Linear Friction Coefficient Research Articles

Stationary regimes and parametrization of ekman friction in the Karman model of flow induced by external vortical body force

The detailed study of stationary regimes of Karman axisimmetric flow induced by external vortical body force is done. It is extracted two stationary regimes – with small (Batchelor regime) and with substantial (Stewartson regime) secondary circulation. The diagram of regimes existence is plotted in the space of flow parameters – Rossby and small Ekman numbers. For the flow decaying to the stationary flow in the Batchelor regime a theoretical model is proposed with which it was possible to derive a parametrization of linear friction coefficient, Ekman pumping velocity, stationary pressure from mean flow characterictics (vorticity and divergence). In the Stewartson regime a parameterization of the stationary flow is proposed and also numerically studied a decay rate. It is shown a good agreement between theoretical and numerical model results.

Delayed and fractional-order dynamics of a model for earthquake induced by stress perturbations

Fractional calculus and time delay provide a powerful tool to model complex systems with memory and fractal systems and, the viscoelastic systems. Earthquakes are both complex systems with long-memory and some of their faults have fractal properties and, the rocks constituting faults have viscoelastic behavior. In this paper, we examined the dynamics of the spring-block considering the fractional viscous damping force and interaction between the blocks. The shear stress response is studied using the harmonic balance method and the numerical simulations are performed through Adams-Bashforth-Moulton scheme. The effects of the fractional-order and time delay on the amplitude-frequency curves and on the transition between steady state and seismic regime are investigated. The system response shows the existence of the resonance and anti-resonance. It is appears that the resonance amplitude and resonance frequency are strongly dependent on the time delay and fractional-order. This resonance phenomenon results in an accumulation of energy which can lead to the destabilization of the fault system. At the anti-resonance the system response has minimum amplitude, and the blocks move without accumulated energy. The results show that the delay and fractional viscous can affect the properties of the rock, which is characterized by the modified linear stiffness coefficient, modified linear damping coefficient and the modified linear friction coefficient. The stability and hopf bifurcation are investigated and the critical value of the time delay for the occurrence of Hopf bifurcation is determined. The transition from stationary state to the periodic orbit and vice-versa through the hopf bifurcation is observed in the system.

A novel approach to investigate temperature field evolution of water lubricated stern bearings (WLSBs) under hydrodynamic lubrication

Water lubricated stern bearings (WLSBs) are the critical component of ship propulsion system and have important effect on navigation safety. Operating temperature plays a main role on the performance of WLSBs. This paper aims to investigate the effect of operating conditions on bearing temperature characteristics under hydrodynamic lubrication. A novel CFD simulation method developed to improve calculation accuracy. Finite difference method was used to decrease the error of geometric modeling while the experiment and experimental correction formula were exploited to obtain improved boundary conditions. Based on the new method, the effects of operating conditions on temperature characteristics for two typical WLSBs were studied, and mechanisms of bearing temperature field evolution were discussed. Results show that the max friction coefficient appears when bearings are in low velocity and low load condition. Total heat flux density is a function of linear velocity, pressure and friction coefficient. Max temperature of bearing at 0.4 MPa decrease along with increased velocity, while decrease first and then increase at 0.2 MPa. Moreover, peak temperature appears at eccentric side and beyond minimum water film thickness position about 4–40°. High temperature area mainly located at the position of 80–140° in circumferential direction and 0.2–0.13 m in axial direction. With the increase of inlet water velocity, the max temperature of bearing changes slightly. It is appropriate to set the inlet velocity at 2 m/s to obtain better cooling performance. This work can provide theoretical basis for the operation monitoring of WLSBs and the development of new materials.

Mathematical Study on Wave Propagation through Emergent Vegetation

In this paper, the problem of the interaction between a periodic linear wave and offshore aquatic vegetation is investigated. The aquatic vegetation field is considered as a flexible permeable system. A vegetation medium theory is proposed based on Lan–Lee’s poro-elastomer theory, in which linearizing vegetation friction resistance is used to describe fluid motion in the vegetation medium. The study involves boundary conditions for free surface water in emergent vegetation media that have been of less concern in previous studies. The analytical solutions of the vegetation medium and wave fields are derived by the partitioning method combined with matching boundary conditions for neighboring regions. An estimation formula for a modification factor is proposed to evaluate the linear vegetation friction coefficient, which can reasonably compare the analytical solution with relevant past cases in terms of wave transmission. Wave reflection, transmission, and attenuation induced by the effects of the characteristics of the vegetation are studied. The results indicate that an increase in the drag coefficient, stem diameter, stem density, spatial coverage, and plant stiffness leads to the emergency vegetation inducing higher wave energy dissipation and reducing the wave transmission. Vegetation stiffness is a significant factor affecting the drag coefficient.

The impact of organic fibers on the tribotechnical properties of phenylone aromatic polyamide

The impact of such organic fibers as Lola, Oxalon and Tanlon on the tribotechnical properties of phenylone aromatic polyamide is considered in the article. It was found that the most intensive improvement of tribotechnical properties of initial polymer, reduce in the intensity of linear wear and friction coefficient 1,8 - 6,5 and 1,7 - 2,3 times is observed for the composites reinforced with organic Lola and Oxalon fibers. The obtained results are due to the introduction of Lola and Oxalon fibers that leads to the formation of new structural elements – fibrils which give improved complex of tribotechnical properties to composites. The use of Tanlon fiber as a filler for formation of organoplastics of tribotechnical purpose leads to modest improvement of the intensity of linear wear and friction coefficient (on average by 20 %) that is due to the proximity of structure of binder and filler

Time-varying storm surges on Lorentz\u2019s Wadden Sea networks

We present an idealized network model for storm surges in the Wadden Sea, specifically including a time-dependent wind forcing (wind speed and direction). This extends the classical work by H.A. Lorentz who only considered the equilibrium response to a steady wind forcing. The solutions obtained in the frequency domain for the linearized shallow-water equations in a channel are combined in an algebraic system for the network. The velocity scale that is used for the linearized friction coefficient is determined iteratively. The hindcast of the storm surge of 5 December 2013 produces credible time-varying results. The effects of storm and basin parameters on the peak surge elevation are the subject of a sensitivity analysis. The formulation in the frequency domain reveals which modes in the external forcing lead to the largest surge response at coastal stations. There appears to be a minimum storm duration, of about 3–4 h, that is required for a surge to attain its maximum elevation. The influence of the water levels at the North Sea inlets on the Wadden Sea surges decreases towards the shore. In contrast, the wind shearing generates its largest response near the shore, where the fetch length is at its maximum.

Cross-shelf transport induced by coastal trapped waves along the coast of East China Sea

Cross-shelf transport is important due to its role in the transport of nutrients, larvae, sediments, and pollutants. The role of coastal trapped waves (CTWs) and their contribution to the cross-shelf transport is presently unknown. The impact of wind-driven CTWs on the structure of the cross-shelf currents and transport is investigated in the East China Sea (ECS) starting from theory. The cross-shelf currents are divided into four terms: the geostrophic balance (GB) term, the second-order wave (SOW) term, the bottom friction (BF) term and Ekman (EK) term, as well as three modes: the Kelvin wave (KW) mode, the first shelf wave (SW1) mode and the second shelf wave (SW2) mode. Comparison among these decompositions shows that (1) for the four terms, the effect of the GB and EK terms is continual, while that of the BF term is confined to 60–240 km offshore, and the contribution of the SOW term can be ignored; (2) for the three modes, the KW and SW1 modes are dominant in cross-shelf transport. The results show that the total cross-shelf transport travels onshore under idealized wind stress on the order of 10-1, and it increases along the cross-shelf direction and peaks about -0.73 Sv at the continental shelf margin. With the increase of linear bottom friction coefficient, the cross-shelf transport declines with distance with the slope becoming more uniform.

Thermodynamic geometry of minimum-dissipation driven barrier crossing.

We explore the thermodynamic geometry of a simple system that models the bistable dynamics of nucleic acid hairpins in single molecule force-extension experiments. Near equilibrium, optimal (minimum-dissipation) driving protocols are governed by a generalized linear response friction coefficient. Our analysis demonstrates that the friction coefficient of the driving protocols is sharply peaked at the interface between metastable regions, which leads to minimum-dissipation protocols that drive rapidly within a metastable basin, but then linger longest at the interface, giving thermal fluctuations maximal time to kick the system over the barrier. Intuitively, the same principle applies generically in free energy estimation (both in steered molecular dynamics simulations and in single-molecule experiments), provides a design principle for the construction of thermodynamically efficient coupling between stochastic objects, and makes a prediction regarding the construction of evolved biomolecular motors.

Influence of resonance on tide and storm surge in the Gulf of Thailand

A numerical simulation is used to determine the effective resonance period, quality factor Q and linear friction coefficient and mechanism of tide and storm surge in the Gulf of Thailand. The results indicated that the resonance response is triggered by the forced wave with the period of 20.25 hours. The Q factor and linear friction coefficient are approximately 3.15 and 2.76×10−5ms−1, respectively. The gulf is regarded as a moderately dissipative system, which may yield small amplification for the oscillating forced wave. The resonance structure of the basin can play an important role in spatial distribution and amplification of tidal waves in the Gulf of Thailand and nearby area. Distance from the effective resonance period and the corresponding Q factor can be employed in characterizing of tidal amplification in the gulf. The study found that phase difference in the incoming tidal waves can induce the distortion of a nodal band to the normal mode analysis results. The resonance in the north–south direction is the principal mechanism to control tidal waves, specifically for the upper part of the gulf (the Gulf of Thailand). However, significant effect of resonance in the west–east direction on the amplification of tidal waves near the southern part of the gulf (Vietnam, Malaysia and Singapore coast) may be pronounced. From the reproduced historic storm surge and hypothetical results, the spatial distribution of storm surge elevation and the response ratio are in good agreement with the resonance mode and Q factor of the basin. Individually, the contribution of resonance factor to induce severe storm surge (positive surge) tends to be insignificant. Conversely, the interaction process between the disturbance system and the propagating surge wave in the gulf can induce large positive surge near the landfall location significantly.

Parametric oscillations and the stability of a mechanical system with considerable dissipation

A detailed investigation is carried out into the problem of parametric oscillations when there is linear dissipation. Using constructive numerical-analytical methods, the boundaries of the domains of stability are constructed for a wide range of variation of the parameters, that is, the modulation factor and the friction coefficient. By solving non-self-adjoint eigenvalue and eigenfunction problems, the phase vectors of the three lower oscillation modes are determined and the principal features of the behaviour of the boundaries when the linear friction coefficient is varied are established. The eigenvalues and eigenfunctions of the adjoint boundary value problem are found. A complete biorthogonal system is constructed and its functional properties are determined. Modified expressions are obtained for scalar products and the squares of the norms of the characteristic phase vectors.

Thermal Casimir drag in fluctuating classical fields

A uniformly moving inclusion which locally suppresses the fluctuations of a classical thermally excited field is shown to experience a drag force that depends on the dynamics of the field. It is shown that in a number of cases the linear friction coefficient is dominated by short distance fluctuations and takes a very simple form. Examples where this drag can occur are for stiff objects, such as proteins, nonspecifically bound to more flexible ones such as polymers and membranes.

Formula omitted]-thermostatistics of noise-driven Van der Pol oscillator

We study the noise-driven Van der Pol oscillator whose dissipative term yields stationary distributions of the q-exponential form. The thermostatistical observables such as internal energy and temperature are also calculated. Since this model depends on a control parameter which acts as a coupling parameter between the system and environment, the noise-driven Van der Pol oscillator also serves as a nice model where the interplay of both nonextensivity and open character of the system can be considered. We observe that the model behaves as if it is coupled to a finite heat bath for small values of control parameter. As the control parameter increases, the effect of the linear friction coefficient disappears, and the stationary distribution becomes a q-Gaussian, thereby breaking the coupling with the finite heat bath. Finally, we remark that negative temperature values are not observed contrary to an earlier analysis of a similar model. The elucidation of this point is commented in the framework of the misidentification of the correct form of the q-exponentials and the nonextensivity index q.

Modeling fiber interactions in semiconcentrated fiber suspensions

A set of rheological equations is developed for semiconcentrated suspensions of rigid fibers in a Newtonian fluid taking into account hydrodynamic and fiber-fiber interactions. The force generated by the fiber interactions is modeled using a linear hydrodynamic friction coefficient proportional to the relative velocity at the contact point, and weighted by the probability for contacts to occur. The equation of evolution of the second-order orientation tensor, containing advection and diffusion terms due to fiber interactions, is derived to predict fiber orientation under flow. The well known fourth-order orientation tensor, related to the hydrodynamic contribution, and a newly proposed fourth-order interaction tensor are used to evaluate the total stress in the composite. A linear and a quadratic closure approximation are proposed to describe the fourth-order interaction tensor. Results are presented using the quadratic form, which is found to be more accurate than the linear one. The model is shown to describe well simple shear data of suspensions of glass fibers in a Newtonian polybutene. Moreover, fiber orientation and the average number of contacts per fiber are predicted. The newly proposed interaction coefficient varies with fiber orientation, which appears to be realistic.

Linear frictional forces cause orbits to neither circularize nor precess

For the undamped Kepler potential the lack of precession has historically been understood in terms of the Runge–Lenz symmetry. For the damped Kepler problem this result may be understood in terms of the generalization of Poisson structure to damped systems suggested recently by Tarasov (2005 J. Phys. A: Math. Gen. 38 2145). In this generalized algebraic structure the orbit-averaged Runge–Lenz vector remains a constant in the linearly damped Kepler problem to leading order in the damping coefficient. Beyond Kepler, we prove that, for any potential proportional to a power of the radius, the orbit shape and precession angle remain constant to leading order in the linear friction coefficient.

Acceleration of a Stratified Current over a Sloping Bottom, Driven by an Alongshelf Pressure Gradient*

Abstract An idealized theoretical model is developed for the acceleration of a two-dimensional, stratified current over a uniformly sloping bottom, driven by an imposed alongshelf pressure gradient and taking into account the effects of buoyancy advection in the bottom boundary layer. Both downwelling and upwelling pressure gradients are considered. For a specified pressure gradient, the model response depends primarily on the Burger number S = Nα/f, where N is the initial buoyancy frequency, α is the bottom slope, and f is the Coriolis parameter. Without stratification (S = 0), buoyancy advection is absent, and the alongshelf flow accelerates until bottom stress balances the imposed pressure gradient. The e-folding time scale to reach this steady state is the friction time, h/r, where h is the water depth and r is a linear bottom friction coefficient. With stratification (S ≠ 0), buoyancy advection in the bottom boundary layer produces vertical shear, which prevents the bottom stress from becoming large enough to balance the imposed pressure gradient for many friction time scales. Thus, the alongshelf flow continues to accelerate, potentially producing large velocities. The acceleration increases rapidly with increasing S, such that even relatively weak stratification (S > 0.2) has a major impact. These results are supported by numerical model calculations.

A note on tidal current rotation

The rotational form of the vertically averaged equations of motion is applied to derive a formula, linear friction included, which establishes a direct connection between sense of rotation of tidal currents and features of tidal amphidromic systems. Two factors in the formula, called α and β, influence the sense of rotation of tidal currents; the factor α involves the frequency of the tidal signal ω, the Coriolis parameter f, and the linear friction coefficient r. The sign of the cross-product of the logarithm of sea-surface elevation (ζ), and phase (ϕζ) gradients Open image in new window determines whether the factor β favors clockwise or anticlockwise sense of rotation. Open image in new window is a unit vector and γ is the angle between ∇lnζ and ∇ϕζ. The limits |∇ζ|→0, |∇ϕζ|→0 and γ→0 lead to a clockwise sense of rotation in the Northern Hemisphere. 0≤γ≤π favors anticlockwise rotation in the Northern Hemisphere. Friction and low frequencies favor an anticlockwise sense of rotation. The theory works well in semi-enclosed regions like the North Sea. Although only linear friction and sea-surface elevation gradients were considered, there are ocean regions where the agreement between theory and observations is also good.

Sea-breeze forced diurnal surface currents in the Thermaikos Gulf, North-west Aegean

Energetic rotary diurnal surface currents of up to 40 cm/s are observed in the Thermaikos Gulf, North-west Aegean. They are principally confined above the pycnocline in the upper 3 m of the water column. Beneath this depth they are much weaker, less regular and oscillate in anti-phase with those at the surface. Averaged over 10-days, the current cycles are seen to vary sinusoidally with the northward component leading the eastward by 0.2 of a cycle (0.4 π), corresponding to clockwise rotating current ellipses. The mean amplitude ratio between the northward and eastward component amplitudes ( u/ v) is 0.83. A simple analytical model, representing the dynamical balance of a homogeneous surface layer, predicts diurnal wind forcing, i.e. a sea-breeze, should drive diurnal currents whose amplitude will be particularly energetic close to 30° latitude, where the diurnal and inertial periods are similar. Assuming that a 3 m deep surface layer is subject to linear frictional drag, the model is used to hindcast the phase of a northward diurnal wind required to force the observed current components. A linear friction coefficient (of 0.6 ω) is derived from the phase difference between the eastward and northward current components. Using this friction coefficient the phase of a diurnal northward wind is hindcast from the absolute phase of the current components. This hindcast wind phase of 1.70 rad is consistent with the observed northward wind of 1.66 rad with a phase difference of 0.04 rad (<10 min), which provides confirmatory evidence of the role of the sea-breeze wind stress cycle in forcing these motions. The model is finally used to predict the variation in the amplitude, ellipticity and rotation of these currents with latitude.

Surface Wind over Tropical Oceans: Diagnosis of the Momentum Balance, and Modeling the Linear Friction Coefficient

Abstract Previous diagnostic studies of surface wind momentum balances over tropical oceans showed that, under a linear friction assumption, the meridional friction coefficient is two to three times larger than the zonal friction coefficient, and that both friction coefficients exhibit a pronounced meridional dependence. The authors’ diagnosis of a global marine surface dataset confirms these results. Furthermore, it is shown that to first approximation the friction coefficients are independent of longitude and season in the tropical band between ∼20°S and ∼20°N. Poleward of 20°N and 20°S, the coefficients are no longer solely a function of latitude. To explain these empirical results, a simple analytical model of the friction coefficient is formulated based on the simplest K-theory mixed-layer parameterization, assuming constant viscosity. The model does a good job of reproducing the observed zonal friction coefficient, but does poorly for meridional friction. The poor result is thought to be from model ...

EXPERIMENTAL SCALE AND CHARACTERISTICS OF TRANSMISSION OF WAVE IN THE UPRIGHT PERMEABLE BREAKWATER

Effect of Reynolds number on model experiment of wave transformation was examined for permeable breakwaters with a precast concrete armour unit in shallow water region.Transmission coefficient, KT increases by the increase in Reynolds number, Re and experiment magnification, N at logarithmic.Then, linearized friction coefficient, f is decreased with the increase in Reynolds number, and transmission coefficient increases.As a result of examining transmission coefficient in the field using the equation of the authors which is possible to calculation of transmission coefficient. Then, transmission coefficient becomes almost constant at Re>50×104 and it is about 50%.

Friction coefficients and directed motion of asymmetric test particles

The behavior of a test particle in a rarefied gas of classical particles is investigated. considering different interaction mechanisms (specular and diffuse reflection, respectively). For large mass ratio between test and gas particles, analytical expressions for the linear friction coefficient are derived. Moreover, the existence of directed motion of asymmetric test particles with distinct initial conditions (but in the absence of any gradients) is shown. The analytical results are supported by a numerical simulation technique applicable to systems with any mass ratio, which is described here in detail.