Initial Velocity Profile Research Articles

On the Response of an Ionic Liquid to External Perturbations and the Calculation of Shear Viscosity

In this article, attention is directed to three related problems: (1) the response of the ionic liquid (IL) 1-hexyl-3-methylimidazolium chloride ([HMIM+][Cl-]) to different external perturbations, (2) the calculation of its shear viscosity, and (3) the investigation of the range of validity of linear response theory for these types of systems. For this purpose, we derive a set of equations linking bulk hydrodynamic predictions with microscopic simulations which are valid when linear response theory is applicable. As far as we are aware, this article reports results from the largest atomistic simulations ever performed on this liquid. Our study shows that even for systems with a box length as large as 0.03 mu the viscosities computed from perturbation frequencies compatible with this box size have not yet reached the bulk hydrodynamic limit. This is in sharp contrast with the case of other solvents such as water in which the hydrodynamic limit can be achieved by using perturbations on a length scale of typical molecular dynamics simulation box sizes. In order to achieve our goals, we comprehensively investigated how the IL relaxed upon weak external perturbations at different wavenumbers. We also studied the steady-state flow created by external shear acceleration fields. The short time behavior of instantaneous velocity profiles was compared with the results of linear response theory. The short time response appears to match the prediction from linear response theory, while the long time response deviates as the external field becomes stronger. From this study, the range on which a perturbation can be considered "weak" in the linear response sense can be established. The relaxation of initial velocity profiles was also examined and correlated to the decay of the transverse-current autocorrelation function. Even though none of our calculations reached the bulk hydrodynamic limit, we are able to make predictions for the shear viscosity of the bulk system at different temperatures which qualitatively agree with experimental data.

Validating CFD predictions of respiratory aerosol deposition: Effects of upstream transition and turbulence

A number of computational fluid dynamics (CFD) studies have explored local deposition patterns of inhaled aerosols in the respiratory tract. These studies have highlighted the effects of multiple physiologic, geometric, and particle characteristics on deposition. However, very few studies have reported local or sub-branch quantitative comparisons to in vitro particle deposition data. The objective of this study is to numerically investigate the effects of transition and turbulence on highly localized particle deposition in a respiratory double bifurcation model in order to quantitatively validate CFD results. To perform the validations, local comparisons have been made to a specific in vitro case study of 10 μm particles depositing in a model of respiratory generations G3–G5. To achieve this objective, two geometric cases have been considered. The first case includes only the double bifurcation model. The second case includes a portion of the experimental particle delivery geometry, where transitional flow is expected. To evaluate the effectiveness of two-equation turbulence models in this system, the flow field solutions have been computed using laminar, standard k – ω , and low Reynolds number (LRN) k – ω approximations. Results indicate that even though the Reynolds number remained below the critical limit required for full turbulence, transition and turbulence have a significant impact on the flow field and local particle deposition patterns. For the experimental case considered, turbulence impacted the local deposition of 10 μm particles primarily by influencing the initial velocity and particle profiles. As such, both the laminar and LRN k – ω flow models provided good local quantitative matches to the in vitro deposition data, provided that the correct initial particle profile was specified. Implications of this study include the need for local quantitative validations of particle deposition results, the importance of correct inlet conditions, and the need to consider upstream effects in experimental and computational studies of the respiratory tract. Applications of these results to realistic respiratory geometries will require consideration on upstream flow conditions in the lung, transient flow, and intermittent turbulent structures.

Controlling traffic flow near the transition to the synchronous flow phase

For constant incoming flow far upstream of a freeway on-ramp, the flow downstream (throughput) and the rate of merging are studied with simulations using a generalized optimal velocity model. For large enough merge rates, a transition to synchronous flow occurs and the throughput is reduced by 0.5–0.7 vehicle on average for each vehicle that merges. For smaller merge rates there is free flow on the freeway and the throughput is the sum of the merge rate and the flow upstream of the on-ramp. Thus, there is an optimum merge rate that maximizes the throughput for a given incoming flow rate. These results hold for a wide range of initial vehicle position and velocity profiles and for single- as well as double-lane freeways. The results show that the transition to synchronous flow is due to the dynamics of the merge process, rather than to a limitation on the capacity of the downstream portion of the freeway. As a consequence, a new on-ramp metering algorithm, which controls the merge rate to prevent the transition to synchronous flow and concomitantly to maximize flow, has been developed.

Modelling debris flows down general channels

Abstract. This paper is an extension of the single-phase cohesionless dry granular avalanche model over curved and twisted channels proposed by Pudasaini and Hutter (2003). It is a generalisation of the Savage and Hutter (1989, 1991) equations based on simple channel topography to a two-phase fluid-solid mixture of debris material. Important terms emerging from the correct treatment of the kinematic and dynamic boundary condition, and the variable basal topography are systematically taken into account. For vanishing fluid contribution and torsion-free channel topography our new model equations exactly degenerate to the previous Savage-Hutter model equations while such a degeneration was not possible by the Iverson and Denlinger (2001) model, which, in fact, also aimed to extend the Savage and Hutter model. The model equations of this paper have been rigorously derived; they include the effects of the curvature and torsion of the topography, generally for arbitrarily curved and twisted channels of variable channel width. The equations are put into a standard conservative form of partial differential equations. From these one can easily infer the importance and influence of the pore-fluid-pressure distribution in debris flow dynamics. The solid-phase is modelled by applying a Coulomb dry friction law whereas the fluid phase is assumed to be an incompressible Newtonian fluid. Input parameters of the equations are the internal and bed friction angles of the solid particles, the viscosity and volume fraction of the fluid, the total mixture density and the pore pressure distribution of the fluid at the bed. Given the bed topography and initial geometry and the initial velocity profile of the debris mixture, the model equations are able to describe the dynamics of the depth profile and bed parallel depth-averaged velocity distribution from the initial position to the final deposit. A shock capturing, total variation diminishing numerical scheme is implemented to solve the highly non-linear equations. Simulation results present the combined effects of curvature, torsion and pore pressure on the dynamics of the flow over a general basal topography. These simulation results reveal new physical insight of debris flows over such non-trivial topography. Model equations are applied to laboratory avalanche and debris-flow-flume tests. Very good agreement between the theory and experiments is established.

Thermocapillary control of rupture in thin viscous fluid sheets

We consider the evolution of a thin viscous fluid sheet subject to thermocapillary effects. Using a lubrication approximation we find, for symmetric interfacial deflections, coupled evolution equations for the interfacial profile, the streamwise component of the fluid velocity and the temperature variation along the surface. Initial temperature profiles change the initial flow field through Marangoni-induced shear stresses. These changes then lead to preferred conditions for rupture prescribed by the initial temperature distribution. We show that the time to rupture may be minimized by varying the phase difference between the initial velocity profile and the initial temperature profile. For sufficiently large temperature differences, the phase difference between the initial velocity and temperature profiles determines the rupture location.

Temporal deconvolution of the hydrogen coma I. A hybrid model

This paper describes a semi-analytical model, tentatively called the time-resolved model (TRM), for calculating the proper temporally resolved column density and Lyman-alpha intensity profiles of the extended cometary hydrogen coma, with potentially arbitrary number of photodissociation sources with different initial velocity profiles. The non-analytical part consists of a true 3D particle simulator whose results are used to obtain the necessary corrective parameters for the analytical, spherically symmetric formulas for the column density and intensity profiles. The hybrid approach provides a physically accurate and computationally effective method to recreate the extended coma profiles and supports a new analysis method that can provide hydrogen lifetime estimates and a much enhanced temporal resolution for the water production curve, for which a method is described. The ability to recreate the water production profile by different analysis methods is studied with a combination of real and simulated data. This is the first part of a two part publication with the second part dedicated to real data analysis.

Formation of voids in the Universe within the Lemaître-Tolman model

We develop models of void formation starting from a small initial fluctuation at recombination and growing to a realistic present day density profile in agreement with observations of voids. The model construction is an extension of previously developed algorithms for finding a Lemaitre-Tolman metric that evolves between two profiles of either density or velocity specified at two times. Of the 4 profiles of concern -- those of density and velocity at recombination and at the present day -- two can be specified and the other two follow from the derived model. We find that, in order to reproduce the present-day void density profiles, the initial velocity profile is more important than the initial density profile. Extrapolation of current CMB observations to the scales relevant to proto-voids is very uncertain. Even so, we find that it is very difficult to make both the initial density and velocity fluctuation amplitudes small enough, and still obtain a realistic void by today.

Effect of Initial Temperature Profile on Recovery Factor Computations

Effect of Initial Temperature Profile on Recovery Factor Computations

Analytical solutions for the nonlinear longitudinal drift compression (expansion) of intense charged particle beams

To achieve high focal spot intensities in heavy-ion fusion, the ion beam must be compressed longitudinally by factors of 10–100 before it is focused onto the target. The longitudinal compression is achieved by imposing an initial velocity profile tilt on the drifting beam. In this paper, the problem of longitudinal drift compression of intense charged-particle beams is solved analytically for the two important cases corresponding to a cold beam, and a pressure-dominated beam, using a one-dimensional warm-fluid model describing the longitudinal beam dynamics.

Asymptotic freeze-out of the perturbations generated inside a corrugated rarefaction wave

Based on previous work [J. G. Wouchuk and R. Carretero, Phys. Plasmas 10, 4237 (2003)], the conditions of asymptotic freeze-out of the ripples at the tail of a corrugated rarefaction wave are analyzed. The precise location of the freezing-out regions in the space of preshock parameters is tried, and an efficient algorithm for their determination is given. It is seen that asymptotic freeze-out can only happen for gases that have an isentropic exponent γ<γcr≈2.2913…. It is shown that the late time freeze-out of the ripple perturbations is correlated to the initial tangential velocity profile (at t=0+) inside the expansion fan.

Loop Density Enhancement by Nonlinear Magnetohydrodynamic Waves

We study the possibility that waves in coronal loops can produce density enhancements at loop tops. The mechanism involved is the ponderomotive force of standing magnetohydrodynamic (MHD) waves. We study the effect of large-amplitude waves in loops by first using a simple second-order one-dimensional MHD model for which analytical expressions are available. This simple model shows how Alfven waves can excite density fluctuations on slow timescales. Next, we solve the time-dependent nonlinear 2.5-dimensional MHD equations in an arcade model, in order to study the effect of nonuniform Alfven speed along the loop on large-amplitude waves. Finally, we solve the nonlinear three-dimensional MHD equations in a flux-tube configuration. Waves are launched by an initial transverse velocity profile in the loop, with footpoints fixed in the photosphere. We find that large initial disturbances produce a pressure imbalance along the loop, which results in an upflow from its legs. The accumulation of mass at the top of the oscillating loop can produce significant density enhancements for typical coronal conditions. In a later stage, the pressure gradient becomes dominant and inhibits the concentration of mass at the loop top. We find that oscillating loops observed by the EUV telescope on board TRACE on 1998 July 14 exhibit emission measure enhancements consistent with this mechanism.

Formation of a galaxy with a central black hole in the Lemaître-Tolman model

We construct two models of the formation a galaxy with a central black hole, starting from a small initial fluctuation at recombination. This is an application of previously developed methods to find a Lemaitre-Tolman model that evolves from a given initial density or velocity profile to a given final density profile. We show that the black hole itself could be either a collapsed object, or a non-vacuum generalisation of a full Schwarzschild-Kruskal-Szekeres wormhole. Particular attention is paid to the black hole's apparent and event horizons.

Magnetically Driven Accretion Flows in the Kerr Metric. I. Models and Overall Structure

This is the first in a series of papers that investigate the properties of accretion flows in the Kerr metric through three-dimensional, general relativistic magnetohydrodynamic simulations of tori with a near-Keplerian initial angular velocity profile. We study four models with increasing black hole spin, from a/M=0 to 0.998, for which the structural parameters of the initial tori are maintained nearly constant. The subsequent accretion flows arise self-consistently from stresses and turbulence created by the magnetorotational instability. We investigate the overall evolution and the late-time global structure in the resulting non-radiative accretion flows, including the magnetic fields within the disks, the properties of the flow in the plunging region, and the flux of conserved quantities into the black hole. Independent of black hole spin, the global structure is described in terms of five regions: the main disk body, the coronal envelope, the inner disk, consisting of an inner torus and plunging region, an evacuated axial funnel, and a bi-conical outflow confined to the corona-funnel boundary. We find evidence for lower accretion rates, stronger funnel-wall outflows, and increased stress in the near hole region with increasing black hole spin.

Comparisons of Initially Turbulent, Low-Velocity-Ratio Circular and Square Coaxial Jets

A qualitative and quantitative comparison between unforced flows emanating from equivalent geometries of axisymmetric (circular) and square coaxial nozzles is presented. The initial state of the jets is turbulent, as in nozzles relevant to practical applications. Flow visualization and velocity measurements were performed at a coflow-jet Reynolds number of 1.9 × 10 4 and at an inner-to-outer jet velocity ratio of 0.3. Scaling of mean velocity and turbulence profiles has been examined for the three shear layers formed in the near field of axisymmetric and square coaxial flows. Visualizations and local velocity measurements have indicated modest mixing enhancement when square nozzles are used compared to the axisymmetric ones, and this is largely attributed to differences in initial velocity profiles between these two configurations. Low-coherence, large-scale periodic structures were observed for both nozzle configurations in the midfield of the inner mixing region, which has wake characteristics

Effect of initial turbulence intensity and velocity profile on liquid jets for IFE beamline protection

Current designs for thick liquid protection of heavy ion inertial fusion reactors utilize banks of liquid jets and vortex flow tubes to protect sensitive beam line components from neutrons and debris following target explosions. These hydraulic protection systems have issues regarding their formation and flow characteristics that need to be further understood as part of the ongoing chamber technology program for IFE. In this paper, modeling and experimental observations and quantitative data for rectangular and circular jets are compared in an effort to illuminate the critical phenomena involved. For rectangular jets a variety of wave patterns have been observed owing to competing effects of turbulence, surface tension and boundary layer formation in nozzles. Modeling of these jet flows using a Large Eddy Simulation technique is a useful tool for understanding the various origin of these waves, and experimenting with techniques to control their behavior. Recommendations for nozzle designs within IFE constraints are presented based on the numerical simulations.

On the streamwise evolution of turbulent boundary layers in arbitrary pressure gradients

A new approach to the classic closure problem for turbulent boundary layers is presented. This involves, first, using the well-known mean-flow scaling laws such as the log law of the wall and the law of the wake of Coles (1956) together with the mean continuity and the mean momentum differential and integral equations. The important parameters governing the flow in the general non-equilibrium case are identified and are used for establishing a framework for closure. Initially closure is achieved here empirically and the potential for achieving closure in the future using the wall-wake attached eddy model of Perry & Marusic (1995) is outlined. Comparisons are made with experiments covering adverse-pressure-gradient flows in relaxing and developing states and flows approaching equilibrium sink flow. Mean velocity profiles, total shear stress and Reynolds stress profiles can be computed for different streamwise stations, given an initial upstream mean velocity profile and the streamwise variation of free-stream velocity. The attached eddy model of Perry & Marusic (1995) can then be utilized, with some refinement, to compute the remaining unknown quantities such as Reynolds normal stresses and associated spectra and cross-power spectra in the fully turbulent part of the flow.

Dynamics of monopolar vortices on a topographic beta-plane

The dynamics of a cyclonic monopolar vortex on a topographic beta-plane are studied experimentally and theoretically. Detailed measurements of the vortex structure are conducted using high-resolution quantitative velocity measurements. The initial velocity profiles were described in terms of a radius Rvm, maximum azimuthal velocity vθm, and a dimensionless parameter α which characterizes the steepness of the velocity profile. The initial direction of motion of the monopolar vortex is critically dependent on α and weakly dependent of the initial strength and size of the vortex: isolated vortices (α ∼ 3) move north, whereas non-isolated vortices characterized by α ∼ 1 move northwest. When the azimuthal velocity decays slowly with radial distance (α < 1.4), Rossby wave generation dominates the vortex dynamics and the translational speed of the vortex correlates with the Rossby wave speed. When the azimuthal velocity decays rapidly with radial distance (α > 1.4) the vortex is isolated and the translational speed is much slower than the Rossby wave speed. To interpret the effect of the vortex structure on the direction of motion, a mechanistic model is developed which includes the Rossby force and a lift force arising from circulation around the vortex, but does not include the effect of Rossby waves. The Rossby force results from the integrated effect of the Coriolis force on the vortex and drives the vortex north; the lift force is determined from the circulation around the vortex and drives the vortex west. Comparison with the experimental data reveals two regimes: α < 1.4, where the vortex dynamics are dominated by Rossby waves whereas for α > 1.4 Rossby waves are weak and favourable agreement is found with the mechanistic model.

Chromospheric Leakage of Alfvén Waves in Coronal Loops

The recently observed rapid damping of coronal loop oscillations generated discussion regarding the physical mechanism responsible for the damping, with the leakage into the chromosphere suggested as one of the possible mechanisms. I study the leakage of Alfven waves into the chromospheric footpoints of a coronal loop using the nonlinear viscoresistive 1.5-dimensional MHD model. The waves were launched by an initial transverse velocity profile in the loop. I find that the leakage time of long-wavelength transverse oscillations, such as the ones observed recently by the Transition Region and Coronal Explorer (TRACE), is 5 times longer than the observed damping time of the oscillations. For the loop recently observed by TRACE, I conclude that the observed damping of the long-wavelength oscillations is not due to leakage into the chromosphere. However, depending on particular chromospheric and coronal properties, chromospheric leakage may be significant in some events of coronal loop oscillations.

Singular flow dynamics in three space dimensions driven by advection

The initial value problem of an ideal, compressible fluid is investigated in three space dimensions (3D). Starting from a situation where the inertia terms dominate over the force terms in Euler’s equation we explore by means of the Lagrangian flow description the basic flow properties. Special attention is drawn to the appearance of singularities in the flow pattern at finite time. Classes of initial velocity profiles giving rise to collapses of density and vorticity are found. This paper, hence, furnishes evidence of focused singularities for coherent structures obeying the 3D Euler equation and applies to potential as well as vortex flows.

Low‐frequency oscillations and transport processes induced by multiscale transverse structures in the polar wind outflow: A three‐dimensional simulation

Multiscale transverse structures in the magnetic‐field‐aligned flows have been frequently observed in the auroral region by FAST and Freja satellites. A number of multiscale processes, such as broadband low‐frequency oscillations and various cross‐field transport effects are well correlated with these structures. To study these effects, we have used our three‐dimensional multifluid model with multiscale transverse inhomogeneities in the initial velocity profile. Self‐consistent generation of the low‐frequency mode driven by local transverse gradients in the field‐aligned ion flow and associated transport processes were simulated. Effects of particle interaction with the self‐consistent time‐dependent three‐dimensional wave potential have been modeled using a distribution of test particles. For typical polar wind conditions it has been found that even large‐scale (∼ 50 – 100 km) transverse inhomogeneities in the flow can generate low‐frequency oscillations that lead to significant flow modifications, cross‐field particle diffusion, and other transport effects. It has also been shown that even small‐amplitude (∼ 10 – 20%) short‐scale (∼ 10 km) modulations of the original large‐scale flow profile significantly increases low‐frequency mode generation and associated cross‐field transport, not only at the local spatial scales imposed by the modulations but also on global scales. Note that this wave‐induced cross‐field transport is not included in any of the global numerical models of the ionosphere, ionosphere‐thermosphere, or ionosphere‐polar wind. The simulation results indicate that the wave‐induced cross‐field transport not only affects the ion outflow rates but also leads to a significant broadening of particle phase‐space distribution and tranverse particle diffusion.