Phase-lag Effects Research Articles

Laboratory investigations of wave-induced transport of plastic debris over a rippled bottom

Laboratory experiments are conducted in a wave flume to investigate the effect of water waves on the transport of plastic pellets over a rippled bottom. The horizontal velocities of plastic debris are analyzed over the rippled bottom for different wave conditions and plastic elements with different properties. Laboratory investigations determined the characteristic transport patterns of wave-induced plastic debris with a density of ∼2.0g/cm3 moving along the rippled bottom. In the first, swing-type motion, the grains move only in the ripple trough with velocities lower than 0.10 m/s. For sliding-type movement, the grains move along the entire rippled surface with velocities in the range of 0.10–0.13 m/s. For higher velocities in the range of 0.15–0.20 m/s, a saltation-type motion becomes dominant. The results show that plastic grains may move up to 2–3 cm above the ripple crest depending on hydrodynamic conditions. The analysis shows that for velocity-skewed flows, sliding-type motion and onshore transport dominate. For acceleration-skewed flows, saltation-type motion and offshore transport dominate, which is attributed to higher boundary layer thickness and phase lag effects. The analysis of the relationship between the particle Reynolds number and the thickness of the turbulent boundary layer reveals that for values of Rep≥1000 and a boundary layer thicknessδ≥50 mm saltation-type motion becomes dominant. The direction of transport is affected not only by the density of the sediment and the wave skewness coefficients but also by the dimensions of the bottom ripples. The laboratory investigations also provide insight into the hydrodynamic conditions affecting the transport of plastic debris along the bottom covered with ripples in oscillating nonlinear water flows.

Phase-lag effect on the instantaneously-liquefied seabed depth under progressive waves: Explicit approximations

Instantaneous liquefaction can be induced by the upward seepage force while waves propagating over a porous seabed. In this study, the instantaneous liquefaction within a non-cohesive seabed under progressive waves is analytically investigated and verified with the existing offshore observations. To characterize the instantaneous liquefaction potential, the vertical gradient of excess pore-pressure is employed, and the explicit solutions for the liquefied soil depth are then derived to reflect the phase-lag effect. Wave scale effect is further examined by comparative analysis of the liquefaction potential between laboratory and field conditions. It is indicated that, due to the phase-lag effect, the maximum liquefaction potential and the maximum liquefied soil depth no longer appear exactly under the wave trough; nevertheless, such phase difference relative to the wave trough wouldn't exceed π/4. Neglecting the phase-lag effects would considerably underestimate the liquefaction potential as well as the liquefaction depth. Moreover, both the liquefaction potential and the corresponding liquefied soil depth are predominantly related to the non-dimensional parameter Ic for characterizing the combined influence of wave and seabed properties.

An Experimental Study on Progressive and Reverse Fluxes of Sediments with Fine Fractions in Wave Motion

The purpose of the study was to collect experimental data on the vertical structure of sediment fluxes during the wave crest and trough phase. The first stage of the experimental work included measurements of these fluxes using the particle image method, while in the second stage, measurements of sediment transport rates and granulometric distributions of sediments were collected in the traps on both sides of the initial area. The experimental data were compared with the results of a theoretical analysis based on a three-layer model of graded sediment transport. The comparison of the calculations with the measurements was conducted separately for fluxes of fine and very fine fractions in the diameter range di < 0.20 mm, coarse, and total fractions all outgoing in the crest and trough phase from the initial area and deposited in adjacent control areas. As this model did not take into account both the effects of vertical mixing and the phase-lag effects related to the presence of fine and very fine fractions, a modification of this model was proposed that was based on four coefficients that corrected for fluxes. The consistency of the sediment transport calculations according to the modified model with measurements was achieved within plus/minus a factor of 2 of the measurements.

Quantitative feedback control of health care demand via non‐pharmaceutical interventions during an epidemic

AbstractOnce an infectious disease has become an epidemic and can no longer be contained, non‐pharmaceutical public health interventions may be used to reduce infection rates so as to control demand on health care resources including staff and hospital facilities. Feedback control is shown to have limited possibilities due to (often unmodeled) non‐minimum phase lag; uncertainty in model parameters and measurements; and the discrete time nature of practical controller implementation for the interventions. Classical susceptible‐exposed‐infected models do not capture real time delays in disease progression, or phase lag effects of discrete time feedback control. Non‐minimum phase lag constraints are more severe if the number of hospitalized individuals rather than the number of infected individuals is used as the measurement variable.

Thermoelastic diffusion phase-lag model for a layer with internal heat and mass sources

This paper analyses a problem of unsteady bulk thermoelastic diffusion perturbations propagation in a multi-component layer. The local equilibrium model describes one-dimensional physical processes in the continuum. It includes the coupled equations of elastic medium motion, heat transfer and mass transfer with cross-diffusion effects. The model also considers phase-lag effects in a continuum with internal heat and mass sources. The unknown functions of displacement, temperature and concentration increments are investigated in the Green's functions and the boundary conditions integral convolution form. We use the integral Laplace transform to time and the Fourier expansion into series by a spatial coordinate to find Green's functions. It allows us to reduce the problem to a system of linear algebraic equations. The Fourier series coefficients originals are found using known theorems and operational calculus tables. The numerical algorithms used is minimised, and Green's functions are analytically found. Calculation examples are represented and analysed.

A Numerical Study of Sheet Flow Driven by Skewed-Asymmetric Shoaling Waves Using SedWaveFoam

SedWaveFoam, an OpenFOAM-based two-phase model that concurrently resolves the free surface wave field, and the bottom boundary layer is used to investigate sediment transport throughout the entire water column. The numerical model was validated with large-scale wave flume data for sheet flow driven by shoaling skewed-asymmetric waves with two different grain sizes. Newly obtained model results were combined with previous nonbreaking and near-breaking wave cases to develop parameterization methods for time-dependent bed shear stress and sediment transport rate under various sediment sizes and wave conditions. Gonzalez-Rodriguez and Madsen (GRM07) and quasi-steady approaches were compared for intra-wave bed shear stress. The results show that in strongly asymmetric flows, considering the separated boundary layer development processes at each half wave-cycle (i.e., GRM07) is essential to accurately estimating bed shear stress and highlights the impact of phase-lag effects on sediment transport rates. The quasi-steady approach underpredicts (∼60%) sediment transport rates, especially for fine grains under large velocity asymmetry. A modified phase-lag parameter, incorporating velocity asymmetry, sediment stirring, and settling processes is proposed to extend the Meyer-Peter and Mueller type power law formula. The extended formula accurately estimated the enhanced net onshore sediment transport rate observed under skewed-asymmetric wave conditions.

Thermoelastic interactions on thick granular plate with three-phase-lag model under axisymmetric temperature distribution

The theory of thermoelasticity with three-phase-lag is used to study the phase lag effects on wave propagation in granular medium. A two-dimensional thick granular plate with axisymmetric temperature distribution is considered under the type III and three-phase-lag thermoelasticity. The plate’s lower and upper surfaces are assumed to be stress free and subjected to a thermal condition. The analytical solution of the different fields like temperature, displacement, stresses, rotation, and couple stresses is obtained by the Laplace together with the Hankel transform method. The characteristic features of the underlying theory are analyzed by the small-time approximation method with Boley’s theorem and by comparing these results with their counterparts in other generalized thermoelasticity theories (GN III and Lord Shulman theory). The numerical values are evaluated and displayed graphically in the middle plane for different models, and comparison is made.

Numerical evaluation of transient solar radiation effect on concrete-faced rockfill dam with dual mortar contact method

Extrusion damage in the concrete face was widely observed in high concrete-faced rockfill dams in the last two decades. However, the accurate estimation of the concrete stress remains a great challenge. In this paper, a thermo-mechanical coupling method is presented to numerically evaluate the solar radiation effect on the concrete stress within the dual mortar finite element framework. The heat conduction is modelled as a transient time-dependent equation and hence the heat flow can be determined by meteorological data. The thermo-mechanical coupling is conducted in a weak way such that the linear system can be split into two subsystems friendly to the linear solver. The present method based on using nonconforming meshes is validated by the comparisons with node-to-segment method, conforming mesh and analytical solution. The application to a concrete-faced rockfill dam indicates that the phase lag and amplitude damping effects are apparent in the thermal analysis, confirming the importance of using transient heat conduction theory. The observed slab-slab separations emphasis the importance of using dual mortar contact method. The thermal stress is found to be larger than 10 MPa and therefore needs to be considered in the design and safety assessment.

Nonlocal and thermal phase-lag effects on an exponentially graded micropolar elastic material with rotation and gravity

Current research is dedicated to study the influence of angular velocity and gravity field on the thermomechanical interactions in a non-homogeneous, nonlocal, micropolar elastic half-space whose surface is subjected to a mechanical load. The formulation is established in the context of dual-phase-lag model of generalized thermoelasticity. The material is supposed to have non-homogeneous thermoelastic properties in the x-direction. Exact solution of the problem is procured by applying normal mode technique. Numerical computations for nonlocal stresses, displacement components and temperature field are performed for a suitable material and are depicted graphically. Certain special cases of interest have been derived from the current report.

A study of Darcy–Bénard regular and chaotic convection using a new local thermal non-equilibrium formulation

The onset of Darcy–Bénard regular and chaotic convection in a porous medium is studied by considering phase-lag effects that naturally arise in the thermal non-equilibrium heat transfer problem between the fluid and solid phases. A new type of heat equation is derived for both the phases. Using a double Fourier series and a novel decomposition, an extended Vadasz–Lorenz model with three phase-lag effects is derived. New parameters arise due to the phase-lag effects between local acceleration, convective acceleration, and thermal diffusion. The principle of exchange of stabilities is found to be valid and the subcritical instability is discounted. The new perspective supports the finding of an analytical expression for the critical Darcy–Rayleigh numbers representing, respectively, the onset of regular and chaotic convection. The understanding of the transition from the local thermal non-equilibrium situation to the local thermal equilibrium one is also best explained through the new perspective. In its present elegant form, the extended Vadasz–Lorenz system with three phase-lag effects is analyzed using the largest Lyapunov exponent and the bifurcation diagram. It is found that the lag effects not only give rise to a quantitative difference in the above two metrics concerning chaos, but also present a qualitative difference as well in the form of the very nature of chaos.

Synchronization of Kuramoto oscillators with time-delayed interactions and phase lag effect

We investigate the synchronized collective behavior of the Kuramoto oscillators with time-delayed interactions and phase lag effect. Both the phase and frequency synchronization are in view. We first prove the frequency synchronization for both semi-delay and full-delay models with heterogeneous time-delays and phase lags. We also prove the complete and partial phase synchronization for both models with the uniform time-delay and phase lag. Our results show that the Kuramoto models incorporated with small variation of time-delays and/or phase lag effect still exhibit the synchronization. These support that the original Kuramoto model (i.e., no time-delays/phase lags) is qualitatively robust in the perturbation of time-delay and phase lag effects. We also present several numerical experiments supporting our main results.

Transient hygrothermoelastic response in a porous cylinder subjected to ramp-type heat-moisture loading

The classical theory of heat conduction (Fourier theory) predicts an infinite speed for thermal disturbance propagation, which is physically unrealistic. By extending the classical Fourier heat conduction and Fick’s diffusion, this article develops hyperbolic diffusion/heat conduction laws with phase lags of heat/moisture flux to simulate coupled heat-moisture diffusion-propagation behavior with the Defour and Soret effects. A porous cylinder subjected to a ramp-type heating and humidifying at the surface is studied. The Laplace transform is used to obtain a closed-form solution of the temperature, moisture, displacements and stresses in the cylinder. Numerical results are calculated via the inversion of the Laplace transform. Obtained results show that the thermal/moisture relaxation time or phase lag plays a significant role in affecting transient hygrothermoelastic field. For a non-vanishing phase lag, non-Fourier and non-Fickian effects exist and hygrothermal waves have finite propagation speeds. The influences of the phase lag of heat/moisture flux and ramp-type time parameter on the transient response of hygrothermoelastic field are presented graphically. A comparison of the numerical results based on the classical model and the present one is made. The non-Fourier heat conduction and non-Fickian diffusion can effectively avoid the shortcomings induced by the classical Fourier and Fick laws.

Phase-Lag Effects in Skin Tissue During Transient Heating

A three-phase-lag (TPL) model is proposed to describe heat transfer in a finite domain skin tissue with temperature dependent metabolic heat generation. The Laplace transform method is applied to solve the problem. Three special types of heat flux are applied to the boundary of skin tissue for thermal therapeutic applications. The depth of tissue is influenced by the different oscillation heat flux. The comparison between the TPL and dual-phase-lag (DPL) models is analyzed and the effects of phase lag parameters (<i>τq</i>, <i>τt</i> and <i>τv</i>) and material (<i>k</i><sup>*</sup>) on the tissue temperature distribution are presented graphically.

Effect of magnetic field and three-phase-lag in a rotating micropolar thermo-viscoelastic half-space homogeneous isotropic material

This paper is devoted to three-phase-lag theory of thermo-elasticity to study the effects of rotation, ramp parameter and magnetic field in a micropolar generalized thermo-viscoelastic medium. By employing normal mode analysis and Lame’s potential theory, the analytical expressions for the displacement components, stresses components, couple stress and temperature field are obtained in the physical domain. Numerical examples are displayed to illustrate the effects of magnetic field, rotation and ramp parameter on the results. When there is no phase-lag effects, the results of the current paper are reduced to exactly the same results available in the literature. However, the magnetic field and rotation have no effect on the non-dimensional temperature. The results indicate that the effect of magnetic field, rotation, ramp parameter, viscous and Phase-lag on the micropolar thermo-viscoelastic medium are very pronounced.

Wave Boundary Layer Hydrodynamics and Sheet Flow Properties Under Large‐Scale Plunging‐Type Breaking Waves

AbstractWave boundary layer (WBL) dynamics are measured with an Acoustic Concentration and Velocity Profiler (ACVP) across the sheet flow‐dominated wave‐breaking region of regular large‐scale waves breaking as a plunger over a developing breaker bar. Acoustic sheet flow measurements are first evaluated quantitatively in comparison to Conductivity Concentration Meter (CCM+) data used as a reference. The near‐bed orbital velocity field exhibits expected behaviors in terms of wave shape, intrawave WBL thickness, and velocity phase leads. The observed fully turbulent flow regime all across the studied wave‐breaking region supports the model‐predicted transformation of free‐stream velocity asymmetry into near‐bed velocity skewness inside the WBL. Intrawave concentration dynamics reveal the existence of a lower pickup layer and an upper sheet flow layer similar to skewed oscillatory sheet flows, and with similar characteristics in terms of erosion depth and sheet flow layer thickness. Compared to the shoaling region, differences in terms of sheet flow and hydrodynamic properties of the flow are observed at the plunge point, attributed to the locally enhanced wave breaker turbulence. The ACVP‐measured total sheet flow transport rate is decomposed into its current‐, wave‐, and turbulence‐driven components. In the shoaling region, the sand transport is found to be fully dominated by the onshore skewed wave‐driven component with negligible phase lag effects. In the outer surf zone, the total net flux exhibits a three‐layer vertical structure typical of skewed oscillatory sheet flows. However, in the present experiments this structure originates from offshore‐directed undertow‐driven flux, rather than from phase lag effects.

Reflection at the free surface of fiber-reinforced thermoelastic rotating medium with two-temperature and phase-lag

• Wave propagation in a fiber-reinforced thermoelastic rotating medium is considered. • Two-temperature dual-phase-lag theory has been employed for addressing the mathematical analysis. • Effects of different parameters on reflection coefficients have been depicted graphically. • Reflection coefficients and energy ratios for reflected quasi waves are presented in closed form. • It is proved that at each angle of incidence the energy balance law is satisfied at the free surface. The present investigation is concerned with the reflection of plane waves from the free surface of a homogeneous, anisotropic , fiber-reinforced thermoelastic rotating medium under two-temperature and dual-phase-lag model. It has been observed that three coupled plane waves travel in the medium with distinct speeds. Using appropriate boundary conditions, the amplitude and energy ratios for the reflected waves are derived and the numerical computations have been carried out with the help of MATLAB programming. The numerical values of the modulus of reflection coefficients are presented graphically to exhibit the two-temperature, phase lag and rotation parameter effects. The expressions of energy ratios have also been obtained in explicit form and are shown graphically as functions of angle of incidence. It has been verified that during reflection phenomena, the sum of energy ratios is equal to unity at each angle of incidence.

Microscale heat transfer in fusion welding of glass by ultra-short pulse laser using dual phase lag effects

The heat transfer in microscale has very different physical basis than macroscale where energy transport depends on collisions among energy carriers (electron and phonon), mean free path for the lattice (~ 10 – 100 nm) and mean free time between energy carriers. The heat transport is described on the basis of different types of energy carriers averaging over the grain scale in space and collations between them in time scale. The physical bases of heat transfer are developed by phonon-electron interaction for metals and alloys and phonon scattering for insulators and dielectrics. The non-Fourier effects in heating become more and more predominant as the duration of heating pulse becomes extremely small that is comparable with mean free time of the energy carriers. The mean free time for electron – phonon and phonon-phonon interaction is of the order of 1 and 10 picoseconds, respectively. In the present study, the mathematical formulation of the problem is defined considering dual phase lag i.e. two relaxation times in heat transport assuming a volumetric heat generation for ultra-short pulse laser interaction with dielectrics. The relaxation times are estimated based on phonon scattering model. A three dimensional finite element model is developed to find transient temperature distribution using quadruple ellipsoidal heat source model. The analysis is performed for single and multiple pulses to generate the time temperature history at different location and at different instant of time. The simulated results are validated with experiments reported in independent literature. The effect of two relaxation times and pulse width on the temperature profile is studied through numerical simulation.

Boussinesq-Type Modeling of Sediment Transport and Coastal Morphology

A two horizontal dimensional compound model is developed to simulate coastal sediment transport and bed morphology evolution due to wave action. The wave module is a higher-order Boussinesq-type model. The bed load in the surf zone is computed from an advanced semi-empirical formula while the suspended load can be calculated through the solution of the advection-diffusion equation for the sediment or alternatively from a simplified formula. The estimation of the sediment transport in the swash zone is based on the ballistic theory. The unified sediment transport module is valid under combined waves and currents including the wave asymmetry and phase-lag effects. The bathymetry is updated through the sediment conservation equation and the morphological accelerator factor technique accounts for extended simulation time. The model is validated against a number of short-term tests in one horizontal dimension. The response is generally good with most of the morphological features being reproduced in the cross-shore direction. A comparison between various sediment transport formulae and a sensitivity analysis are also performed illustrating the need for inclusion of the phase-lag effects.

Numerical Study for Near-Bed Variables in Velocity-Skewed Oscillatory Sheet Flow Transport

The near-bed sediment concentration and vertical sediment flux are important in sediment transport mechanics, but they are known much less than the horizontal sediment flux, especially for fine sediment in unsteady flows. A developed two-phase model is applied to study the near-bed sediment concentration, vertical sediment flux, and the relevant total sediment amount for the velocity-skewed oscillatory sheet flow transport. With the sediment concentration hindered fall velocity, the classical reference concentration formulas conducted by Engelund and Fredsoe (1976) and Zyserman and Fredsoe (1994) are utilized for the comparison with the two-phase model and illustration of the phase-lag and sediment size effects in near-bed sediment concentration and vertical sediment flux. The concentration and vertical flux predicted by the two-phase model agree well with experimental data and are better than empirical formulas. Furthermore, the sediment size effect for pick-up flux function over starved bed is shown to be quite different from that containing sufficient sediment in oscillatory flows.

Some theorems on linear theory of thermoelasticity for an anisotropic medium under an exact heat conduction model with a delay

The present work is concerned with a very recently proposed heat conduction model—an exact heat conduction model with a delay term for an anisotropic and inhomogeneous material—and some important theorems within this theory. A generalized thermoelasticity theory was proposed based on the heat conduction law with three phase-lag effects for the purpose of considering the delayed responses in time due to the micro-structural interactions in the heat transport mechanism. However, the model defines an ill-posed problem in the Hadamard sense. Subsequently, a proposal was made to reformulate this constitutive equation of heat conduction theory with a single delay term and the spatial behavior of the solutions for this theory have been investigated. A Phragmen–Lindelof type alternative was obtained and it has been shown that the solutions either decay in an exponential way or blow-up at infinity in an exponential way. The obtained results are extended to a thermoelasticity theory by considering the Taylor series approximation of the equation of heat conduction to the delay term and a Phragmen–Lindelof type alternative was obtained for the forward and backward in time equations. In the present work, we consider the basic equations concerning this new theory of thermoelasticity for an anisotropic and inhomogeneous material and make an attempt to establish some important theorems in this context. A uniqueness theorem has been established for an anisotropic body. An alternative characterization of the mixed initial-boundary value problem is formulated and a variational principle as well as a reciprocity principle is established.