Nonlocal Viscosity Research Articles

Reflection of plane waves in a non-local viscothermoelastic half-space under variable thermal conductivity and microelongation effects

The present work is implicated with the investigation of wave propagation in a homogeneous, isotropic, non-local microelongated viscothermoelastic solid half space with variable thermal conductivity under the dual phase lag (DPL) model. It is found analytically that three coupled longitudinal waves and one independent transverse wave exist in the medium which travel with distinct speeds. Reflection coefficients and energy ratios of various reflected waves are obtained analytically and presented graphically for aluminum epoxy-like material. The variations of these reflection coefficients are analyzed for different values of non-local parameter, microelongational parameter, viscosity and variable thermal conductivity. The expressions of energy ratios acquired in explicit form are also represented graphically as functions of the angle of incidence in accordance with the defined rule of conservation of energy.

Adjoint-based computation of nonlocal eddy viscosity in turbulent channel flow

Adjoint-based computation of nonlocal eddy viscosity in turbulent channel flow

A new model of rotating nonlocal fiber-reinforced visco-thermoelastic solid using a modified Green–Lindsay theory

The effect of rotation on a nonlocal fiber-reinforced visco-thermoelastic media was examined in this work using an modified Green and Lindsay theory (MGL). The problem was resolved by using normal mode method to derive the precise expressions of field quantities. In this technique, one gets exact solution without any assumed restrictions on the field variables. The normal mode technique is applicable to a wide range of problems in thermodynamics and thermoelasticity. Graphical representations of the thermal temperature, displacements and stresses are obtained. Comparisons of the physical quantities are shown in figures to study the effects of nonlocal parameter, rotation, viscosity and reinforcement parameters. Some special cases of interest have also been inferred from the present problem. The results indicate that rotation, nonlocal parameter, viscosity and reinforcing factors have a considerable impact on the fluctuations of the variables under consideration. These impacts are examined and described in depth.

Nonlinear phenomena in vibrations of embedded carbon nanotubes conveying viscous fluid

Various nonlinear phenomena such as bifurcations and chaos in the responses of carbon nanotubes (CNTs) are recognized as being major contributors to the inaccuracy and instability of nanoscale mechanical systems. Therefore, the main purpose of this paper is to predict the nonlinear dynamic behavior of a CNT conveying viscous fluid and supported on a nonlinear elastic foundation. The proposed model is based on nonlocal Euler–Bernoulli beam theory. The Galerkin method and perturbation analysis are used to discretize the partial differential equation of motion and obtain the frequency-response equation, respectively. A detailed parametric study is reported into how the nonlocal parameter, foundation coefficients, fluid viscosity, and amplitude and frequency of the external force influence the nonlinear dynamics of the system. Subharmonic, quasi-periodic, and chaotic behaviors and hardening nonlinearity are revealed by means of the vibration time histories, frequency-response curves, bifurcation diagrams, phase portraits, power spectra, and Poincaré maps. Also, the results show that it is possible to eliminate irregular motion in the whole range of external force amplitude by selecting appropriate parameters.

Nonlinear nonlocal damping effects under magnetic loads of a ferromagnetic-viscoelastic nanotube exposed to a nonlinear elastic medium with nonlocal viscosity

This study presents innovative results on a nonlinear dynamic model of a ferromagnetic-viscoelastic nanotube (FVN) whose dissipation effects are captured by material behavior with a linear dissipation law operating in a nonlinear geometric regime. It investigates a possible system derived from a Kelvin–Voigt type dissipation model that describes internal viscoelastic damping in the form of a parallel spring and a dashpot. In addition, a class of losses by linear viscous media in local and nonlocal damping is presented in the modeling. Magnetic load effects are studied using axial rod theory regardless of rotational inertia and shear effects. The governing equation is derived by Hamilton's principle for the FVN subjected to a transverse magnetic field resting on a nonlinear elastic foundation with viscose effects. Formulas have been developed to obtain the nonlinear damping characteristics of a single-walled nanotube. Then, multiple scale method (MSM)-based solutions and Eringen elasticity theory are applied to demonstrate the aforementioned effects on a narrow clamped-clamped (CC) nanotube in detail. The approximate analytical solution is verified by numerical integration methods and a good agreement between the approximate analytical and numerical results is observed. The effect of all important parameters such as local and nonlocal viscosity damping, nonlinear damping coefficient, linear and nonlinear stiffness of the elastic medium due to changes in amplitude vibration of the magnetic field (AVMF) and displacement responses (DR) have been investigated. The original research proposed in this paper may enable the systematic study of nonlinear damping in nanomechanical oscillators, which may help to reveal the underlying physical mechanism.

Strong and periodic solutions of Navier-Stokes equations, in 2D, with non-local viscosity

In this article we study the existence of periodic and strong solutions of Navier-Stokes equations, in two dimensions, with non-local viscosity.

Nonlocal hydrodynamic model for gravity-driven transport in nanochannels.

It has been established that Newton's law of viscosity fails for fluids under strong confinement as the strain-rate varies significantly over molecular length-scales. We thereby investigate if a nonlocal shear stress accounting for the strain-rate of an adjoining region by a convolution relation with a nonlocal viscosity kernel can be employed to predict the gravity-driven isothermal flow of a Weeks-Chandler-Andersen fluid in a nanochannel. We estimate, using the local average density model, the fluid's viscosity kernel from isotropic bulk systems of corresponding state points by the sinusoidal transverse force method. A continuum model is proposed to solve the nonlocal hydrodynamics whose solutions capture the key features and agree qualitatively with the results of non-equilibrium molecular dynamics simulations, with deviations observed mostly near the fluid-channel interface.

Plane waves in nonlocal viscothermoelastic medium with temperature-dependent properties under three-phase-lag theory

The present investigation deals with the study of propagation of plane waves in a homogeneous, isotropic, nonlocal viscothermoelastic half space with temperature-dependent properties in the context of three-phase-lag (TPL) model. The Kelvin–Voigt model of linear viscoelasticity is employed to describe the viscoelastic nature of isotropic material. A set of coupled longitudinal waves and one independent transverse wave are found to travel with distinct speeds in the medium. Reflection coefficients and energy ratios of various reflected waves are presented when (1) a set of coupled longitudinal waves is made incident and (2) a transverse wave is made incident. The results for partition of the energy for various values of the angle of incidence are computed numerically and presented graphically for copper material. It has been verified that there is no dissipation of energy at the boundary surface during reflection. The effects of nonlocal parameter, viscosity and temperature dependent properties on reflection coefficients are depicted graphically. A comparison between the TPL model and GNIII model is also presented by different characteristics of wave propagation like phase velocity and reflection coefficients.

Two-point stress–strain-rate correlation structure and non-local eddy viscosity in turbulent flows

Abstract

Regularity and stability of finite energy weak solutions for the Camassa–Holm equations with nonlocal viscosity

We consider the n-dimensional ( $$n=2,3$$ ) Camassa–Holm equations with nonlocal diffusion of type $$(-\,\Delta )^{s}, \ \frac{n}{4}\le s<1$$ . In Gan et al. (Discrete Contin Dyn Syst 40(6):3427–3450, 2020), the global-in-time existence and uniqueness of finite energy weak solutions is established. In this paper, we show that with regular initial data, the finite energy weak solutions are indeed regular for all time. Moreover, the weak solutions are stable with respect to the initial data. The main difficulty lies in establishing higher order uniform estimates with the presence of the fractional Laplacian diffusion. To achieve this, we need to explore suitable fractional Sobolev type inequalities and bilinear estimates for fractional derivatives. The critical case $$s=\frac{n}{4}$$ contains extra difficulties and a smallness assumption on the initial data is imposed.

Non-local viscosity from the Green-Kubo formula.

We study through MD simulations the correlation matrix of the discrete transverse momentum density field in real space for an unconfined Lennard-Jones fluid at equilibrium. Mori theory predicts this correlation under the Markovian approximation from the knowledge of the non-local shear viscosity matrix, which is given in terms of a Green-Kubo formula. However, the running Green-Kubo integral for the non-local shear viscosity does not have a plateau. By using a recently proposed correction for the Green-Kubo formula that eliminates the plateau problem [Español et al., Phys. Rev. E 99, 022126 (2019)], we unambiguously obtain the actual non-local shear viscosity. The resulting Markovian equation, being local in time, is not valid for very short times. We observe that the Markovian equation with non-local viscosity gives excellent predictions for the correlation matrix from a time at which the correlation is around 80% of its initial value. A local in space approximation for the viscosity gives accurate results only after the correlation has decayed to 40% of its initial value.

High Order Finite Difference/Spectral Methods to a Water Wave Model with Nonlocal Viscosity

High Order Finite Difference/Spectral Methods to a Water Wave Model with Nonlocal Viscosity

Discrete hydrodynamics near solid walls: Non-Markovian effects and the slip boundary condition.

A simple Markovian theory for the prediction of averages and correlations of discrete hydrodynamics near parallel solid walls is presented. The discrete momentum of bins is defined through a finite element basis function. The effect of the walls on the fluid is through irreversible extended friction forces appearing in the very equations of hydrodynamics. The Markovian assumption is critically assessed from the exponential decay of the eigenvalues of the correlation matrix of the discrete transverse momentum. We observe that for bins smaller than molecular dimensions, allowing one to resolve the density layering near the wall, the dynamics near the wall is non-Markovian. Bins larger than the molecular size do behave in a Markovian way. We measure the nonlocal viscosity and frictions kernels that appear in the discrete hydrodynamic equations, which are given in terms of Green-Kubo formulas. They suffer dramatically from the plateau problem. We use a recent procedure for reliably extracting the transport kernels out of the plateau-problematic Green-Kubo formula. With the so-measured transport kernels the nonlocal theory predicts very well the decay of the average of the transverse momentum when the initial velocity profile is a plug flow. The theory allows us to derive the slip boundary condition with microscopic expressions for the slip length and the hydrodynamic position of the wall. The slip boundary condition is not satisfied at the initial stages of the discontinous plug flow, but good agreement is obtained at later stages.

Nonlocal Transport and Implied Viscosity and Diffusivity throughout the Boundary Layer in LES of the Southern Ocean with Surface Waves

AbstractObservations from the Southern Ocean Flux Station provide a wide range of wind, buoyancy, and wave (Stokes) forcing for large-eddy simulation (LES) of deep Southern Ocean boundary layers. Almost everywhere there is a nonzero angle Ω between the shear and the stress vectors. Also, with unstable forcing there is usually a depth where there is stable stratification, but zero buoyancy flux and often a number of depths above where there is positive flux, but neutral stratification. These features allow nonlocal transports of buoyancy and of momentum to be diagnosed, using either the Eulerian or Lagrangian shear. The resulting profiles of nonlocal diffusivity and viscosity are quite similar when scaled according to Monin–Obukhov similarity theory in the surface layer, provided the Eulerian shear is used. Therefore, a composite shape function is constructed that may be generally applicable. In contrast, the deeper boundary layer appears to be too decoupled from the Stokes component of the Lagrangian shear. The nonlocal transports can be dominant. The diagnosed across-shear momentum flux is entirely nonlocal and is highly negatively correlated with the across-shear component of the wind stress, just as nonlocal and surface buoyancy fluxes are related. Furthermore, in the convective limit the scaling coefficients become essentially identical, with some consistency with atmospheric experience. The nonlocal contribution to the along-shear momentum flux is proportional to (1 − cosΩ) and is always countergradient, but is unrelated to the aligned wind stress component.

Large time behavior and convergence for the Camassa–Holm equations with fractional Laplacian viscosity

In this paper, we consider the n-dimensional ( $$n=2,3$$ ) Camassa–Holm equations with fractional Laplacian viscosity in the whole space. In contrast to the Camassa–Holm equations without any nonlocal effect, much less has been known on the large time behavior and convergences of solutions. Here we study first the large time behavior of solutions, then consider the relation between the equations under consideration and the imcompressible Navier–Stokes equations with fractional Laplacian viscosity (INSF). By applying the fractional Leibniz chain rule and the fractional Gagliardo–Nirenberg–Sobolev type estimates, the high and low frequency splitting method and the Fourier splitting method, we shall establish the large time non-uniform decays and algebraic rate decays of solutions. In the critical case $$s=\dfrac{n}{4}$$ , the nonlocal version of Ladyzhenskaya’s inequality along with the smallness of initial data in suitable Sobolev spaces is needed. In addition, by estimates for the fractional heat kernels, we prove that the solutions to the Camassa–Holm equations with nonlocal viscosity converge strongly as the filter parameter $$\alpha \rightarrow ~0$$ to solutions of the equations INSF.

Local controllability to stationary trajectories of a Burgers equation with nonlocal viscosity

This article studies the local controllability to trajectories of a Burgers equation with nonlocal viscosity. By linearization we are led to an equation with a non local term whose controllability properties are analyzed by using Fourier decomposition and biorthogonal techniques. Once the existence of controls is proved and the dependence of their norms with respect to the time is established for the linearized model, a fixed point method allows us to deduce the result for the nonlinear initial problem.

Investigation of model parameters for high-resolution wind energy forecasting: Case studies over simple and complex terrain

Wind power forecasting, turbine micrositing, and turbine design require high-resolution simulations of atmospheric flow. Case studies at two West Coast North American wind farms, one with simple and one with complex terrain, are explored using the Weather Research and Forecasting (WRF) model. Both synoptically and locally driven events that include some ramping are considered. The performance of the model with different grid nesting configurations, turbulence closures, and grid resolutions is investigated through comparisons with observation data. For the simple terrain site, no significant improvement in the simulation results is found when using higher resolution. In contrast, for the complex terrain site, there is significant improvement when using higher resolution, but only during the locally driven event. This suggests the possibility that computational resources could be spared under certain conditions, for example when the topography is adequately resolved at coarser resolutions. Physical parameters such as soil moisture have a very large effect, but mostly for the locally forced events for both simple and complex terrain. The effect of the PBL scheme choice varies significantly depending on the meteorological forcing and terrain. On average, prognostic TKE equation schemes perform better than non-local eddy viscosity schemes.

Nonlocal viscosity kernel of mixtures

In this Brief Report we investigate the multiscale hydrodynamical response of a liquid as a function of mixture composition. This is done via a series of molecular dynamics simulations in which the wave-vector-dependent viscosity kernel is computed for three mixtures, each with 7-15 different compositions. We observe that the viscosity kernel is dependent on composition for simple atomic mixtures for all the wave vectors studied here; however, for a molecular mixture the kernel is independent of composition for large wave vectors. The deviation from ideal mixing is also studied. Here it is shown that the Lorentz-Berthelot interaction rule follows ideal mixing surprisingly well for a large range of wave vectors, whereas for both the Kob-Andersen and molecular mixtures large deviations are found. Furthermore, for the molecular system the deviation is wave-vector dependent such that there exists a characteristic correlation length scale at which the ideal mixing goes from underestimating to overestimating the viscosity.

Continuous Dependence Estimates for Nonlinear Fractional Convection-diffusion Equations

We develop a general framework for finding error estimates for convection-diffusion equations with nonlocal, nonlinear, and possibly degenerate diffusion terms. The equations are nonlocal because they involve fractional diffusion operators that are generators of pure jump Levy processes (e.g. the fractional Laplacian). As an application, we derive continuous dependence estimates on the nonlinearities and on the Levy measure of the diffusion term. Estimates of the rates of convergence for general nonlinear nonlocal vanishing viscosity approximations of scalar conservation laws then follow as a corollary. Our results both cover, and extend to new equations, a large part of the known error estimates in the literature.

Nonlocal viscosity of polymer melts approaching their glassy state

The nonlocal viscosity kernels of polymer melts have been determined by means of equilibrium molecular dynamics upon cooling toward the glass transition. Previous results for the temperature dependence of the self-diffusion coefficient and the value of the glass transition temperature are confirmed. We find that it is essential to include the attractive part of the interatomic potential in order to observe a strong glass transition. The width of the reciprocal space kernel decreases dramatically near the glass transition, being described by a deltalike function near and below the glass transition, leading to a very broad kernel in physical space. Thus, spatial nonlocality turns out to play an important role in polymeric fluids at temperatures near the glass transition temperature.