Nonlinear Inertial Effects Research Articles

Nonlinear inertia and its effect within an X-shaped mechanism – Part II: Nonlinear influences and experimental validations

In this study, the effects of nonlinear inertia are further investigated and verified with prototyping and experimental validation. The new inertia unit integrated within a well-designed X-shaped mechanism can produce 3 different typical nonlinear inertia forms which have different nonlinear influence on dynamic response. A critical parametric indicator (Ratio of Inertia) is thus proposed to identify and indicate different types of nonlinearities and a new performance assessment indicator (F-stability) is proposed to assess the performance improvement compared to different nonlinearity with respect to linear counterparts in a dynamic excitation sense. A method for testing different nonlinear inertia is also proposed. It is uniquely revealed that (a) the Ratio of Inertia can be well used to tune different types of inertia nonlinearities; (b) the symmetrical nonlinear inertia (HCHE-type) is generally better in vibration isolation with smaller peak/anti-peak values, peak/anti-peak frequencies (∼ 1 Hz and 3∼4Hz in our prototype), and faster decay rate (∼ -50dB/Dec with our prototype) but higher high-frequency transmissibility compared to the two asymmetric nonlinearities; (c) the nonlinear inertia contributes significantly to tune the interactive force between vibration source and object in the low frequency range (<10Hz in our prototype) and obviously helpful and robust to stronger excitations. All the theoretical analysis results are verified with our developed prototype. These results should for the first time provide a comprehensive and in-depth understanding of nonlinear inertia and its effects in different cases and thus definitely shed light on various engineering applications.

Dynamics and isolation performance of a vibration isolator with a yoke-type nonlinear inerter

Previous studies have shown that nonlinear inerters can achieve superior vibration suppression compared to linear inerters, such as broadening the effective frequency band of the vibration isolator. However, nonlinear inerters are typically implemented by incorporating linear inerters into nonlinear configurations, resulting in indirect configurations and extra connections. This study introduces a direct and simple way to realize a yoke-type nonlinear inerter by employing the Scotch yoke mechanism, which is named the Scotch yoke inerter (SYI). The primary contributions of this paper are introducing a concept about the physical realization of a nonlinear inerter capable of providing both apparent mass and nonlinear inertial effects and investigating the dynamic responses and isolation performances of a vibration isolator enhanced by the proposed nonlinear inerter. The working mechanism for how the proposed SYI generates the nonlinear inertia is introduced and a simple configuration that facilities the application of this nonlinear inerter is proposed. The mechanical model of the SYI is built to describe its inertial behavior using the Euler-Lagrange method. Then, the SYI is incorporated into a vibration isolator to improve its performances. The averaging method is adopted to obtain the analytical responses and dynamic characteristics of the isolator with SYI subjected to force excitation. The stability of this nonlinear isolator is analyzed, and numerical integration using the fourth-order Runge-Kutta method is employed to verify the analytical results. The isolation performance evaluation of the isolator with SYI is conducted through three indices including the peak dynamic displacement, peak force transmissibility and effective isolation frequency band. The mechanical behavior indicates that the SYI can successfully generate the apparent mass effect of an inerter and nonlinear inertial behavior. The analytical responses agree well with the numerical results for different parameters of the isolator with SYI, which verifies the analytical solutions. The use of SYI in the vibration isolator can bend the backbone curve to the low frequencies, which indicates the softening characteristic of the frequency response. The isolator with SYI demonstrates beneficial performances in terms of force transmissibility and effective isolation frequency band. It is concluded that the proposed SYI can be seen as an alternative nonlinear inerter and is beneficial for improving the performance of the vibration isolator.

Dynamics of curved domain walls in hard ferromagnets with nonlinear dissipative and inertial effects

This article investigates the field-driven motion of curved domain walls in ferromagnetic nanostructures under the framework of modified Landau–Lifshitz–Gilbert equation with inertial effects. The considered governing equation involves the torques arising from nonlinear dissipative (viscous and dry friction) and inertial effects. We study the most relevant dynamical features in the steady dynamical regime for the considered model by employing the reductive perturbation technique. Finally, we illustrate the results numerically for the various domain wall surfaces (plane, cylinder, and sphere) and discuss their physical significance. The results obtained here agree with the recent theoretical and experimental observations.

Dimples, jets and self-similarity in nonlinear capillary waves

Numerical studies of dimple and jet formation from a collapsing cavity often model the initial cavity shape as a truncated sphere, mimicking a bursting bubble. In this study, we present a minimal model containing only nonlinear inertial and capillary forces, which produces dimples and jets from a collapsing capillary wave trough. The trough in our simulation develops from a smooth initial perturbation, chosen to be an eigenmode to the linearised ${O}(\epsilon )$ problem ( $\epsilon$ is the non-dimensional amplitude). We explain the physical mechanism of dimple formation and demonstrate that, for moderate $\epsilon$ , the sharp dimple seen in simulations is well captured by the weakly nonlinear ${O}(\epsilon ^3)$ theory developed here. For $\epsilon \gg 1$ the regime is strongly nonlinear, spreading surface energy into many modes, and the precursor dimple now develops into a sharply rising jet. Here, simulations reveal a novel localised window (in space and time) where the jet evolves self-similarly following inviscid (Keller &amp; Miksis, SIAM J. Appl. Maths, vol. 43, issue 2, 1983, pp. 268–277) scales. We develop an analogy of this regime to a self-similar solution of the first kind, for linearised capillary waves. Our first-principles study demonstrates that, at sufficiently small scales, dimples and jets can form from radial inward focusing of capillary waves, and the formation of this may be described by a relatively simple model employing (nonlinear) inertial and capillary effects. Viscosity and gravity can, however, significantly influence the focusing process, either intensifying the singularity or weakening it (Walls et al., Phys. Rev. E, vol. 92, issue 2, 2015, 021002; Gordillo &amp; Rodríguez-Rodríguez, J. Fluid Mech., vol. 867, 2019, pp. 556–571). This leads, in particular, to critical values of Ohnesorge and Bond numbers, which cannot be obtained from our minimal model.

Static and Dynamic Nonlinear In-Plane Effect in the Response of a Cantilevered Plate With Tip Mass Load: Theory and Experiment

Abstract In this article, two nonlinear effects are investigated. One is the effect of the static stiffness nonlinearity in changing the linear dynamic natural frequency, and the other is the combination of nonlinear stiffness and nonlinear inertia effects in changing the nonlinear dynamic transient response due to a change in the initial release state of the system. A theoretical model has been developed for a cantilevered thin plate with a range of length-to-width ratio using beam theory and considering both stiffness and inertial nonlinearities in the model. Lagrange's equation was used to deduce nonlinear inertia and stiffness matrices for a modal representation. Some insights into how these nonlinear components influence the beam response are presented. Measurements with both a hammer test and also a release test of cantilevered thin plates were done using different configurations and tip mass values. Results from static and dynamic analyses using the linear and the nonlinear theoretical models show good agreement between theory and experiment for natural frequencies and the amplitude displacements versus time.

The effect of large-scale forcing on small-scale dynamics of incompressible turbulence

The subtle but crucial effects of large-scale forcing on the small-scale velocity-gradient (VG) dynamics is examined using direct numerical simulation (DNS) data of incompressible turbulence. The interplay among large-scale forcing, inertia, pressure and viscous effects is characterised as a function of local streamline geometry and VG magnitude (Frobenius norm). When conditioned on local topology, forcing: (i) counteracts inertial and viscous action in the strain-dominated nodal topologies; and (ii) balances pressure action in the rotation-dominated unstable focal topologies. Unexpectedly, forcing acts to reduce VG magnitudes in regions of strong dissipation. In these regions, forcing balances the non-local pressure effects whereas viscous action offsets the nonlinear inertial effects. In regions of very low dissipation, forcing combines with inertia and pressure effects to offset viscous action. With regard to the probability distribution of the normalised VG invariants, the primary role of forcing is to nullify certain features (dilatational probability currents) of inertia, pressure and viscous action. This results in the emergence of universal statistical features (solenoidal probability currents) that are determined largely by inertia–pressure–viscous interactions. These findings serve to enhance our understanding of small-scale processes in turbulence and guide VG model development.

Dynamic equations of motion for inextensible beams and plates

The large deflections of cantilevered beams and plates are modeled and discussed. Traditional nonlinear elastic models (e.g., that of von Karman) employ elastic restoring forces based on the effect of stretching on bending, and these are less applicable to cantilevers. Recent experimental work indicates that elastic cantilevers are subject to nonlinear inertial and stiffness effects. We review a recently established (quasilinear and nonlocal) cantilevered beam model, and consider some natural extensions to two dimensions -- namely, inextensible plates. Our principal configuration is that of a thin, isotropic, homogeneous rectangular plate, clamped on one edge and free on the remaining three. We proceed through the geometric and elastic modeling to obtain equations of motion via Hamilton's principle for the appropriately specified energies. We enforce {\em effective} inextensibility constraints through Lagrange multipliers. Multiple plate analogs of the established 1D model are obtained, based on various assumptions. For each plate model, we present the modeling hypotheses and the resulting equations of motion. It total, we present three distinct nonlinear partial differential equation models, and, additionally, describe a class of ``higher order" models. Each model has particular advantages and drawbacks for both mathematical and engineering analyses. We conclude with an in depth discussion and comparison of the various systems and some analytical problems.

Nonlinear electro-elastic dynamics of a hub–cantilever bimorph rotor structure

Dynamics of a rotating mini hub–bimorph structure excited by periodic torque supplied to the hub is studied in this paper. The mathematical model of the system is formulated by means of the extended Hamilton’s principle. In the analysis the nonlinear constitutive behaviour of the piezoceramic material is adopted based on experimental results published in literature. Moreover, nonlinear inertia effects related to the system rotation are taken into account. The derived system of three integro-partial differential equations represents the electro-mechanical behaviour of the beam (transverse displacement and transducer output voltage) and the hub rotation coordinate. The state equations are discretized and solved numerically around the first resonance zone for the system excited by a periodic torque supplied to the hub. The obtained response curves reveal strong softening behaviour with additional unstable solutions identified out of the resonance zones. Within the framework of the performed numerical simulations the impact of torque excitation amplitude, torque mean value, hub inertia and electrical load resistance on system behaviour is discussed. Finally, the responses of the system with parallel vs series connected transducers are compared.

Theory of Solutions for an Inextensible Cantilever

Recent equations of motion for the large deflections of a cantilevered elastic beam are analyzed. In the traditional theory of beam (and plate) large deflections, nonlinear restoring forces are due to the effect of stretching on bending; for an inextensible cantilever, the enforcement of arc-length preservation leads to quasilinear stiffness effects and inertial effects that are both nonlinear and nonlocal. For this model, smooth solutions are constructed via a spectral Galerkin approach. Additional compactness is needed to pass to the limit, and this is obtained through a complex procession of higher energy estimates. Uniqueness is obtained through a non-trivial decomposition of the nonlinearity. The confounding effects of nonlinear inertia are overcome via the addition of structural (Kelvin–Voigt) damping to the equations of motion. Local well-posedness of smooth solutions is shown first in the absence of nonlinear inertial effects, and then shown with these inertial effects present, taking into account structural damping. With damping in force, global-in-time, strong well-posedness result is obtained by achieving exponential decay for small data.

Bio-Inspired Vibration Isolation: Methodology and Design

AbstractVarious bio-inspired vibration isolators have been emerged in recent decades and applied successfully in the protection of sensitive components, improvement of operating comfort, enhancement of control accuracy, etc. They are generally developed by exploiting favorable nonlinearities in biological structures. The main contribution of this work is to provide a comprehensive review of recent studies on the bio-inspired isolators. The methodology of bio-inspired vibration isolation is proposed from the perspective of mechanics based on the elemental theory and design principles. The key isolation mechanisms are classified into three categories according to different dominant forces: stiffness adjustment mechanism, auxiliary mass mechanism, and damping mechanism, respectively. Some representative designs, performance analyses, and practical applications of each type of bio-inspired isolators are also provided. In bio-inspired isolators with variable stiffness, the inherent structural performances can be adjusted to deal with variation in external load. The auxiliary mass mechanism utilizes nonlinear inertial effects to achieve ultralow frequency vibration isolation. Unique damping mechanism of bio-inspired structures is often studied to protect devices and equipment from impact loads. Bio-inspired vibration methods can also be applied in active/semi-active control systems with advantages of low energy consumption and high robustness. Finally, the review ends with conclusions, which highlight resolved and unresolved issues and provide a brief outlook on future perspectives. This review aims to give a comprehensive understanding of bio-inspired isolation mechanism. It also provides guidance on designing new bio-inspired isolators for improving their vibration isolation performance.

Breakup of a leaky dielectric drop in a uniform electric field.

Electrohydrodynamic (EHD) breakup phenomena for a leaky dielectric drop suspended in another immiscible viscous dielectric and subjected to a uniform electric field are examined using the leaky dielectric theory and the explicit forcing lattice Boltzmann method, by taking into account full nonlinear inertia effects. The breakup modes are first computed for varied conductivity of the drop fluid, as the viscosity ratio λ (=μ_{in}/μ_{out}) is momentarily set to unity, that is, for the slightly conducting (R=σ_{in}/σ_{out}<10), moderately conducting (10≤R≤20), and highly conducting (R>20) cases. For slightly conducting drops (R=5) only one breakup mode via two symmetrical necks persists for permittivity ratios 0.05<Q=ɛ_{in}/ɛ_{out}<3.0 and electric capillary number Ca_{E}>Ca_{E,critical} (ratio of electric and surface tension forces), despite significant length-scale variation of mother and daughter drops. At higher Q (for increased drop permittivity) two necks move closer to the bulbous midpart of the extended droplet, which helps enlarge two daughter drops. However, in the case of moderately conducting drops (10≤R≤20) the number of necks increased to four for increased Ca_{E}. Accordingly two pairs of symmetrical daughter drops are created because of recurrent fluctuations of the electrical shear stress and centerline momentum flux. For highly conducting cases of R>20, depending on Ca_{E}, three distinctly elongated droplet states are formed prior to breakup, which results in the onset of three different breakup modes, namely, via formations of lobed ends (Ca_{E}≤0.264), pointed ends (Ca_{E}≤0.68), and nonpointed ends (Ca_{E}>0.83). While being consistent with past measurements, here we precisely characterize the associated breakup mechanisms and physics in terms of the interactive electric pressure, electric shear stress, and hydrodynamic pressure plus velocity gradients. Since the EHD drop breakup is a dynamic process, on an elongated slender drop the activated locally distinct driving forces, i.e., electric pressure at the end regions and tangential electric stress in the midsection, effectively lead to neck formations by virtue of the created high centerline velocity gradient. Accordingly, resulting variations of local extension rate and net mass flux toward drop ends or into intermediate bulbous regions facilitate the multiple-mode drop breakup via the inertia effect, whereas the developed negative curvature around a neck encourages capillary breakup. We also explicitly reveal the effect of the viscosity contrast λ, which particularly influences the breakup characteristics over a broader range of conductivity ratios.

Transverse to longitudinal mode conversion via nonlinear inertial effects in a locally resonant metamaterial plate

Acoustic and elastic metamaterials have potential for tailoring wave propagation in ways beyond the capabilities of conventional materials and have been shown to exhibit a myriad of rich dynamical effects, such as negative effective properties, cloaking, extreme damping, and non-reciprocity. However, most of the existing literature has been focused on linear dynamics in which these behaviors are restricted to narrow frequency bands. More recently, nonlinearity has been investigated as a method of increasing this bandwidth, as well as a means to broaden the palette of available dynamics. Past studies on nonlinear acoustic and elastic metamaterials have demonstrated effects not easily accessible in the linear regime, including harmonic generation, mode hopping and conversion, tunable band gaps, chaos, and intrinsic localized modes. In this work, we present a model for a nonlinear elastic plate metamaterial that exhibits mode conversion between transverse and longitudinal waves. The mode conversion is enabled by cantilevered beam attachments undergoing large-angle out-of-plane oscillations. By analyzing the unit cell of this locally-resonant plate, we interpret the transverse-longitudinal coupling as a nonlinear, anisotropic effective mass density. The mode conversion effect is demonstrated via direct numerical simulations. [Work supported by NSF and ARL:UT.]

On transcritical states in viscous flow passing the edge of a horizontal plate

AbstractThis contribution puts forward some recent advances in the rigorous (asymptotic) theory of gravity‐ (and capillarity‐)driven shallow flow of a viscous liquid past a horizontal plate, originating in jet impingement oblique to it. Hence, our concern is twofold: with steady developed flow over the distance from the jet centre to the trailing edge of the plate, referred to as a pronounced hydraulic jump blurred by viscous diffusion; with the predominantly inviscid transcritical limit arising near the edge due to scale reduction given an intrinsic expansive singularity taking place there. In the latter situation envisaged briefly, condensing nonlinear inertial effects, weak time dependence, and (very) weak streamline curvature as the essential ingredients into a distinguished limit demonstrates the generation of a weak (transcritical) hydraulic jump by a plate‐mounted obstacle. (© 2017 Wiley‐VCH Verlag GmbH &amp; Co. KGaA, Weinheim)

Integration of geometry and analysis for the study of liquid sloshing in railroad vehicle dynamics

A new continuum-based liquid sloshing approach that accounts for the effect of complex fluid and tank-car geometry on railroad vehicle dynamics is developed in this investigation. A unified geometry/analysis mesh is used from the outset to examine the effect of liquid sloshing on railroad vehicle dynamics during curve negotiation and during the application of electronically controlled pneumatic (ECP) brakes that produce braking forces uniformly and simultaneously across all cars. Using a non-modal approach, the geometry of the tank-car and fluid is accurately defined, a continuum-based fluid constitutive model is employed, and a fluid-tank contact algorithm is developed. The liquid sloshing model is integrated with a three-dimensional multibody system (MBS) railroad vehicle algorithm which accounts for the nonlinear wheel/rail contact. The three-dimensional wheel/rail contact force formulation used in this study accounts for the longitudinal, lateral, and spin creep forces that influence the vehicle stability. In order to examine the effect of the liquid sloshing on the railroad vehicle dynamics during curve negotiation, a general and precise definition of the outward inertia force is defined, and in order to correctly capture the fluid and tank-car geometry, the absolute nodal coordinate formulation (ANCF) is used. The balance speed and centrifugal effects in the case of tank-car partially filled with liquid are studied and compared with the equivalent rigid body model in curve negotiation and braking scenarios. In particular, the results obtained in the case of the ECP brake application of two freight car model are compared with the results obtained when using conventional braking. The traction analysis shows that liquid sloshing has a significant effect on the load distribution between the front and rear trucks. A larger coupler force develops when using conventional braking compared with ECP braking, and the liquid sloshing contributes to amplifying the coupler force in the ECP braking case compared to the equivalent rigid body model which does not capture the fluid nonlinear inertia effects. Furthermore, the results obtained in this study show that liquid sloshing can exacerbate the unbalance effects when the rail vehicle negotiates a curve at a velocity higher than the balance speed.

Linear Versus Nonlinear Response of a Cantilevered Beam Under Harmonic Base Excitation: Theory and Experiment

A computational and experimental study of a uniform cantilever beam with a tip mass under base excitation was performed. The beam was excited at various levels of base displacement to provoke tip displacements greater than 15% of the beam length. Damping and yield stress of the beam were both considered. It was found that a large tip displacement causes nonlinear inertial (NLI) and structural (NLS) effects to arise. Each of the structural and inertial nonlinearities has an opposite effect on the resulting resonance frequency, which are nearly mutually canceling. The result was that resonant frequency calculated using the full nonlinear (FNL) model was essentially equal to the value calculated by linear (LIN) theory, and the tip displacement amplitude varied only modestly from the LIN value. It was also observed that the damping in this system is likely nonlinear, and depends on tip displacement amplitude. A theoretical model for fluid damping is suggested. Initial investigation shows encouraging agreement between the theoretical fluid damping and the measured values.

Electrohydrodynamics of a viscous drop with inertia.

Most of the existing numerical and theoretical investigations on the electrohydrodynamics of a viscous drop have focused on the creeping Stokes flow regime, where nonlinear inertia effects are neglected. In this work we study the inertia effects on the electrodeformation of a viscous drop under a DC electric field using a novel second-order immersed interface method. The inertia effects are quantified by the Ohnesorge number Oh, and the electric field is characterized by an electric capillary number Ca_{E}. Below the critical Ca_{E}, small to moderate electric field strength gives rise to steady equilibrium drop shapes. We found that, at a fixed Ca_{E}, inertia effects induce larger deformation for an oblate drop than a prolate drop, consistent with previous results in the literature. Moreover, our simulations results indicate that inertia effects on the equilibrium drop deformation are dictated by the direction of normal electric stress on the drop interface: Larger drop deformation is found when the normal electric stress points outward, and smaller drop deformation is found otherwise. To our knowledge, such inertia effects on the equilibrium drop deformation has not been reported in the literature. Above the critical Ca_{E}, no steady equilibrium drop deformation can be found, and often the drop breaks up into a number of daughter droplets. In particular, our Navier-Stokes simulations show that, for the parameters we use, (1) daughter droplets are larger in the presence of inertia, (2) the drop deformation evolves more rapidly compared to creeping flow, and (3) complex distribution of electric stresses for drops with inertia effects. Our results suggest that normal electric pressure may be a useful tool in predicting drop pinch-off in oblate deformations.

On inertia nonlinearity in irregular-plan isolated structures under seismic excitations

The influence of nonlinear inertia as a function of acceleration, velocity, and displacement is investigated for an asymmetric isolated structure. Six degrees of freedom (6-DOFs) are defined to illustrate translational and rotational displacements of the superstructure and base isolation. Motion equations of such DOFs are derived using the Lagrangian formalism. Two coordinate systems of the reference are defined, one fixed on the building base (global coordinate) and the other at the torsional isolation level (local coordinate). The motion governing equations in the conventional approach is formulated on a linear form in the global coordinate system, whereas in the novel approach, the local coordinate system leads to a nonlinear form of dynamic equations. The difference between two linear and nonlinear models is appeared because of the existence of nonlinear inertia terms just in the nonlinear one. Afterwards, three particular types of isolated structures are employed with the peculiar ratio of torsional–lateral coupled frequency on symmetric frequency. Numerical analysis is applied to investigate the performance of two structural models by exerting harmonic excitations and earthquakes. The results are obtained while analyzing time history and frequency content and show that the coupling effects of nonlinear inertia lead to differences in the responses of linear and nonlinear models of such structures; also, some nonlinear phenomena such as energy transfer between modes, saturation, rigid displacement, and super-harmonic created due to geometrical (inertial) nonlinearities are studied.

An Immersed Interface Method for Axisymmetric Electrohydrodynamic Simulations in Stokes flow

AbstractA numerical scheme based on the immersed interface method (IIM) is developed to simulate the dynamics of an axisymmetric viscous drop under an electric field. In this work, the IIM is used to solve both the fluid velocity field and the electric potential field. Detailed numerical studies on the numerical scheme show a second-order convergence. Moreover, our numerical scheme is validated by the good agreement with previous analytical models, and numerical results from the boundary integral simulations. Our method can be extended to Navier-Stokes fluid flow with nonlinear inertia effects.

Inertial effects at moderate Reynolds number in thin-film rimming flows driven by surface shear

In this paper, we study two-dimensional thin-film flow inside a stationary circular cylinder driven by an imposed surface shear stress. Modelling is motivated by a need to understand the cooling and film dynamics provided by oil films in an aero-engine bearing chamber characterised by conditions of very high surface shear and additional film mass flux from oil droplets entering the film through the surface. In typical high-speed operation, film inertial effects can provide a significant leading-order mechanism neglected in existing lubrication theory models. Inertia at leading-order is included within a depth-averaged formulation where wall friction is evaluated similar to hydraulic models. This allows key nonlinear inertial effects to be included while retaining the ability to analyse the problem in a mathematically tractable formulation and compare with other approaches. In constructing this model, a set of simplified mass and momentum equations are integrated through the depth of the film yielding a spatially one-dimensional depth-averaged formulation of the problem. An a priori assumed form of velocity profile is needed to complete the system. In a local Stokes flow analysis, a quadratic profile is the exact solution for the velocity field though it must be modified when inertial effects become important. Extension of the velocity profile to a cubic profile is selected enabling specification of a wall friction model to include the roughness of the cylinder wall. A modelling advantage of including the inertia term, relevant to the applications considered, is that a smooth progression in solution can be obtained between cases of low Reynolds number corresponding to lubrication theory, and high Reynolds number corresponding to uniform rimming-flow. Importantly, we also investigate the effect of inertia on some typical solutions from other studies and present a greater insight to existing and new film solutions which arise from including inertia effects.

Non-linear effects on solute transfer between flowing water and a sediment bed

A previously developed model of periodic pore water flow in space and time, and associated solute transport in a stream bed of fine sand is extended to coarse sand and fine gravel. The pore water flow immediately below the sediment/water interface becomes intermittently a non-Darcy flow. The periodic pressure and velocity fluctuations considered are induced by near-bed coherent turbulent motions in the stream flow; they penetrate from the sediment/water interface into the sediment pore system and are described by a wave number (χ) and a period ( T) that are given as functions of the shear velocity ( U ∗) between the flowing water and the sediment bed. The stream bed has a flat surface without bed forms. The flow field in the sediment pore system is described by the continuity equation and a resistance law that includes both viscous (Darcy) and non-linear (inertial) effects. Simulation results show that non-linear (inertial) effects near the sediment/water interface increase flow resistance and reduce mean flow velocities. Compared to pure Darcy flow, non-linear (inertial) effects reduce solute exchange rates between overlying water and the sediment bed but only by a moderate amount (less than 50%). Turbulent coherent flow structures in the stream flow enhance solute transfer in the pore system of a stream bed compared to pure molecular diffusion, but by much less than standing surface waves or bed forms.