Stability and stable modes of coastal fronts

Abstract

The stability of a single layer, geostrophic front of zero potential vorticity bounded by a vertical coast (wall) is investigated by means of a Rayleigh integral. It is proved that the flow of the density-driven current is stable at all wavenumbers provided the mean velocity of basic flow exceeds fL (where f is the Coriolis parameter and L is the distance between the wall and the free streamline). The frequency of the stable long waves is either zero or super-inertial.     

Instability of a geostrophic front and its energetics

Abstract

The instability of a current with a geostrophic surface density front is investigated by means of a reduced gravity model having a velocity profile with nearly uniform potential vorticity. It is shown that currents are unstable when the mean potential vorticity decreases toward the surface front at the critical point of the frontal trapped waves investigated by Paldor (1983). This instability is identical with that demonstrated by Killworth (1983) in the longwave limit.

The cross-stream component of mass flux and the rates of energy conversions among the five energy forms defined by Orlanski (1968) are also calculated. The main results are as follows, (a) The mass flux toward the surface front is positive near the front and negative around the critical point. The positive mass flux near the front does not vanish at the position of the undisturbed surface front, so that the mean position of the front moves outward and the region of the strong current spreads. (b) The potential energy of the mean flow integrated over the fluid is released through the work done by the force of the pressure gradient of the mean flow on the fluid, and is converted into the kinetic energy of the mean flow. (c) In the critical layer, the mean flow is rapidly accelerated with the growth of the unstable wave. This acceleration is caused by the rapid phase shift of the unstable wave in the critical layer.     

Hamiltonian description of almost geostrophic flow

Abstract

Geostrophic flow in the theory of a shallow rotating fluid is exactly analogous to the drift approximation in a strongly magnetized electrostatic plasma. This analogy is developed and exhibited in detailed to derive equations for the slow nearly geostrophic motion. The key ingredient in the theory is the isolation, to whatever order in Rossby number desired, of the fast motion near the inertial frequency. One of the remaining degrees of freedom represents a new approximate constant of the motion for nearly geostrophic flow. This is the analogue of the familiar magnetic moment adiabatic invariant in the plasma problem.

The procedure is a Rossby number expansion of the Hamiltonian for the fluid expressed in Lagrangian, rather than Eulerian variables. The fundamental Poisson brackets of the theory are not expanded so desirable properties such as energy conservation are maintained throughout.     

Structure of triads in geostrophic turbulence

The interaction between Fourier waves, which results in energy transfer over the spectrum, has been considered using the Boussinesq model in a plane layer during rapid rotation as an example. It has been indicated that the wave triangle spectrum strongly differs on the scales shorter (longer) than the scale of a cyclonic turbulence leading mode.     

Resistive instabilities in rapidly rotating fluids: Linear theory of the convective modes

Abstract

This paper analyzes the linear stability of a rapidly-rotating, stratified sheet pinch in a gravitational field, g, perpendicular to the sheet. The sheet pinch is a layer (O ? z ? d) of inviscid, Boussinesq fluid of electrical conductivity σ, magnetic permeability μ, and almost uniform density ρ _o; z is height. The prevailing magnetic field. B _o(z), is horizontal at each z level, but varies in direction with z. The angular velocity, Ω, is vertical and large (Ω ? V_A/d, where V_A = B₀√(μρ₀) is the Alfvén velocity). The Elsasser number, Λ = σB² ₀/2Ωρ₀, measures σ. A (modified) Rayleigh number, R = gβd²/ρ₀V² _A, measures the buoyancy force, where β is the imposed density gradient, antiparallel to g. A Prandtl number, P_K = μσK, measures the diffusivity, k, of density differences.     

Linear stability analysis for the differentially heated rotating annulus

We use linear stability analysis to approximate the axisymmetric to nonaxisymmetric transition in the differentially heated rotating annulus. We study an accurate mathematical model that uses the Navier–Stokes equations in the Boussinesq approximation. The steady axisymmetric solution satisfies a two-dimensional partial differential boundary value problem. It is not possible to compute the solution analytically, and thus, numerical methods are used. The eigenvalues are also given by a two-dimensional partial differential problem, and are approximated using the matrix eigenvalue problem that results from discretizing the linear part of the appropriate equations.

A comparison is made with experimental results. It is shown that the predictions using linear stability analysis accurately reproduce many of the experimental observations. Of particular interest is that the analysis predicts cusping of the axisymmetric to nonaxisymmetric transition curve at wave number transitions, and the wave number maximum along the lower part of the axisymmetric to nonaxisymmetric transition curve is accurately determined. The correspondence between theoretical and experimental results validates the numerical approximations as well as the application of linear stability analysis.

A linear stability analysis is also performed with the effects of centrifugal buoyancy neglected. Along the lower part of the transition curve, the results are significantly qualitatively and quantitatively different than when the centrifugal effects are considered. In particular, the results indicate that the centrifugal buoyancy is the cause of the observation of a wave number maximum along the transition curve, and is the cause of a change in concavity of the transition curve.     

Dispersion relation for ballooning modes and condition of their stability in the near-earth plasma

The ballooning disturbances in a finite-pressure plasma in a curvilinear magnetic field are described by a system of coupled equations for Alfvén and slow magnetosonic modes. The local dispersion relation obtained in a WKB approximation is the simplest and most evident method that can be used to characterize the properties of these disturbances. This dispersion relation is widely used to predict the possible instabilities and spectral properties of LF oscillations in the nightside magnetosphere. The formal derivation of the dispersion relation from the initial system of coupled MHD modes and the transition to different limiting cases have been traced. The behavior of dispersion curves in different oscillation branches and the possible development of instabilities and formation of regions where waves cannot propagate have been studied in detail. This made it possible to specify the results of previous works and even indicate the incorrectness in some works. In particular, it has been indicated that a fast Alfvén branch of oscillations is always stable and an aperiodic instability can originate on a slow magnetosonic oscillation branch.     

Linear hydromagnetic stability of a differentially rotating non-uniformly stratified fluid layer

Summary Our discussion is concerned with the common effect of the non-uniformity of layer rotation and stratification. We have assumed a model of differential rotation with the upper part of the layer rotating more slowly, the bottom part more quickly. The upper part of the layer is stratified stably, the bottom part unstably.The thermal instabilities are preferred in the strong differential rotation case and they are the most easily excited by a strong magnetic field (10²–10³). The direction of its propagation is westward in the uniformly stratified layer and eastward in the non-uniformly stratified layer.     

Internal waves and temperature fronts on slopes

Time series measurements from an array of temperature miniloggers in a line at constant depth along the sloping boundary of a lake are used to describe the ‘internal surf zone” where internal waves interact with the sloping boundary. More small positive temperature time derivatives are recorded than negative, but there are more large negative values than positive, giving the overall distribution of temperature time derivatives a small negative skewness. This is consistent with the internal wave dynamics; fronts form during the up-slope phase of the motion, bringing cold water up the slope, and the return flow may become unstable, leading to small advecting billows and weak warm fronts. The data are analysed to detect ‘events’, periods in which the temperature derivatives exceed a set threshold. The speed and distance travelled by ‘events’ are described. The motion along the slope may be a consequence of (a) instabilities advected by the flow (b) internal waves propagating along-slope or (c) internal waves approaching the slope from oblique directions. The propagation of several of the observed ‘events’ can only be explained by (c), evidence that the internal surf zone has some, but possibly not all, the characteristics of the conventional ‘surface wave’ surf zone, with waves steepening as they approach the slope at oblique angles.     

Some interactions between small numbers of baroclinic,geostrophic vortices

Abstract

Various interactions between small numbers (two and four) of baroclinic, geostrophic point vortices in a two-layer system are studied with attention to the qualitative changes in behavior which occur as size of the deformation radius is varied.

A particularly interesting interaction, which illustrates the richness of baroclinic vortex dynamics, is a collision between two hetons. (A heton is a vortex pair in which the constituent vortices have opposite signs and are in opposite layers. The “breadth” of a heton is the distance between its constituent vortices. A translating heton transports heat.) When two hetons, which initially have different breadths, collide, the result is either an exchange of partners, or a “slip-through” collision in which the initial structures are preserved. It is shown here that the outcome is always an exchange, provided the deformation radius is sufficiently small. This strongly contrasts with a collision between pairs of classical, one-layer vortices in which no exchange occurs if the initial ratio of the breadths is sufficiently extreme.

Finally the transport of passive fluid by a translating baroclinic pair is investigated. A pair of vortices in the top layer transports no lower layer fluid if the distance between the vortices is less than 1.72 deformation radii. By contrast, the size of the region trapped by a heton increases without bound as the spacing between the vortices increases.     

A heuristic framework for next-generation models of geostrophic convective turbulence

Many geophysical and astrophysical phenomena are driven by turbulent fluid dynamics, containing behaviors separated by tens of orders of magnitude in scale. While direct simulations have made large strides toward understanding geophysical systems, such models still inhabit modest ranges of the governing parameters that are difficult to extrapolate to planetary settings. The canonical problem of rotating Rayleigh-Bénard convection provides an alternate approach - isolating the fundamental physics in a reduced setting. Theoretical studies and asymptotically-reduced simulations in rotating convection have unveiled a variety of flow behaviors likely relevant to natural systems, but still inaccessible to direct simulation. In lieu of this, several new large-scale rotating convection devices have been designed to characterize such behaviors. It is essential to predict how this potential influx of new data will mesh with existing results. Surprisingly, a coherent framework of predictions for extreme rotating convection has not yet been elucidated. In this study, we combine asymptotic predictions, laboratory and numerical results, and experimental constraints to build a heuristic framework for cross-comparison between a broad range of rotating convection studies. We categorize the diverse field of existing predictions in the context of asymptotic flow regimes. We then consider the physical constraints that determine the points of intersection between flow behavior predictions and experimental accessibility. Applying this framework to several upcoming devices demonstrates that laboratory studies may soon be able to characterize geophysically-relevant flow regimes. These new data may transform our understanding of geophysical and astrophysical turbulence, and the conceptual framework developed herein should provide the theoretical infrastructure needed for meaningful discussion of these results.     

Kinetic features of bursty bulk flows and dipolarization fronts

正Bursty bulk flows(BBFs)and dipolarization fronts(DFs)are two important phenomena responsible for the transport of energy,mass and magnetic flux from the Earth's magnetotail to the inner magnetosphere during magnetosphere substorms.The BBFs are defined as the high-speed flows of several hundred km/s in the central plasma sheet lasting about 10 minutes,while DFs are defined as,with much shorter time scale of several seconds,sharp increases in the northward magnetic field component in the plasma sheet.These two phenomena     

Magnetotail dipolarization fronts and particle acceleration: A review

In this paper, the particle acceleration processes around magnetotail dipolarization fronts(DFs) were reviewed. We summarize the spacecraft observations(including Cluster, THEMIS, MMS) and numerical simulations(including MHD, testparticle, hybrid, LSK, PIC) of these processes. Specifically, we(1) introduce the properties of DFs at MHD scale, ion scale, and electron scale,(2) review the properties of suprathermal electrons with particular focus on the pitch-angle distributions,(3)define the particle-acceleration process and distinguish it from the particle-heating process,(4) identify the particle-acceleration process from spacecraft measurements of energy fluxes, and(5) quantify the acceleration efficiency and compare it with other processes in the magnetosphere(e.g., magnetic reconnection and radiation-belt acceleration processes). We focus on both the acceleration of electrons and ions(including light ions and heavy ions). Regarding electron acceleration, we introduce Fermi,betatron, and non-adiabatic acceleration mechanisms;regarding ion acceleration, we present Fermi, betatron, reflection, resonance, and non-adiabatic acceleration mechanisms. We also discuss the unsolved problems and open questions relevant to this topic, and suggest directions for future studies.     

Lagrangian approach to geostrophic adjustment of frontal anomalies in a stratified fluid

Geostrophic adjustment of frontal anomalies in a rotating continuously stratified fluid is studied in the standard framework of strictly rectilinear fronts and jets. Lagrangian approach to this problem is developed allowing to analyze, in a conceptually and technically simple way, both major problems of the nonlinear adjustment: the existence of a smooth adjusted state for a given set of initial conditions and the attainability of the adjusted state during the adjustment process. Dynamical splitting into balanced (adjusted state) and unbalanced (inertia-gravity waves) motions becomes transparent in the Lagrangian approach. Conditions of existence of the balanced state in the unbounded domain are established. It is shown that nonexistence of a smooth adjusted state in the vertically bounded domains is generic and a parallel with the classical scenario of deformation frontogenesis is developed. Small perturbations around smooth adjusted states are then studied with special emphasis on the wave-trapping inside the jet/front. Trapped modes with horizontal scales comparable to the width of the jet are explicitly constructed for a barotropic jet and their evolution is studied with the help of the WKB-approximation for weakly baroclinic jets. Modifications of the standard scenario of adjustment due to subinertial (quasi-) trapped modes and implications for data analysis are discussed.     

Linear stability of a non-constantly stratified horizontal layer penetrated by an azimuthal magnetic field

Summary The convection in a rapidly rotating, electrically conducting, horizontal fluid layer, non-constantly stratified and penetrated by an inhomogeneous magnetic field, is studied. The convection is investigated for various ratios of the thickness of the stable and unstable stratified part of the layer. The thermal model of the layer, as well as the analysis of the results have been treated with regard to the physical conditions in the liquid core of the Earth.

---

am u¶rt;m u m aa mn¶rt; u¶rt;uma nm mamuuau, nua ¶rt;¶rt; aum n. u u¶rt;m ¶rt; a mu m u mu u mu mamuuuao amu . ua ¶rt; , a u aau mam, n¶rt;a anm uuu u u¶rt; ¶rt; u.

     

Tomographic measurements of pore filling at infiltration fronts

For certain porous media and initial conditions, constant flux infiltrations show a saturation profile which exhibits overshoot. This overshoot is the cause of gravity driven fingering, cannot be described by standard models of unsaturated flow, and is likely controlled by the exact nature of the pore filling at the initial front. Here we report synchrotron X-ray micro-tomography measurements of the porous medium and measure which pores are filled by water and air at the initial wetting front as a function of flux. We find that at high fluxes all the pores are filled with water; for intermediate fluxes, the pores along the edge of the column remain unsaturated; and for low fluxes the pores in the bulk of the experimental column remain unsaturated. This suggests that the unsaturated overshoot conditions observed at higher fluxes are primarily an edge effect of the column. The results can help delineate the correct continuum models that can capture overshoot and gravity driven fingering.     

The motion of magnetic fronts in spiral galaxies

Abstract

We study the nonlinear asymptotic thin disc approximation to the mean field dynamo equations, as applicable to spiral galaxies. The circumstances in which sharp magnetic field structures (fronts) can propagate radially are investigated, and an expression for the speed of propagation derived. We find that the speed of an interior front is proportional to η//R _? (where η is the diffusivity and R_t the galactic radius), whereas an exterior front moves with speed of order , where γ is the local growth rate of the dynamo. Numerical simulations are presented, that agree well with our asymptotic results. Further, we perform numerical experiments using the 'no-z' approximation for thin disc dynamos, and show that the propagation of magnetic fronts in this approximation can also be understood in terms of our asymptotic results.     

Comparison of geostrophic and nonlinear balanced winds from LIMS data and implications for derived dynamical quantities

Nimbus 7 LIMS geopotential height data are utilized to infer the rotational wind distribution in the Northern Hemisphere stratosphere and lower mesosphere during a period of substantial wave-mean flow interaction in January, 1979. Rotational winds are derived from the application of a successive relaxation numerical procedure which incorporates the spherical polar coordinate iterative algorithm ofPaegle andTomlinson (1975) for the nondivergent nonlinear balance equation. Optimum convergence of the numerical solutions is found to occur when under-relaxation is utilized. The LIMS height analyses were also latitudinally smoothed and constrained to obey the ellipticity criterion for spherical coordinates. The balanced winds are compared with geostrophically derived values and within situ radiosonde reports for 100 mb to 10 mb over Berlin.From a localized perspective, the Berlin-LIMS comparison indicates that radiosonde and balanced wind vectors exhibit somewhat closer agreement in direction than is associated with the geostrophic estimates. However, substantial quantitative differences between radiosonde, balanced, and geostrophic wind speeds are also evident, suggesting that caution should be exercised in the local application of derived winds, as for example in the quantitative interpretation of trajectories derived from satellite height analyses during periods of enhanced stratospheric wave activity.On a longitudinally averaged basis, balanced zonal-mean wind speeds are typically 20% weaker than geostrophic values in polar latitudes, and as much as 50% weaker in tropical and midlatitude regions. Meridional balanced wind velocities, at a given longitude, are generally within ±10% of geostrophic values. Although these alterations in horizontal wind components result in only modest differences between balanced and geostrophic meridional eddy heat fluxes, a more substantial change appears in the meridional eddy momentum flux analysis. The corresponding patterns of Eliassen-Palm flux divergence are found to be somewhat more (less) intense for the balanced wind case in the stratosphere (lower mesosphere) in polar latitudes.