Effect Of Density Gradient Research Articles

The effect of density gradient on boundary flow

Based on Prandtl's mixing-length theory, this study proposes new theoretical formulae of velocity profiles resulting from the forcing by a constant horizontal buoyancy gradient in unstratified and stably stratified flows. Based on the one-dimensional water column momentum equation, the vertical turbulent shearing stress profile is found to deviate from a linear distribution and follow a parabolic distribution, differing from that in neutral flow. The shearing stress curves upward with the current following the density gradient, and curves downward with the currents opposite to the density gradient. For a constant eddy viscosity, the well-known estuarine circulation is obtained through the parabolic shearing distribution. For a vertically parabolic eddy viscosity, the new-proposed velocity profile by Burchard & Hetland (2010) is obtained. In this paper, we estimate the viscosity profile based on Prandtl's mixing-length theory and then derive the new formulae of the velocity profiles. Through comparison with the numerical turbulence model, the velocity profiles presented in the paper agree well with the numerical results. In addition, the new velocity profiles can be applied to determine the valid range and evaluate errors of the log-fit in baroclinic boundary flows.

Magnetorotational stability in a self-consistent three dimensional axisymmetric magnetized warm plasma equilibrium with a gravitational field

Magnetorotational stability is revisited for self-consistent three-dimensional magnetized hot plasma equilibria in a gravitational field. The eikonal analysis presented finds that magnetorotational stability analysis must be performed with some care to retain compressibility and density gradient effects, and departures from strict Keplerian motion. Indeed, retaining these effects highlights differences between the magnetorotational instability found in the absence of gravity (Velikhov, Sov. Phys. JETP, vol. 36, 1959, pp. 995–998) and that found the presence of gravity (Balbus & Hawley, Astrophys. J., vol. 376, 1991, pp. 214–222). In the non-gravitational case, compressibility and density variation alter the stability condition, while these effects only enter for departures from strict Keplerian motion in a gravitational field. The conditions for instability are made more precise by employing recent magnetized equilibrium results (Catto et al., J. Plasma Phys., vol. 81, 2015, 515810603), rather than employing a hydrodynamic equilibrium. We focus on the stability of the $\unicode[STIX]{x1D6FD}>1$ limit for which equilibria were found in the absence of a toroidal magnetic field, where $\unicode[STIX]{x1D6FD}=$ plasma/magnetic pressure.

Coupled effect of viscosity and density gradients on fingering instabilities of a miscible slice in porous media

Miscible displacements in porous media exhibit interesting spatio-temporal patterns. A deeper understanding of the physical mechanisms of these emergent patterns is relevant in a number of physicochemical processes. Here, we have numerically investigated the instabilities in a miscible slice in vertical porous media. Depending on the viscosity and density gradients at the two interfaces, four distinct flow configurations are obtained, which are partitioned into two different groups, each containing a pair of equivalent flows until the interaction between the two interfaces. An analysis of the pressure drop around the respective unstable interface(s) supports numerical results. We classify the stabilizing and destabilizing scenarios in a parameter space spanned by the log-mobility ratio (R) and the displacement velocity (U). When the viscosity and density gradients are unstably stratified at the opposite interfaces, the stability characteristics are very complex. The most notable findings of this paper are the existence of a stable region between two unstable regions in the R–U plane and occurrence of secondary instabilities. We further show that the stability regions in the R–U plane depend strongly on the slice width, and beyond a threshold value of it the stable zone remains almost unaltered. For thin sample, the stable region expands and the secondary instabilities disappear.

Mitigating the hosing instability in relativistic laser-plasma interactions

A new physical model of the hosing instability that includes relativistic laser pulses and moderate densities is presented and derives the density dependence of the hosing equation. This is tested against two-dimensional particle-in-cell simulations. These simulations further examine the feasibility of using multiple pulses to mitigate the hosing instability in a Nd:glass-type parameter space. An examination of the effects of planar versus cylindrical exponential density gradients on the hosing instability is also presented. The results show that strongly relativistic pulses and more planar geometries are capable of mitigating the hosing instability which is in line with the predictions of the physical model.

Analytical and numerical study of the transverse Kelvin–Helmholtz instability in tokamak edge plasmas

Sheared flows perpendicular to the magnetic field can be driven by the Reynolds stress or ion pressure gradient effects and can potentially influence the stability and turbulent saturation level of edge plasma modes. On the other hand, such flows are subject to the transverse Kelvin–Helmholtz (KH) instability. Here, the linear theory of KH instabilities is first addressed with an analytic model in the asymptotic limit of long wavelengths compared with the flow scale length. The analytic model treats sheared $\boldsymbol{E}\times \boldsymbol{B}$ flows, ion diamagnetism (including gyro-viscous terms), density gradients and parallel currents in a slab geometry, enabling a unified summary that encompasses and extends previous results. In particular, while ion diamagnetism, density gradients and parallel currents each individually reduce KH growth rates, the combined effect of density and ion pressure gradients is more complicated and partially counteracting. Secondly, the important role of realistic toroidal geometry is explored numerically using an invariant scaling analysis together with the 2DX eigenvalue code to examine KH modes in both closed and open field line regions. For a typical spherical torus magnetic geometry, it is found that KH modes are more unstable at, and just outside of, the separatrix as a result of the distribution of magnetic shear. Finally implications for reduced edge turbulence modelling codes are discussed.

Rayleigh-Taylor instability in non-uniform magnetized rotating strongly coupled viscoelastic fluid

The Rayleigh-Taylor instability (RTI) in an incompressible strongly coupled viscoelastic fluid is investigated considering the effects of inhomogeneous magnetic field, density gradient, and uniform rotation. The generalized hydrodynamic equations have been formulated, and linear dispersion relation is derived taking appropriate density and magnetic field profiles for the considered system. The gravity induced stable and unstable configurations of RTI are analyzed in hydrodynamic and kinetic limits. In the kinetic limit, shear wave modified dispersion relation and the condition of RTI are derived in terms of magnetic-viscoelastic Mach number and viscoelastic Froude number. The criteria of RTI and critical wavenumber for the growth of RTI to be unstable are estimated numerically for white dwarf and inertial confinement fusion target. It is observed that magnetic field, rotation, and viscoelastic effects play a significant role in the suppression of RTI in these systems. The stabilizing influence of magnetic field, rotation, and magnetic-viscoelastic Mach number while the destabilizing influence of viscoelastic Froude on the growth rate of RTI number is observed graphically. The growth rate of RTI decreases faster in kinetic limit as compared to the hydrodynamic limit.

Stabilization of electron-scale turbulence by electron density gradient in national spherical torus experiment

Theory and experiments have shown that electron temperature gradient (ETG) turbulence on the electron gyro-scale, k⊥ρe ≲ 1, can be responsible for anomalous electron thermal transport in NSTX. Electron scale (high-k) turbulence is diagnosed in NSTX with a high-k microwave scattering system [D. R. Smith et al., Rev. Sci. Instrum. 79, 123501 (2008)]. Here we report on stabilization effects of the electron density gradient on electron-scale density fluctuations in a set of neutral beam injection heated H-mode plasmas. We found that the absence of high-k density fluctuations from measurements is correlated with large equilibrium density gradient, which is shown to be consistent with linear stabilization of ETG modes due to the density gradient using the analytical ETG linear threshold in F. Jenko et al. [Phys. Plasmas 8, 4096 (2001)] and linear gyrokinetic simulations with GS2 [M. Kotschenreuther et al., Comput. Phys. Commun. 88, 128 (1995)]. We also found that the observed power of electron-scale turbulence (when it exists) is anti-correlated with the equilibrium density gradient, suggesting density gradient as a nonlinear stabilizing mechanism. Higher density gradients give rise to lower values of the plasma frame frequency, calculated based on the Doppler shift of the measured density fluctuations. Linear gyrokinetic simulations show that higher values of the electron density gradient reduce the value of the real frequency, in agreement with experimental observation. Nonlinear electron-scale gyrokinetic simulations show that high electron density gradient reduces electron heat flux and stiffness, and increases the ETG nonlinear threshold, consistent with experimental observations.

Experimental study on fundamental phenomena in HTGR small break air-ingress accident

This study experimentally investigates fundamental phenomena in the HTGR small break air-ingress accident. Several important parameters including density ratio, break angle, break size, and main flow velocity are considered in the measurement and the analysis. The test-section is made of a circular pipe with small holes drilled around the surface and it is installed in the helium/air flow circulation loop. Oxygen concentrations and flow rates are recorded during the tests with fixed break angles, break sizes, and flow velocities for measurement of the air-ingress rates. According to the experimental results, the higher density difference leads to the higher rates of air-ingress with large sensitivity of the break angles. It is also found that the break angle significantly affects the air-ingress rates, which is gradually increased from 0° to 120° and suddenly decreased to 180°. The minimum air ingress rate is found at 0° and the maximum, at 110°. The air-ingress rate increases with the break size due to the increased flow-exchange area. However, it is not directly proportional to the break area due to the complexity of the phenomena. The increased flow velocity in the channel inside enhances the air-ingress process. However, among all the parameters, the main flow velocity exhibits the lowest effect on this process. In this study, the Froude Number relevant to the small break air-ingress conditions are newly defined considering both heavy and light fluids, and break angles. Based on this definition, the experimental data can be well re-arranged and collected. Finally, this study develops and proposes a non-dimensional parameter and a criteria for determination of the small break air-ingress flow regimes. As a result, the non-dimensional parameter higher than 0.49 indicates that the air-ingress is mainly controlled by density gradient effect. On the other hand, that lower than 0.47 indicates that the other effects such as inertia or diffusion are dominant air-ingress mechanisms.

Elastic bone-column buckling including bone density gradient effect within the context of adaptive elasticity

ObjectivesOur main goal is to improve, from theoretical point of view, the mechanistic understanding of bone buckling failure which is known as at the core of important clinical problems such as osteoporosis. Material and methodsWhat is well argued is that in older bone, stability-initiated failure dominates because of the instability of the individual trabeculae which is prone to inelastic buckling at stresses far less than expected for strength-based failure. Taking advantage of our previous work, an improved original Euler's adaptive-beam buckling equation incorporating density gradient effect is investigated. ResultsFor one, we indicate that resorption can leads to new elastic instabilities that can conduct to bone-buckling mechanism of fracture. For another, we demonstrate that bone density gradient play a key role in the initiation of the bone-column elastic buckling instability. ConclusionAs a result, it is clearly stated here that firstly, the number of these elastic instabilities which are potentially implied in the mechanisms of bone fracture, localized at the trabecular element scale, depends strongly upon the material parameter η and secondly; the bone density gradient affect notably the stability of the bone-column deflection.

The Role of the Collisions on the Weibel Instability Growth Rate in the Fast Ignition Scenario

In this paper, the effects of Coulomb elctron-ion collisions and plasma density gradient, $$\eta$$ , on the Weibel instability in inertial confinement fusion are investigated. The results are indicative that the corrected collision of Weibel instability growth rate of the relativistic region near the corona, $$\eta >0.3$$ , increases with increasing relativistic parameter, $$\upgamma$$ . Also, near the fuel core as $$\eta$$ goes down, the corrected collisional growth rate decreases with increasing $$\upgamma$$ for $$\mathrm{{\upgamma }}<6$$ and and increases with increasing $$\upgamma$$ for $$\upgamma >6$$ . Therefore, for $$\upgamma <6$$ , the effect of collision and fuel density gradient tend to stabilize the Weibel instability in fuel core, with the Weibel growth rate below the collisionless value. Also deposition condition of relativistic electron beam energy can be shifted to the fuel core for the suitable ignition.

Density Gradient Effect on the Non-Linear Spectrum of the Rayleigh–Taylor Instability

Nonlinear spectrum of the deceleration phase Rayleigh–Taylor instability (RTI) has been investigated in the inertial confinement fusion. Growth rate of the deceleration phase RTI has been expressed well in the form of $$ \upgamma_{\text{k}} =\upalpha_{2} \sqrt {\frac{\text{kg}}{{1 + {\text{kL}}_{\text{m}} }}} -\upbeta_{2} {\text{ku}}_{\text{a}} , $$ where α and β are constants. g, k, L m and u a are the target acceleration, the wave number, the finite density gradient scale length and the ablation velocity, respectively (Betti et al. in Phys Plasmas 5:1446, 1998). Analytically obtained results indicate that the mass power spectrum can be described as an inverse power law with an approximate spectral index of 2.3 in the limit of $$ {\text{kL}}_{0} \ll 1 $$ , where k is the wave number and L 0 is the ablation front thickness and we have shown that power-law slope for kL m ≫ 1 is the most that it is changing with k −4. Furthermore, it has been found that nonlinear power spectrum decreases slowly by increasing of the hot spot radius. Our obtained value is in agreement with theoretical findings (Keskinen et al. in Phys. Plasmas 14:012705, 2007).

Delayed settling of marine snow: Effects of density gradient and particle properties and implications for carbon cycling

Marine snow aggregates are often a dominant component of carbon flux and are sites of high bacterial activity; thus, small-scale changes in the settling behavior of marine snow can affect the vertical locations of carbon export and remineralization in the surface ocean. In this study, we experimentally investigated the sinking velocities of marine snow aggregates formed in roller tanks as they settled through sharp density gradients. We observed between 8 and 10 aggregates in 3 different experiments, each of which displayed delayed settling behavior — that is, a settling velocity minimum — as they crossed the density transitions. Characteristics of delayed settling behavior were also compared to density stratification and aggregate density and size; aggregate settling velocity decreased more, and for longer periods of time, when density gradients were sharper and when aggregates were less dense. The observed relationships between non-dimensional parameters and aggregate settling allow for direct application of our results to the field, providing insight into the conditions under which strong delayed settling behavior is likely to occur. Activities of extracellular enzymes (the initial step in microbial remineralization of organic matter) were more than an order of magnitude higher in the aggregates compared to the surrounding water from which the aggregates were derived. Coupling measured enzyme activities with observations of delayed settling behavior demonstrates that the extent as well as the vertical location of enzyme activity is strongly affected by aggregate settling behavior: total enzyme activity within the region of the density transition increased by a factor of 18 with increasing stratification. This study, which combines direct measurements of small-scale aggregate settling and microbial enzyme activity, offers an opportunity to determine the potential implications of delayed settling behavior for local and larger-scale carbon cycling in the ocean.

Prolonged river water pollution due to variable‐density flow and solute transport in the riverbed

AbstractA laboratory experiment and numerical modeling were used to examine effects of density gradients on hyporheic flow and solute transport under the condition of a solute pulse input to a river with regular bed forms. Relatively low‐density gradients due to an initial salt pulse concentration of 1.55 kg m−3 applied in the experiment were found to modulate significantly the pore‐water flow and solute transport in the riverbed. Such density gradients increased downward flow and solute transport in the riverbed by factors up to 1.6. This resulted in a 12.2% increase in the total salt transfer from the water column to the riverbed over the salt pulse period. As the solute pulse passed, the effect of the density gradients reversed, slowing down the release of the solute back to the river water by a factor of 3.7. Numerical modeling indicated that these density effects intensified as salt concentrations in the water column increased. Simulations further showed that the density gradients might even lead to unstable flow and result in solute fingers in the bed of large bed forms. The slow release of solute from the bed back to the river led to a long tail of solute concentration in the river water. These findings have implications for assessment of impact of pollution events on river systems, in particular, long‐term effects on both the river water and riverbed due to the hyporheic exchange.

The Quantum Effects Role on Weibel Instability Growth Rate in Dense Plasma

The Weibel instability is one of the basic plasma instabilities that plays an important role in stopping the hot electrons and energy deposition mechanism. In this paper, combined effect of the density gradient and quantum effects on Weibel instability growth rate is investigated. The results have shown that, by increasing the quantum parameter, for large wavelengths, the Weibel instability growth rate shrinks to zero. In the large wavelengths limit, the analysis shows that quantum effects and density gradient tend to stabilize the Weibel instability. The density perturbations have decreased the growth rate of Weibel instability in the near corona fuel,η&gt;0.1. In the small wavelengths limit, for the density gradient,η&lt;0.1, the tunneling quantum effects increase anisotropy in the phase space. The quantum tunneling effect leads to an unexpected increase in the Weibel instability growth rate.

Publisher's Note: “The effect of density gradient on the growth rate of relativistic Weibel instability” [Phys. Plasmas 21, 022707 (2014)

Publisher's Note: “The effect of density gradient on the growth rate of relativistic Weibel instability” [Phys. Plasmas <b>21</b>, 022707 (2014)

Novel Design of Multi-Purpose Probe for the Measurement of Plasma Density Gradient, Flow and Transport

We have designed, constructed and installed a multi-purpose probe (MPP) for the measurements of plasma density gradient, flow and turbulent transport in edge plasma of IR-T1 tokamak. Moreover, the effects of radial density gradient and parallel flow on turbulent transport have been investigated. The radial gradient density and the parallel flow variation were measured by the electrical part of MPP. The probability distribution function and the expected value between turbulence, density and parallel flow have been computed.

Growth partitioning in forest stands is affected by stand density and summer drought in sessile oak and Douglas-fir

Context: Growth partitioning among trees in forest stands is pivotal to silviculture, making it crucial to understand its control by factors such as stand development, stand density, or thinning. Since growth partitioning primarily depends on the partitioning of environmental resources among individuals, climatic change further calls for extending this framework to explicit climatic factors. Recent debate on adapting management to such changes also requires larger density gradients to be encompassed. Methods: We primarily aimed to investigate the effects of stand density and climatic factors on growth partitioning, in even-aged stands of sessile oak and Douglas-fir, two species currently managed under contrasted silvicultural regimes. We used two original permanent plot networks designed to explore effects of large density gradients, from open-grown to self-thinning situations. Growth partitioning was assessed on basal area growth, using both the growth dominance index, and the within-stand size-growth relationship. Their dependence on stand density, age, thinning, and climatic predictors was modeled statistically. A one-at-a-time sensitivity analysis of these models was performed to evaluate the magnitude of the effect of each predictor on growth partitioning. Simulations of the effect of extreme climatic conditions on stand growth, and on dominant, intermediate and close-to-suppressed trees growth were also performed. Results: For both species, stand density was found to strongly increase growth partitioning toward the biggest trees. Stand growth in sessile oak was reduced by high summer soil water deficit, with a particularly severe growth reduction for suppressed trees, suggesting asymmetric belowground competition for water in this species. In Douglas-fir, a stand growth reduction was found for high summer temperatures, with an increase in growth dominance that suggested a higher temperature-driven stress for suppressed trees. In addition, age slightly increased/decreased growth dominance in sessile oak/Douglas-fir, respectively. Conclusions: Growth dominance and size-growth relationships offered complementary insight into growth partitioning. Stand density appears to be the major driver of growth partitioning. Climatic factors were also shown to significantly affect growth partitioning, with species differences, in addition to stand density and ageing. These results suggest to maintain stands at medium density levels to reduce rotation length and minimize risk of exposure to extreme climatic events.

Influence of combustion on principal strain-rate transport in turbulent premixed flames

The transport of principal strain-rates (si) was experimentally investigated using high-repetition-rate (10kHz) tomographic particle image velocimetry (T-PIV) and OH planar laser induced fluorescence (PLIF) in a Rej=13,000 turbulent premixed flame. These measurements allowed calculation of the source terms in the si transport equation associated with the strain-rate and vorticity fields. Furthermore, the Lagrangian derivatives of si could be calculated by tracking theoretical Lagrangian fluid particles through space and time using the T-PIV data. These Lagrangian derivatives and the resolved source terms allowed the combined effects of the unresolved source terms to be inferred, namely the pressure Hessian, viscous dissipation, density gradients, and viscosity gradients. Statistics conditioned on the location of the Lagrangian fluid particles relative to the flame showed slight reductions in the strain-rate and vorticity source terms in the flame, indicating that these aspects of the turbulence were attenuated by the flame. Comparing the difference between the inferred source terms in the vicinity of the flame to the non-reacting flow showed that attenuation of si arose due to the combined effects of density and pressure gradients in the flame. The effects of flame-induced dilatation were small relative to the turbulent strain-rate and no change was found in the relative alignment of vorticity and strain-rate in the flame.

Density gradient effects on transverse shear driven lower hybrid waves

Shear driven instabilities are commonly observed in the near-Earth space, particularly in boundary layer plasmas. When the shear scale length (LE) is much less than the ion gyro-radius (ρi) but greater than the electron gyro-radius (ρe), the electrons are magnetized in the shear layer, but the ions are effectively un-magnetized. The resulting shear driven instability, the electron-ion hybrid (EIH) instability, is investigated in a new interpenetrating plasma configuration in the Auburn Linear EXperiment for Instability Studies. In order to understand the dynamics of magnetospheric boundary layers, the EIH instability is studied in the presence of a density gradient located at the boundary layer between two plasmas. This paper reports on a recent experiment in which electrostatic lower hybrid waves are identified as the EIH instability, and the effect of a density gradient on the instability properties are investigated.

Inhomogeneity Effect on Solitary Structures in a Magnetized Warm Plasma: Ionization Versus Recombination

In a magnetized inhomogeneous warm plasma having ionization/recombination, usual version of the KdV equation is found to be modified by two additional terms arising due to the inclusion of ionization/recombination and the density gradient in the plasma. The density gradient in the plasma shows its dependence on the ionization/recombination rate, ion-to-electron temperature ratio, obliqueness of the magnetic field and drift velocity of the ions. In the considered plasma, only the compressive solitary structures are found to propagate corresponding to two different types of modes. A significant effect of magnetic field and ion temperature is found on these structures in both the cases of ionization and recombination, though these structures show weak dependence on the charge of the ions. Interestingly the solitons with prominent tailing structures are evolved in the plasma under the effect of stronger density gradient and higher ionization or recombination. The tailing structure with bigger size evolves in the plasma in the case of only recombination, suggesting that the exchange/transfer of energy from the main soliton to its tail is on a greater scale in the case of recombination than the case of ionization. There exists a critical value of the ionization rate at which the tailing structure associated with only the fast (not slow) solitary structure is vanished. Similarly, the tailing structure associated with only the slow (not fast) solitary structure is disappeared at a critical value of recombination rate.