Presence Of Density Gradients Research Articles

Dynamics of ice melting by an immiscible liquid layer heated from above

A series of experiments were conducted to investigate the melting of ice adjacent to a water-immiscible liquid layer (n-dodecane) exposed to radiation from above. The experimental setup consisted of a borosilicate container containing an ice wall and a layer of n-dodecane heated from above. In addition to tracking the movement of the melt front, Particle Image Velocimetry (PIV) and Background Oriented Schlieren (BOS) measurements were conducted on the liquid-phase. Two distinct melting regimes were found to dominate the melting process. First was the uniform melting across the contact area with the immiscible liquid layer for low radiation levels (∼1 kW/m2). Second was the lateral intrusion regime, where a depression near free surface of the liquid forms in ice and grows laterally for radiation level greater than ∼ 1 kW/m2. The ice surface remained flat and smooth in uniform melting regime, whereas in the lateral intrusion regime a series of rivulets were formed that carved valleys on the ice. PIV measurements showed a surface flow toward the ice for all heat flux levels caused by surface-tension forces. Increase of the heat flux levels caused a transition to multi-roll structure in the flow field. This multi-roll structure, which is accompanied by a recirculation zone near the ice, increased heat transfer near the surface of the liquid causing lateral intrusion regime. BOS measurements indicated presence of density gradients below the free surface of n-dodecane and in regions near the ice that are caused by local small-scale temperature gradients. The current experiments were conducted to explore the melting dynamics and to shed light on the processes that influence the ice melting. Implications of such mechanisms in a real-life scenario, i.e. oil spill in ice-infested waters, needs to be explored further by using more liquids and improved accuracy of the diagnostic techniques.

Turbulence mitigation in maximum-J stellarators with electron-density gradient

In fusion devices, the geometry of the confining magnetic field has a significant impact on the instabilities that drive turbulent heat loss. This is especially true of stellarators, where the density-gradient-driven branch of the ‘trapped electron mode’ (TEM) is predicted to be linearly stable if the magnetic field has the maximum-J property, as is very approximately the case in certain magnetic configurations of the Wendelstein 7-X experiment (W7-X). Here we show, using both analytical theory and simulations, that the benefits of the optimisation of W7-X also serve to mitigate ion-temperature-gradient (ITG) modes as long as an electron density gradient is present. We find that the effect indeed carries over to nonlinear numerical simulations, where W7-X has low TEM-driven transport, and reduced ITG turbulence in the presence of a density gradient, giving theoretical support for the existence of enhanced confinement regimes, in the presence of strong density gradients (e.g. hydrogen pellet or neutral beam injection).

Ultra-slow and arrested density-fluctuations as precursor of spatial heterogeneity

Dynamical heterogeneities in glass-forming liquids subjected to cooling processes are studied by a theoretical framework based on the non-equilibrium self-consistent generalized Langevin equation theory. This theory predicts that slow cooling rates permit the relaxation to the equilibrium state distinguished by a homogeneous local density. In contrast, fast cooling rates provoke dynamically arrested density-fluctuations and the establishment of permanent spatial heterogeneities even in the presence of density gradients. We further show that the dynamics toward the arrested state has two steps: a truncated relaxation followed by a second relaxation of the diluted part of the system.

Flow Field Study of a Top Heated Immiscible Liquid Layer Adjacent to Ice

A series of experiments were conducted to investigate the flow field of a top-heated liquid fuel adjacent to an ice block. The experimental setup consisted of a borosilicate container containing an ice wall and a layer of n-heptane heated from above. Particle Image Velocimetry (PIV) and Background Oriented Schlieren (BOS) measurements were conducted on the liquid -phase. PIV measurements showed a surface flow toward the ice caused by surface -tension forces, which is driven by the horizontal temperature gradients on the liquid surface. A recirculation zone was observed under the free surface and near the ice. The combination of the two flow patterns caused lateral intrusion in the ice, instead of a uniform melting across ice surface. BOS measurements indicated presence of density gradients below the free surface of n-heptane and in regions near the ice block. These density gradients were created by local small-scale temperature gradients. The current experiments were conducted to explore the processes that influence the ice melting by immiscible liquid layers.

Mesoscale-submesoscale interactions in the Gulf of Mexico: From oil dispersion to climate

In the ocean, forcing acts at planetary scales and dissipation at the microscales. In between are the mesoscales, in a lot of respects akin to nearly two-dimensional, quasi-geostrophically, balanced turbulence. Eddies and fronts, extending from ten to hundred kilometers, represent their best-known dynamical expression. At the ocean boundary layers, near the surface and at the bottom, smaller ageostrophic, coherent flow structures may appear in the form of vorticity filaments, density fronts or coherent vortices, with typical scales of hundreds of meters to few kilometers and a lifespan of few days. These so-called submesoscale circulations provide a pathway for energy transfer towards smaller scales, contribute to the global overturning budget, and impact substantially lateral and diapycnal mixing. They develop in presence of density gradients in the turbulent boundary layers, and their statistics are not well known in a global sense, but are likely to change in the future due to projected changes in near surface stratification.This perspective presents an overview of recent studies illustrating physical and biogeochemical interactions across mesoscale and submesoscale flows focusing on the Gulf of Mexico, where much modeling and observational work has been taking place following the 2010 Deepwater Horizon blow-out. The physical interpretation of several biogeochemical data-sets illustrates how mesoscale and submesoscale circulations impact the dispersion of biologically and climatically relevant tracers, from coral larvae to carbon.The ultimate goal is present the reader with examples of spatial and temporal multiscale interactions in a complex, chaotic system such as the ocean that is key to the future evolution of the climate system with its enormous storage capacity of heat and carbon.

Kinetic Instability of Anisotropic Drift Wave Accompanied by Field Aligned Currents in Solar Coronal Loop

Solar coronal loops are frequently accompanied by the field-aligned currents, which drive instabilities if the drift velocity u0 > vA the Alfvén velocity. For our choice of parameters, the critical threshold value of u0/vA is ∼ 3.0 for growth and the corresponding current filling factor ∼ 10−3 − 10−4. Below this value we are no longer in the kinetic regime. The coronal loops also have short-scale density gradients within each loop. The electron resonance in the presence of density gradient causes the drift mode to grow. We study the effect of these two free energy sources, the electron drift and the density gradient, in the presence of temperature anisotropy T⊥α > T∥α. These effects simultaneously exist in the coronae. Using gyrokinetic theory, we investigate the influence of these effects, examine how they interplay with each other and study the consequent growth of the magnetosonic wave. We observe that kinetic instability driven by density gradient can be suppressed by field-aligned currents. The temperature anisotropy with chosen signatures causes further stabilizing effect. The results may prove useful to study the heating mechanism of solar coronal loops, acceleration of particles and confinement of particles in the thermonuclear reactors.

Coronal Heating & Solar Wind Acceleration by Drift Waves

An alternative approach to the coronal heating problem, based on the theory of drift waves, has been proposed. The drift mode is the only mode that is able to survive the drastically different (collisional/collisionless) extremes in the different layers of the solar atmosphere. As a matter of fact, this mode is over stable, i.e. able to grow, in both of these extreme situations, and has been called the universally growing mode in the literature. In collisional plasma of the lower layers of the solar atmosphere, the drift mode grows due to the electron collisions and this can be described within the two-fluid model. In the collisionless coronal plasma, however, the mode grows due to a pure kinetic effect, viz. the electron resonance effect in the presence of a density gradient.It has been shown, with qualitative and quantitative arguments, that the drift waves have the potential to satisfy all coronal heating requirements. The basic ingredient required for the heating is the presence of density gradients in the direction perpendicular to the magnetic flux surfaces. The drift wave theory is well-established and has been explicitly verified experimentally in laboratory (fusion) plasmas, similar (hot, low-beta, highly conductive) to those in the solar atmosphere. In these circumstances, two mechanisms of the energy exchange and heating take place simultaneously: Landau damping in the direction parallel to the magnetic field, and stochastic heating in the perpendicular direction. The latter, in fact, is more effective on ions than on electrons, acts predominantly in the perpendicular direction, and heats heavy ions more efficiently than lighter ions. Moreover, for plasmas at a temperature of 1MK and beyond, the parallel wave field resulting from the drift waves exceeds the Dreicer field so that the bulk plasma species (primarily electrons) can be accelerated/decelerated by the wave in the parallel direction. In addition, this acceleration is more effective on the particles that are already more energetic, resulting in a distribution function considerably different from a Maxwellian, similar to the observed kappa-distribution in the outer solar atmosphere and in the solar wind.

Displacement of yield-stress fluids in a fracture

We consider a displacement of several yield-stress fluids in a Hele-Shaw cell. The topic is relevant to the development of a model for the flow of multiple phases inside a narrow fracture with application to hydraulically fracturing a hydrocarbon-bearing underground formation. Existing models for fracturing flows include only pure power-law models without yield stress, and the present work is aimed at filling this gap. The fluids are assumed to be immiscible and incompressible. We consider fluid advection in a plane channel in the presence of density gradients. Gravity is taken into account, so that there can be slumping and gravitational convection. We use the lubrication approximation so that governing equations are reduced to a 2D width-averaged system formed by the quasi-linear elliptic equation for pressure and transport equations for volume concentrations of fluids. The numerical solution is obtained using a finite-difference method. The pressure equation is solved using an iterative algorithm and the Multigrid method, while the transport equations are solved using a second-order TVD flux-limiting scheme with the superbee limiter. This numerical model is validated against three different sets of experiments: (i) gravitational slumping of fluids in a closed Hele-Shaw cell, (ii) viscous fingering of fluids with a high viscosity contrast due to the Saffman–Taylor (S–T) instability in a Hele-Shaw cell at microgravity conditions, (iii) displacement of Bingham fluids in a Hele-Shaw cell with the development of fingers due to the S–T instability. Good agreement is observed between simulations and laboratory data. The model is then used to investigate the joint effect of fingering and slumping. Numerical simulations show that the slumping rate of yield-stress fluid is significantly less pronounced than that of a Newtonian fluid with the same density and viscosity. If a low-viscosity Newtonian fluid is injected after a yield-stress one, the S–T instability at the interface leads to the development of fingers. As a result, fingers penetrating into a fluid with a finite yield stress locally decrease the pressure gradient and unyielded zones develop as a consequence.

Intra- and inter-tidal variability of the vertical current structure in the Marsdiep basin

The vertical structure of the along-stream current in the main channel of the periodically-stratified estuarine Marsdiep basin is investigated by combining velocity measurements collected during three different seasons with a one-dimensional water column model. The observed vertical shears in the lowest part of the water column are greater during ebb than during flood due to an asymmetry in drag coefficient (i.e. bed friction), which is most likely determined by the surrounding complex bathymetry. This asymmetry is usually not incorporated in models. Furthermore, a mid-depth velocity maximum is observed and simulated during early and late flood which is generated by along-stream and cross-stream tidal straining, respectively. Negative shears are present in the upper part of the water column during flood, which correlate well with the along-stream salinity gradient. The mid-depth velocity maximum during late flood results in an early current reversal in the upper part of the water column. The elevated vertical shears during ebb are able to reduce vertical stratification induced by along-stream tidal straining, whereas cross-stream tidal straining during late flood promotes the generation of vertical stratification. The simulations suggest that these processes are most important during spring tide conditions. This study has demonstrated that an asymmetry in bed friction and the presence of density gradients both have a strong impact on the vertical structure of along-stream velocity in the Marsdiep basin.

Fast growing resistive two fluid instabilities in hybrid-like tokamak configuration

An analytic derivation of the dispersion relation for resistive instabilities in a low-shear tokamak configuration is presented. The resistive infernal mode model (Charlton et al 1989 Phys. Fluids B 1 798) is generalized to include plasma diamagnetism, subsonic equilibrium toroidal flow shear and viscosity. An estimate of the transition point between the fast S−3/13 infernal-like (S is the Lundquist number) and the slow S−3/5 tearing-like scaling is given. A novel S−3/8 scaling is found close to the ideal ion-diamagnetic magnetohydrodynamic stability boundary. New moderately fast scalings in S are also found when sheared toroidal E × B flow and viscosity are considered. An analytic treatment of the m = n = 1 quasi-interchange mode in presence of density gradients with flat temperature profiles has been made.

Linear mode conversion of Langmuir/z-mode waves to radiation in plasmas with various magnetic field strength

Linear mode conversion of Langmuir/z waves to electromagnetic radiation near the plasma and upper hybrid frequency in the presence of density gradients is potentially relevant to type II and III solar radio bursts, ionospheric radar experiments, pulsars, and continuum radiation for planetary magnetospheres. Here, we study mode conversion in warm, magnetized plasmas using a numerical electron fluid simulation code when the density gradient has a wide range of angle, δ, to the ambient magnetic field, B0, for a range of incident Langmuir/z wavevectors. Our results include: (1) Left-handed polarized ordinary (oL) and right-handed polarized extraordinary (xR) mode waves are produced in various ranges of δ for Ω0 = (ωL/c)1/3(ωce/ω) < 1.5, where ωce is the (angular) electron cyclotron frequency, ω is the angular wave frequency, L is the length scale of the (linear) density gradient, and c is the speed of light; (2) the xR mode is produced most strongly in the range, 40° < δ < 60°, for intermediately magnetized p...

Quasi-Biennial Modulation of the Solar Neutrino Flux: A “Telescope” for the Solar Interior

An oscillating magnetic field deep within the solar radiative region can significantly alter the helioseismic g-modes. The presence of density gradients along g-modes, can excite Alfven waves resonantly, the resulting waveforms show sharp spikes in the density profile at radii comparable with the neutrino’s resonant oscillation length. This process should explain the observed quasi-biennial modulation of the solar neutrino flux. If confirmed, the coupling between solar neutrino flux and g-modes should be used as a “telescope” for the solar interior.

The universally growing mode in the solar atmosphere: coronal heating by drift waves

The heating of the plasma in the solar atmosphere is discussed within both frameworks of fluid and kinetic drift wave theory. We show that the basic ingredient necessary for the heating is the presence of density gradients in the direction perpendicular to the magnetic field vector. Such density gradients are a source of free energy for the excitation of drift waves. We use only well established basic theory, verified experimentally in laboratory plasmas. Two mechanisms of the energy exchange and heating are shown to take place simultaneously: one due to the Landau effect in the direction parallel to the magnetic field, and another one, stochastic heating, in the perpendicular direction. The stochastic heating i) is due to the electrostatic nature of the waves, ii) is more effective on ions than on electrons, iii) acts predominantly in the perpendicular direction, iv) heats heavy ions more efficiently than lighter ions, and v) may easily provide a drift wave heating rate that is orders of magnitude above the value that is presently believed to be sufficient for the coronal heating, i.e., $\simeq 6 \cdot 10^{-5} $J/(m$^3$s) for active regions and $\simeq 8 \cdot 10^{-6} $J/(m$^3$s) for coronal holes. This heating acts naturally through well known effects that are, however, beyond the current standard models and theories.

Analysis of narrowband emission observed in the Saturn magnetosphere

Narrowband emission is observed at Saturn centered near 5 kHz and 20 kHz and harmonics of 20 kHz. This emission appears to be in many ways similar to Jovian narrowband emission observed at higher frequencies. We analyze one example of this emission near a possible source region. In situ electron distributions suggest narrowband emission has a source region associated with electrostatic cyclotron harmonic and upper hybrid emission. Linear growth rate calculations indicate that the observed plasma distributions are unstable to the growth of electrostatic harmonic emissions. In addition, it is found that when the local upper hybrid frequency is close to 2 fce or 3 fce (fce is the electron cyclotron frequency), electromagnetic Z mode and weak ordinary (O mode) emission can be directly generated by the cyclotron maser instability. In the presence of density gradients, Z mode emission can mode‐convert into O mode emission, and this might explain the narrowband emission observed by the Cassini spacecraft.

Quasilinear dynamics of a cloud of hot electrons propagating through a plasma with decreasing density and temperature

The effects of plasma inhomogeneities on the propagation of a cloud of hot electrons through a cold background plasma and generation of Langmuir waves are investigated using numerical simulations of the quasilinear equations. It is found that in a plasma with decreasing density the quasilinear relaxation of the electron distribution in velocity space is accelerated and the levels of the generated Langmuir waves are enhanced. The magnitude of the induced emission rate is increased and its maximum value moves to lower velocities. Due to density gradient the height of plateau shows an increase at small distances and a corresponding decrease at large distances. It is also found that in a plasma with decreasing temperature, the relaxation of the beam is retarded, the spectral density of Langmuir waves is broadened, and the height of the plateau decreases below its value in a uniform plasma. In the presence of both density and temperature gradients, at given position, the height and upper boundary of the plateau and the level of Langmuir waves are all increased at small velocities. The spatial expansion of the beam is increased by the plasma inhomogeneities, but its average velocity of propagation decreases. Initially, at a given position, the velocity at the upper boundary of the plateau is smaller in the presence of the density gradient than in the uniform plasma but the reverse is true at longer times. Due to temperature gradient, at large times and small distances, the upper boundary of the plateau is increased above its value in the uniform plasma. Because of fast relaxation, the value of the lower boundary of the plateau in the plasma with decreasing density is always less than its value in the uniform plasma. It is found that the local velocity of the beam decreases when the density gradient is present. The local velocity spread of the beam remains unchanged during the propagation of the beam in the uniform plasma, but increases in the presence of inhomogeneities.

Growing drift-Alfvén modes in collisional solar plasma

Context. Solar plasmas are structured and stratified both vertically and horizontally. The presence of density gradients and magnetic fields results in an additional wave which can be electrostatic (the drift wave) and electromagnetic (the drift-Alfven wave). Aims. The stability is discussed of the drift-Alfven wave which is driven by the equilibrium density gradient, in both unbounded and bounded, collisional solar plasmas, including the effects of both hot ions and a finite ion Larmor radius. The density gradient in combination with the electron collisions with heavier plasma species is the essential source of the instability of the electrostatic drift mode which is coupled to the dispersive Alfven mode. Methods. An analytical linear normal mode analysis is used for the description of the waves in spatially unlimited plasma. In the application to the magnetic structures the complex eigen-modes and the corresponding complex discrete eigen-frequencies in cylindric, radially inhomogeneous, collisional and bounded plasma are derived and discussed. Results. A detailed derivation of the hot ion (the finite ion Larmor radius) contribution is performed within the two fluid model. In the analysis of modes in an unbounded plasma the exchange of identity between the electrostatic and electromagnetic modes is demonstrated. Due to this, the frequency of the electromagnetic part of the mode becomes very different compared to the case without the density gradient. In the case of a bounded plasma the dispersion properties of modes involve a discrete poloidal mode number, and eigen-functions in terms of Bessel functions with discrete zeros at the boundary. The results are applied to coronal and chromospheric plasmas.

The fluid-dynamic disturbances induced on the ISS, based on the first acceleration measurements on board the space station

The different acceleration components on the ISS that are responsible for the generation of convective motions in a fluid cell either in the presence of density gradients or in quasi-isodense processes, are analyzed. The NASA measurements of the quasi-steady and periodic acceleration on the ISS are considered and their effects on fluid-dynamic experiments are computed and discussed under different assumptions. In particular, numerical simulations are carried out to identify the relative importance of linear and pendular accelerations, due to possible rotations of the P/L around its center of mass. The effects caused by variable accelerations created by an isolation mount that exhibits an attenuation factor not constant within the payload volume, caused by the reaction forces of the umbilicals, are computed and analyzed.

Electromagnetic instabilities in unmagnetized plasmas

It is shown that local perturbations in nonuniform unmagnetized plasmas can give rise to linearly growing electromagnetic fields on both electron and ion time scales. The plasma vorticity and compressibility couple due to density inhomogeneity, giving rise to instabilities with partially transverse and partially longitudinal characteristics in electron plasmas for omega(pe)</=omega and in electron-ion plasmas for omega(pe)</=omega as well as omega<<omega(pe) (where omega(pe) is the electron plasma oscillation frequency). It is reconfirmed that the pure transverse modes due to the thermoelectric term do not appear in nonuniform unmagnetized electron plasmas. Furthermore, it has been found that the thermal fluctuations in a collisionless inhomogeneous electron plasma happen on a slower time scale of the order of 1/c(s)k (where c(s) is the ion sound speed). It seems that in the presence of a steep density gradient the ion acoustic wave becomes electromagnetic. Since the curl of electric field becomes nonvanishing in the presence of a density gradient, any nonuniform plasma can have magnetic field fluctuations in the limit omega<<omega(pe) as well. It is suggested that in the limit omega<<omega(pe) the ion dynamics becomes important and a pure electron plasma model to study magnetic field instability is not useful. The estimate for the magnitude of slowly and rapidly growing magnetic fields using the electron-ion plasma model in a special range of parameters turns out to be of the order of megagauss, in good agreement with the experimental observations.

Rapid dissipation of magnetic fields due to the hall current

We propose a mechanism for the fast dissipation of magnetic fields which is effective in a stratified medium where ion motions can be neglected. In such a medium, the field is frozen into the electrons, and Hall currents prevail. Although Hall currents conserve magnetic energy, in the presence of density gradients they are able to create current sheets which can be sites for efficient dissipation of magnetic fields. We recover the frequency omega(MH) for Hall oscillations modified by the presence of density gradients. We show that these oscillations can lead to an exchange of energy between different components of the field. We calculate the time evolution, and show that magnetic fields can dissipate on a time scale of order 1/omega(MH). This mechanism can play an important role in magnetic dissipation in systems with very steep density gradients, where the ions are static such as those found in the solid crust of neutron stars.

Effect of impurity ions on the charge separation and velocity shear at a plasma edge

The problem of the formation of charge separation in a plasma in the presence of a steep density gradient, the self-consistent electric field and the associated E×B velocity, are studied using a two-dimensional (2D) gyro-kinetic Vlasov code for the ions, with electrons following an adiabatic law. The code shows the formation of a one-dimensional (1D) equilibrium charge at the plasma edge. It is also shown that the presence of a small fraction of impurity ions at the plasma edge can have a significant effect in increasing the effective charge separation and the associated electric field. The present results show that only a kinetic code can solve the problem of the equilibrium electric field in the presence of a density gradient, and point to the important role played by the ions’ gyro-radius in establishing a charge separation at a plasma edge.