Baroclinic instability in a reduced gravity, three-dimensional, quasi-geostrophic model

2000 ◽  
Vol 403 ◽  
pp. 1-22 ◽  
Author(s):  
P. RIPA
Keyword(s):  
Kinetic Energy ◽  
Lower Layer ◽  
Baroclinic Instability ◽  
Three Dimensional ◽  
Normal Modes ◽  
Lower Boundary ◽  
External Potential ◽  
Present System ◽  
Integrals Of Motion ◽  
The Difference

The classical quasi-geostrophic model in an active layer with an arbitrary vertical structure is modified by adding a boundary condition at the interface with a passive (motionless) lower layer: the difference between isopycnal and interface elevations is a Lagrangian constant, so that a particle in this boundary remains there and conserves its density. The new model has the appropriate integrals of motion: in particular, a free energy quadratic and positive definite in the deviation from a state with a uniform flow, made up of the internal and ‘external’ potential energies (due to the displacement of the isopycnals and the interface) and the kinetic energy.Eady's model of baroclinic instability is extended with the present system, i.e. including the effect of the free lower boundary. The integrals of motion give instability conditions that are both necessary and sufficient. If the geostrophic slope of the interface is such that density increases in opposite directions at the top and bottom boundaries, then the basic flow is nonlinearly stable. For very weak internal stratification (as compared with the density jump at the interface) normal modes instability is similar to that of a simpler model, with a rigid but sloping bottom. For stronger stratification, though, the deformation of the lower boundary by the perturbation field also plays an important role, as shown in the dispersion relation, the structure of growing perturbations, and the energetics of the instability. The energy of long growing perturbations is mostly internal potential, whereas short ones have an important fraction of kinetic energy and, for strong enough stratification, external potential.

Uncertainties of Estimates of Inertia–Gravity Energy in the Atmosphere. Part I: Intercomparison of Four Analysis Systems

2009 ◽  
Vol 137 (11) ◽  
pp. 3837-3857 ◽  
Author(s):  
N. Žagar ◽  
J. Tribbia ◽  
J. L. Anderson ◽  
K. Raeder
Keyword(s):  
Three Dimensional ◽  
Normal Modes ◽  
Atmospheric Model ◽  
Kelvin Wave ◽  
Energy Field ◽  
Inverse Projection ◽  
Zonal Wavenumber ◽  
The Difference ◽  
Analysis System ◽  
The Tropics

Abstract This paper presents the application of the normal-mode functions to diagnose the atmospheric energy spectra in terms of balanced and inertia–gravity (IG) contributions. A set of three-dimensional orthogonal normal modes is applied to four analysis datasets from July 2007. The datasets are the operational analysis systems of NCEP and ECMWF, the NCEP–NCAR reanalyses, and the Data Assimilation Research Testbed–Community Atmospheric Model (DART–CAM), an ensemble analysis system developed at NCAR. The differences between the datasets can be considered as a measure of uncertainty of the IG contribution to the global energetics. The results show that the percentage of IG motion in the present NCEP, ECMWF, and DART–CAM analysis systems is between 1% and 2% of the total energy field. In the wave part of the flow (zonal wavenumber k ≠ 0), the IG energy contribution is between 9% and 15%. On the contrary, the NCEP–NCAR reanalyses contain more IG motion, especially in the Southern Hemisphere extratropics. Each analysis contains more energy in the eastward IG motion than in its westward counterpart. The difference is about 2%–3% of the total wave energy and it is associated with the motions projected onto the Kelvin wave in the tropics. The selected truncation parameters of the expansion (zonal, meridional, and vertical truncation) ensure that the projection provides the optimal fit to the input data on model levels. This approach is different from previous applications of the normal modes and under the linearity assumption it allows the application of the inverse projection to obtain details of circulation associated with a selected type of motion. The bulk of the IG motion is confined to the tropics. For the successful reproduction of three-dimensional circulations by the normal modes it is important that the expansion includes a number of vertical modes.

scholarly journals Rayleigh–Bénard Instability of an Ellis Fluid Saturated Porous Channel with an Isoflux Boundary

Fluids ◽  
2021 ◽  
Vol 6 (12) ◽  
pp. 450
Author(s):  
Pedro Vayssière Brandão ◽  
Michele Celli ◽  
Antonio Barletta
Keyword(s):  
Linear Stability ◽  
Three Dimensional ◽  
Normal Modes ◽  
Lower Boundary ◽  
Shear Thinning ◽  
Porous Channel ◽  
Uniform Heat Flux ◽  
Thermal Boundary Conditions ◽  
Transverse Modes ◽  
Ellis Model

The onset of the thermal instability is investigated in a porous channel with plane parallel boundaries saturated by a non–Newtonian shear–thinning fluid and subject to a horizontal throughflow. The Ellis model is adopted to describe the fluid rheology. Both horizontal boundaries are assumed to be impermeable. A uniform heat flux is supplied through the lower boundary, while the upper boundary is kept at a uniform temperature. Such an asymmetric setup of the thermal boundary conditions is analysed via a numerical solution of the linear stability eigenvalue problem. The linear stability analysis is developed for three–dimensional normal modes of perturbation showing that the transverse modes are the most unstable. The destabilising effect of the non–Newtonian shear–thinning character of the fluid is also demonstrated as compared to the behaviour displayed, for the same flow configuration, by a Newtonian fluid.

Linear baroclinic instability in the presence of heat inflow from the lower boundary

1995 ◽  
Vol 13 (4) ◽  
pp. 419-426
Author(s):  
M. Fantini
Keyword(s):  
Energy Exchange ◽  
Baroclinic Instability ◽  
Normal Modes ◽  
Lower Boundary ◽  
Maximum Growth ◽  
High Wave ◽  
Explosive Cyclones ◽  
Wave Numbers ◽  
Heat Influx ◽  
Heat Inflow

Abstract. A linear Eady model with a parameterization of heat influx from the lower boundary is studied analytically in order to obtain the characteristics of baroclinic normal modes modified by this non-adiabatic source. The results display a secondary maximum of growth rate at high wave numbers and a range of absolutely unstable waves, thus suggesting that the property observed among mid-latitude explosive cyclones of being near-stationary in the phase of maximum growth may be captured by this representation of the air-sea energy exchange.

scholarly journals Three-Dimensional Structure and Dynamics of African Easterly Waves. Part II: Dynamical Modes

2006 ◽  
Vol 63 (9) ◽  
pp. 2231-2245 ◽  
Author(s):  
Nicholas M. J. Hall ◽  
George N. Kiladis ◽  
Chris D. Thorncroft
Keyword(s):  
Baroclinic Instability ◽  
Initial Perturbation ◽  
Three Dimensional ◽  
Normal Modes ◽  
Phase Relationship ◽  
Companion Paper ◽  
Dimensional Structure ◽  
African Easterly Waves ◽  
Easterly Waves ◽  
Basic States

Abstract A primitive equation model is used to study the linear normal modes of the African easterly jet (AEJ). Reanalysis data from the summertime mean (June–September; JJAS) flow is used to provide zonally uniform and wavy basic states. The structure and growth rates of modes that grow over West Africa on these basic states are analyzed. For zonally uniform basic states, the modes resemble African easterly waves (AEWs) as in many previous studies, but they are quite baroclinic and surface intensified. For wavy basic states the modes have a longitudinal structure determined by the AEJ. They have a surface-intensified baroclinic structure upstream and a deep barotropic structure downstream, as confirmed by energy conversion diagnostics. These modes look remarkably similar to the composite easterly wave structures found by the authors in a companion paper. The similarity extends to the phase relationship of vertical velocity with streamfunction, which resembles OLR composites, suggesting a dynamical influence on convection. Without damping, the mode for the wavy basic state has a growth rate of 0.253 day−1. With a reasonable amount of low-level damping this mode is neutralized. It has a period of 5.5 days and a wavelength of about 3500 km. Further results with monthly mean basic states show slight variations, as the wave packet essentially follows displacements of the jet core. Experiments focused on specific active and passive years for easterly waves (1988 and 1990) do not yield significantly different results for the modes. These results, and in particular, the stability of the system, lead to the conclusion that barotropic–baroclinic instability alone cannot explain the initiation and intermittence of AEWs, and a finite-amplitude initial perturbation is required.

A Baroclinic Instability that Couples Balanced Motions and Gravity Waves

2005 ◽  
Vol 62 (5) ◽  
pp. 1545-1559 ◽  
Author(s):  
Riwal Plougonven ◽  
David J. Muraki ◽  
Chris Snyder
Keyword(s):  
Gravity Waves ◽  
Baroclinic Instability ◽  
Normal Modes ◽  
Lower Boundary ◽  
Vertical Shear ◽  
Rossby Number ◽  
Edge Waves ◽  
Spatial Coupling ◽  
The Waves ◽  
Upper Boundary

Abstract Normal modes of a linear vertical shear (Eady shear) are studied within the linearized primitive equations for a rotating stratified fluid above a rigid lower boundary. The authors' interest is in modes having an inertial critical layer present at some height within the flow. Below this layer, the solutions can be closely approximated by balanced edge waves obtained through an asymptotic expansion in Rossby number. Above, the solutions behave as gravity waves. Hence these modes are an example of a spatial coupling of balanced motions to gravity waves. The amplitude of the gravity waves relative to the balanced part of the solutions is obtained analytically and numerically as a function of parameters. It is shown that the waves are exponentially small in Rossby number. Moreover, their amplitude depends in a nontrivial way on the meridional wavenumber. For modes having a radiating upper boundary condition, the meridional wavenumber for which the gravity wave amplitude is maximal occurs when the tilts of the balanced edge wave and gravity waves agree.

scholarly journals Rayleigh–Bénard Instability of an Ellis Fluid Saturated Porous Channel with an Isoflux Boundary

2021 ◽  
Author(s):  
Pedro Vayssière Brandão ◽  
Michele Celli ◽  
Antonio Barletta
Keyword(s):  
Linear Stability ◽  
Three Dimensional ◽  
Normal Modes ◽  
Lower Boundary ◽  
Shear Thinning ◽  
Porous Channel ◽  
Uniform Heat Flux ◽  
Thermal Boundary Conditions ◽  
Transverse Modes ◽  
Ellis Model

The onset of the thermal instability is investigated in a porous channel with plane parallel boundaries saturated by a non–Newtonian shear–thinning fluid and subject to a horizontal throughflow. The Ellis model is adopted to describe the fluid rheology. Both horizontal boundaries are assumed to be impermeable. A uniform heat flux is supplied through the lower boundary, while the upper boundary is kept at a uniform temperature. Such an asymmetric setup of the thermal boundary conditions is analysed via a numerical solution of the linear stability eigenvalue problem. The linear stability analysis is developed for three–dimensional normal modes of perturbation showing that the transverse modes are the most unstable. The destabilising effect of the non-Newtonian shear–thinning character of the fluid is also demonstrated as compared to the behaviour displayed, for the same flow configuration, by a Newtonian fluid.

Defocus ramp correction in spot-scan imaging

1992 ◽  
Vol 50 (1) ◽  
pp. 130-131
Author(s):  
Kenneth H. Downing
Keyword(s):  
Computer Control ◽  
Three Dimensional ◽  
Sufficient Accuracy ◽  
Objective Lens ◽  
Electron Crystallography ◽  
Contrast Transfer Function ◽  
Tilt Axis ◽  
Specimen Height ◽  
The Difference ◽  
Envelope Functions

Three-dimensional structures of a number of samples have been determined by electron crystallography. The procedures used in this work include recording images of fairly large areas of a specimen at high tilt angles. There is then a large defocus ramp across the image, and parts of the image are far out of focus. In the regions where the defocus is large, the contrast transfer function (CTF) varies rapidly across the image, especially at high resolution. Not only is the CTF then difficult to determine with sufficient accuracy to correct properly, but the image contrast is reduced by envelope functions which tend toward a low value at high defocus.We have combined computer control of the electron microscope with spot-scan imaging in order to eliminate most of the defocus ramp and its effects in the images of tilted specimens. In recording the spot-scan image, the beam is scanned along rows that are parallel to the tilt axis, so that along each row of spots the focus is constant. Between scan rows, the objective lens current is changed to correct for the difference in specimen height from one scan to the next.

The iron content of iron superoxide dismutase: determination by anomalous scattering

1983 ◽  
Vol 218 (1210) ◽  
pp. 119-126 ◽  
Keyword(s):  
Superoxide Dismutase ◽  
Iron Content ◽  
Three Dimensional ◽  
Anomalous Scattering ◽  
Total Iron Content ◽  
Iron Site ◽  
Iron Superoxide Dismutase ◽  
Density Map ◽  
The Difference ◽  
Electron Density Map

The number of iron atoms in the dimeric iron-containing superoxide dismutase from Pseudomonas ovalis and their atomic positions have been determined directly from anomalous scattering measurements on crystals of the native enzyme. To resolve the long-standing question of the total amount of iron per molecule for this class of dismutase, the occupancy of each site was refined against the measured Bijvoet differences. The enzyme is a symmetrical dimer with one iron site in each subunit. The iron position is 9 ņ from the intersubunit interface. The total iron content of the dimer is 1.2±0.2 moles per mole of protein. This is divided between the subunits in the ratio 0.65:0.55; the difference between them is probably not significant. Since each subunit contains, on average, slightly more than half an iron atom we conclude that the normal state of this enzyme is two iron atoms per dimer but that some of the metal is lost during purification of the protein. Although the crystals are obviously a mixture of holo- and apo-enzymes, the 2.9 Å electron density map is uniformly clean, even at the iron site. We conclude that the three-dimensional structures of the iron-bound enzyme and the apoenzyme are identical.

scholarly journals SPECTRAL CORRELATIONS IN DISORDERED MESOSCOPIC METALS AND THEIR RELEVANCE FOR PERSISTENT CURRENTS

1996 ◽  
Vol 10 (28) ◽  
pp. 1397-1406 ◽  
Author(s):  
AXEL VÖLKER ◽  
PETER KOPIETZ
Keyword(s):  
Energy Levels ◽  
Three Dimensional ◽  
Average Density ◽  
Electron Interaction ◽  
Energy Window ◽  
Persistent Currents ◽  
Dependent Part ◽  
The Difference ◽  
Aharonov Bohm ◽  
Grand Canonical

We use the Lanczos method to calculate the variance σ2(E, ϕ) of the number of energy levels in an energy window of width E below the Fermi energy for noninteracting disordered electrons on a thin three-dimensional ring threaded by an Aharonov–Bohm flux ϕ. We confirm numerically that for small E the flux-dependent part of σ2(E, ϕ) is well described by the Altshuler–Shklovskii-diagram involving two Cooperons. However, in the absence of electron–electron interactions this result cannot be extrapolated to energies E where the energy-dependence of the average density of states becomes significant. We discuss consequences for persistent currents and argue that for the calculation of the difference between the canonical- and grand canonical current it is crucial to take the electron–electron interaction into account.

scholarly journals Properties of Steady Geostrophic Turbulence with Isopycnal Outcropping

2012 ◽  
Vol 42 (1) ◽  
pp. 18-38 ◽  
Author(s):  
G. Roullet ◽  
J. C. McWilliams ◽  
X. Capet ◽  
M. J. Molemaker
Keyword(s):  
High Resolution ◽  
Large Scale ◽  
Mechanical Energy ◽  
Baroclinic Instability ◽  
Three Dimensional ◽  
Primary Source ◽  
Eddy Diffusivity ◽  
Energy Cycle ◽  
Geostrophic Turbulence ◽  
Pv Gradient

Abstract High-resolution simulations of β-channel, zonal-jet, baroclinic turbulence with a three-dimensional quasigeostrophic (QG) model including surface potential vorticity (PV) are analyzed with emphasis on the competing role of interior and surface PV (associated with isopycnal outcropping). Two distinct regimes are considered: a Phillips case, where the PV gradient changes sign twice in the interior, and a Charney case, where the PV gradient changes sign in the interior and at the surface. The Phillips case is typical of the simplified turbulence test beds that have been widely used to investigate the effect of ocean eddies on ocean tracer distribution and fluxes. The Charney case shares many similarities with recent high-resolution primitive equation simulations. The main difference between the two regimes is indeed an energization of submesoscale turbulence near the surface. The energy cycle is analyzed in the (k, z) plane, where k is the horizontal wavenumber. In the two regimes, the large-scale buoyancy forcing is the primary source of mechanical energy. It sustains an energy cycle in which baroclinic instability converts more available potential energy (APE) to kinetic energy (KE) than the APE directly injected by the forcing. This is due to a conversion of KE to APE at the scale of arrest. All the KE is dissipated at the bottom at large scales, in the limit of infinite resolution and despite the submesoscales energizing in the Charney case. The eddy PV flux is largest at the scale of arrest in both cases. The eddy diffusivity is very smooth but highly nonuniform. The eddy-induced circulation acts to flatten the mean isopycnals in both cases.

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