that has no friction according to the Navier-Stokes equations. The prediction is based on application of Bernoulli’s law to all the closed orbital paths of the fluid particles and the cross-stream force balance on the particles between a pressure gradient and the centrifugal force in each orbital loop.

Wave-Current Propagation over a Frictional Topography

In this paper the parabolic approximation model based on mild-slope equation is used to study wave propagation over a slowly varying and frictional topography under wave-current interaction. A governing equation considering the friction effects is derived by the authors for the first time. A simplified form for the rate of wave energy dissipation is presented on the basis of the wave-current action conservation equation and the bottom friction model given by Yoo and O'connor (1987). Examples reveal that the present computational method can be used for the calculation of wave elements for actual engineering projects with large water areas.

Wave Attenuation and Friction Coefficient on the Coral-Reef Flat

Several sets of S4 direction-wave-current-tide meters have been deployed on the coral-reef flat of Yongshu Reef in the sea area of Nansha Islands.Based on the observational sea wave data, the attenuation characteristics of the waves propagating on the coral reef flat, the bottom friction coefficients and the transfer of wave energy are discussed in the paper. The results show that, in the relative depths of 0.0613～0.0867, the wave height attenuation per unit distance of wave propagation is 22.09%～46.56%, with an average of 31.35%; the wave energy attenuation coefficient, 33.74%～53.22%, with an average of 43.61%. The average of the bottom friction coefficients on the coral-reef flat is 0.1346, which is about 10 times that on the sand or silt bottom. In the course of propagation on the reef flat, the waves sustain more loss in high frequency than in low frequency and the spectral energy transfers to the low frequency. These results may be used for reference in island and reef engineering.

Water Wave Refraction and Diffraction over Frictional Topography

This paper considers the effect of wave energy dissipation induced by sea-bottom friction on the computational results of water wave refraction and diffraction with the parabolic equation method. The presented results show that the friction factor formula adopted in this paper is of higher numerical accuracy than that introduced by Dalrymphe (1984), and it can be used to compute wave propagation over large open areas.

ON LONG-WAVE BREAKING Ⅰ.CONSIDERING nTH POWER BOTTOM FRICTION

Longwave breaking is the agent for many important upper ocean layer processes including the trans-fer of horizontal momentum. In a previous study on the process of longwave breaking, only linear bot-tom friction was considered.In this paper, we discuss the longwave breaking phenomena in the moregeneral case of nth power bottom friction. Using the theory of blowup of solution,the criterion for thetime and location of the longwave breaking can be obtained.

Propagation of harmonic waves through micro gap with consideration of frictional contact

Transmission of elastic waves through a micro gap between two solids with consideration of frictional contact is investigated. By using the Fourier analysis technique and the corrective solution method, the nonlinear boundary problem is reduced to a set of algebraic equations. Numerical results exhibit the locations and extents of separation, slip, and stick zones, the interface tractions, and the energy partition. The effects of gap width, frictional coefficients, and the incident angle on the wave transmission are discussed in detail. The results show that higher harmonics are generated due to the local contact/slip at the interface.

EFFECTS OF A SLOPING THERMOCLINE AND RAYLEIGH FRICTION ON EQUATORIALLY TRAPPED KELVIN WAVES

Based on the observed equatorial ocean dynamic characteristics, the effects of a sloping thermocline and Rayleigh friction on the equatorially trapped free Kelvin waves were theoretically studied with a linear one and one half layer reduced gravity model, the multiple scale method and a small parameter expansion technique. Assuming that main thermocline depth (MTD) variations are slow, i.e. the changes of MTD over one wavelength are smaller than that of the wave amplitude and that wave reflections are negligible, the authors showed by their analytical results that the wavelengths and amplitudes of Kelvin waves are significantly modified by the MTD variations and Rayleigh friction. The results also showed that for an eastward shallowing thermocline, the zonal velocity of the Kelvin waves varies with thermocline depth to the power -7/8. The eastward shallowing of the thermocline depth strengthens Kelvin wave entrapment at the equator. Rayleigh friction reduces the Kelvin wave’s eastward velocity while the thermocline acts in the opposite way. The friction causes dispersion of the Kelvin wave, whose dissipation factor does not depend on its wavelength. The friction increases the lateral decay length and causes phase lines of Kelvin waves to slant westward in parabolic arcs.

Combined effects of topography and bottom friction on shoaling internal solitary waves in the South China Sea

A numerical study to a generalized Korteweg-de Vries (KdV) equation is adopted to model the propagation and disintegration of large-amplitude internal solitary waves (ISWs) in the South China Sea (SCS). Based on theoretical analysis and in situ measurements, the drag coefficient of the Chezy friction is regarded as inversely proportional to the initial amplitude of an ISW, rather than a constant as assumed in the previous studies. Numerical simulations of ISWs propagating from a deep basin to a continental shelf are performed with the generalized KdV model. It is found that the depression waves are disintegrated into several solitons on the continental shelf due to the variable topography. It turns out that the amplitude of the leading ISW reaches a maximum at the shelf break, which is consistent with the field observation in the SCS.Moreover, a dimensionless parameter defining the relative importance of the variable topography and friction is presented.

DYNAMIC INTERACTION OF PLANE WAVES WITH A UNILATERALLY FRICTIONALLY CONSTRAINED INCLUSION-TIME DOMAIN BOUNDARY ELEMENT ANALYSIS

A 2D time domain boundary element method(BEM)is developed to solve the transient scattering of plane waves by a unilaterally frictionally constrained inclusion.Coulomb friction is assumed along the contact interface.The incident wave is assumed strong enough so that localized slip and separation take place along the interface.The present problem is in effect a nonlinear boundary value problem since the mixed boundary conditions involve unknown intervals (slip,separation and stick regions).In order to determine the unknown intervals,an iterative technique is developed.As an example,we consider the scattering of a circular cylinder embedded in an infinite solid.

Dry Friction with Various Frictions Laws: From Wave Modulated Orbit to Stick-Slip Modulated

Choices of excitation signals are important in engineering sciences and in physical simulations;a sufficient excitation can be critical in modelling a complicated nonlinear dynamic system. The discontinuous dynamic of a non-linear, friction-induced with two idealized periodical forced oscillators is studied. The dry friction in the system follows the classical Coulomb law, and various friction characteristics of dry friction laws in engineering sciences. To capture the presence of the two driving forces, the system must be studied as a function of their frequency-modulated and its equivalent amplitude modulated waveforms. Our numerical investigation shows a rich dynamical behaviour including periodic, quasi-periodic motions, thus a variable dynamics phenomenon among others;such as modulated waves, modulated stick-slip, periodic oscillation, and periodic stick-slip. It seems that such excitation forces can be used to conveniently identify the existence of nonlinearity, dry friction effects, and strength degradation in the system. The results achieved via the Coulomb’s law are compared with those obtained via two others particular friction laws: the complete model with Stribeck effect and Coulomb viscosity.

高效铣刀后刀面摩擦应力波传播与衰减特性

高效铣削加工过程中,受高频、断续切削载荷作用,铣刀与工件接触角度、姿态频繁变动,使得刀工界面相对摩擦力及其引起的应力波传播、衰减过程动态变化,导致高效铣削过程摩擦磨损、磨损寿命难以准确识别及预测。构建刀齿误差和铣削振动影响下的铣刀-工件动态接触关系模型,解算铣刀刀齿后刀面摩擦力,根据一维弦线理论,提出刀齿后刀面摩擦应力波传播距离、变化速率与衰减率的解算方法。结果表明,靠近刀尖处应力波峰值和变化速率更大,高效铣刀摩擦应力波衰减过程呈偏态指数型衰减。应力波解算方法的关联度验证结果表明,刀齿后刀面特征点能量与试验累积磨损深度的关联度大于0.8,验证了模型的准确性。

ON THE INTERACTION OF WATER WAVES AND SEABED BY THE POROUS MEDIUM MODEL

The interaction of water waves and seabed is studied by using Yamamoto's model, which takes into account the deformation of soil skeletal frame, compressibility of pore fluid flow as well as the Coulumb friction. When analyzing the propagation of three kinds of stress waves in seabed, a simplified dispersion relation and a specific damping formula are derived. The problem of seabed stability is further treated analytically based on the Mohr-Coulomb theory. The theory is finally applied to the coastal problems in the Lian-Yun Harbour and compared with observations and measurements in soil-wave tank with satisfactory results.

The properties of N-doped diamond-like carbon films prepared by helicon wave plasma chemical vapor deposition

In this paper, N-doped diamond-like carbon(DLC) films were deposited on silicon substrates by using helicon wave plasma chemical vapor deposition(HWP-CVD) with the Ar/CH_4/N_2 mixed gas. The surface morphology, structural and mechanical properties of the N-doped DLC films were investigated in detail by scanning electron microscopy(SEM), x-ray photoelectron spectroscopy(XPS), Raman spectra, and atomic force microscopy(AFM). It can be observed from SEM images that surface morphology of the films become compact and uniform due to the incorporation of N. The maximum of the deposition rate of the films is 143 nm min^(-1), which is related to the high plasma density. The results of XPS show that the N incorporates in the films and the C-C sp^3 bond content increases firstly up to the maximum(20%) at 10 sccm of N_2 flow rate, and then decreases with further increase in the N_2 flow rate. The maximum Young's modulus of the films is obtained by the doping of N and reaches 80 GPa at 10 sccm of N_2 flow rate, which is measured by AFM in the scanning probe microscope mode. Meanwhile, friction characteristic of the N-doped DLC films reaches a minimum value of 0.010.

Monitoring Contact State of Laboratory Fault with Coda Transmission Waves

We monitored the amplitude changes of coda transmission waves around 500 kHz across the frictional interface of a simulated 1. 5-meter-long fault during normal stress holding test.We find that the amplitude of coda transmission waves increases with the logarithm of stationary contact time. Localized increase amounted to a level ranging from 4% to 16%along the fault is observed during the 1-hour experiment. We discuss that the frictional strength at mesoscopic scale,which is related to the amplitude of coda transmission waves,is responsible for the phenomenon. Combining the reported method with other complementary approaches will enhance the understanding of fault mechanism either at laboratory or on-site applications.

轴承副接触对立式转子系统动力学行为的影响研究

考虑轴尖-宝石轴承副的接触力,建立立式转子系统非线性动力学模型,分析轴承副接触参数对转子系统固有特性的影响,讨论横向连接刚度、滑动摩擦系数对转子系统动力学行为的影响。结果表明,引入轴承力模型将导致在轴尖模态频率附近出现共振峰值,轴承副接触区变化将触发低频进动;随着连接刚度增大,轴尖磨损状态将发生从圆环接触逐渐向偏磨接触最终向大范围圆环接触的转变;当处于边界润滑时,滑动摩擦系数不会对转子系统产生影响,处于干摩擦状态时,滑动摩擦系数增加将加速系统产生偏磨;研究结果对立式转子系统动力学优化设计具有重要意义。

Nonlinear Analysis of Nearshore Wave Height Variation Due to Shoaling

Wave formulae derived from the dispersion relation for cnoidal waves are used to find an analytical solution to the problem of nearshore wave height variation on a simple topography, i. e., with an incrementally constant slope. The solution accounts for shoaling, frictional dissipation and will be sufficiently accurate for practical purposes considering the simplified assumptions which are necessary for the treatment of this problem by any method.

Parameterization of Wave Breaking Probability and Whitecap Coverage

The model for whitecap coverage and wave breaking probability are parameterized by the dimensionless wind fetch X^-. This paper aims at replacing X^- with other parameters such as the average wave period T^-, wind speed U10 or wave age ξ in order to improve the suitability and convenience of the model for application. First, W and B are expressed in terms of T^- and U10, which are relatively easy to measure in the field. Further, U10 is replaced with the friction velocity U. by use of the empirical relationship. As wave age has been widely used to parameterize spectral models of ocean waves and air-sea fluxes, W and B are then expressed as a simple function of wave age, respectively. The new forms of the model obtained are W= 1 - Ф（3.02ξ0＂76） and B = exp（ - 4.54ξ^1.52） . The two forms are mere applicable in pracrice, since ξ is relatively easy to measure or determine from wave and wind records. Comparisons between these expressions and data collected from published literature are made and agreement is fairly good.

环形行波超声波电机动态接触摩擦特性建模与分析

超声波电机的接触摩擦模型对电机结构设计和性能优化具有重要作用。该文考虑定子齿结构,基于Dahl摩擦这一动态摩擦定律,分析了定子振动的瞬态响应过程、定子齿质点与转子的法向接触和切向摩擦及转子运动方程,建立了环形行波超声波电机定转子动态接触摩擦解析模型。基于所建立的模型,研究了定转子间的接触状态和法向接触应力,以及相对速度和切向摩擦应力,并分析了电机的输出性能。最后,测量了样机的输出特性,将测量值与所建立模型的计算值进行比较,二者基本吻合。此外,也对比了忽略定子齿结构并采用库仑摩擦定律的接触摩擦模型的计算值,结果表明,所建立模型的计算值能更好地与实验值相吻合,说明所建立的模型能够更准确地描述定转子接触摩擦传动特性。

ON LONG-WAVES BREAKING Ⅱ.IN A HALF INFINITE CHANNEL WITH BOTTOM SLOPE

The propagation of long-waves, such as tidal waves from the coastal oceam into shallow estuarine waters,often produces asymmetries of veolcity and water level in time series resulting in long-wave breaking.Tian (1994) studied the mechanism of long-wave breaking in an infinite channel with constant depth,considering nth power bottom friction. This study is for the case of a half infinite channel with bottomslope, taking linear bottom friction into account. The wave breaking time and wave breaking location areestimated and the criteria for long-wave breaking in this particular case are obtained. The results obtainedcan also be e asily applied to the case considering wind stress.