Sensitivity experiments with a quasi-geostrophic model of stratospheric sudden warming

We describe a series of sensitivity experiments with a quasi-geostrophic model of the interaction of stationary planetary waves with the mean zonal flow in the stratosphere and mesosphere. The model is of the Matsuno type, which neglects wave-wave interaction and includes only a single zonal harmonic of the planetary wave spectrum in each simulation. We employed the model to investigate the source of the double-layer structure previously obtained by several authors for the stratospheric sudden warming with wavenumber one. Our results suggest that this characteristic of the model-produced warming is a property only of models without damping. When reasonable dissipation is included in the model, the double-layer structure disappears. This implies the importance of the drag parameterization in properly simulating warming events and, since the actual drag very probably is effected by breaking internal waves, it suggests that future analysis should include a specific representation of this effect. We also investigated the dependence of stratospheric warming on the structure of the zonal wind field. Our analyses show in particular that substantial reduction of the height of the polar night jet mitigates strongly against the occurrence of a sudden warming event.     

The interaction of two asymmetric quasi-geostrophic vortex patches

ABSTRACT

Herein we study the general interaction of two vortex patches in a single-layer quasi-geostrophic shallow-water flow. Steadily-rotating equilibrium states are found over a wide parameter space spanning the Rossby deformation length, vortex area ratio, potential vorticity ratio, and gap between their innermost edges. A linear stability analysis is then used to identify the critical gap separating stable and unstable solutions, over the entire range of area and potential vorticity ratios, and for selected values of the Rossby deformation length. A representative set of marginally unstable equilibrium states are then slightly perturbed and evolved by an accurate contour dynamics numerical algorithm to understand the long-term fate of the instabilities. Not all instabilities lead to vortex merger; many in fact are characterised by weak filamentation and a small adjustment of the vortex shapes, without merger. Stronger instabilities lead to material being torn from one vortex and either wrapped around the other or reduced to ever thinning filamentary debris. A portion of the vortex may survive, or it may be completely strained out by the other.     

A quasi-geostrophic numerical model of a rotating internally heated fluid

Abstract

A quasi-geostrophic numerical model of flow in a rotating channel is integrated under conditions typical of laboratory experiments with an internally heated annulus system. Compared to a laboratory experiment, or a full Navier-Stokes simulation, the quasi geostrophic numerical model is a simple system. It includes nonlinear interactions, dissipation via conventional parameterizations of Ekman layers and internal diffusion, and a steady forcing term which represents heating near the centre of the channel and cooling near both sides. Explicit boundary layers, cylindrical geometry effects, horizontal variations in static stability and variations in conductivity and diffusivity with temperature are all absent, and ageostrophic advection is incompletely represented. Nevertheless, over a range of parameters, flows are produced which strongly resemble those seen in the laboratory thus suggesting that the most important physical processes are represented. The numerical model is used to map out a regime diagram which includes examples of steady flows, flows with periodic time dependence (wavenumber vacillations) and flows which are irregularly time dependent.     

Numerical experiments with a three-dimensional model of an enclosed basin

A three-dimensional numerical model, for simulating velocity and temperature variations in a basin under various forcing mechanisms, is presented. Vertical structure is analyzed using a Galerkin Method with modified Chebyshev polynomials as expansion functions. With the proper choice of these functions, the barotropic and baroclinic parts of the motion are separated naturally in the model. A time-splitting procedure is then implemented; this makes time integration very efficient.Internal seiching due to windstress is simulated in the first experiment. Results are compared with those obtained using two-layered and 3D models. The geostrophic adjustment of a river flowing into a basin is then simulated. When friction and entrainment is neglected, flow adjusts to geostrophic balance over a distance about one third of the width of the basin. Weak turbulence has a large effect on the flow. For example, with a vertical eddy coefficient of 0.001 m² s⁻¹, isothermals are distorted so that their angle of intersection with the basin axis is large. Geostrophic adjustment still takes place over one third of the width but, due to frictional effects the flow is now quite large all over the lake.     

On the meridional form of baroclinic waves in a two-layer quasi-geostrophic model

Summary It is shown that in laterally bounded two-layer models of the atmosphere the only permissible meridional variation of the wave solutions is of the form sin(/D) whereD is the lateral width.     

Interaction between a surface jet and subsurface vortices in a three-layer quasi-geostrophic model

This study focuses on the interaction between mid depth vortices and surface jets and fronts in a three-layer quasi-geostrophic model. Such vortices may be regarded as an idealisation of meddies, eddies of Mediterranean Water in the Northeastern Atlantic Ocean, interacting with the Azores j t and front. Successively, a single vortex, a vortex doublet and a vortex pair (in the middle layer) are studied. When a single vortex is considered, the jet has a critical effect of its motion, temporarily slowing down its zonal drift and accelerating it meridionally as the vortex crosses the front. On the contrary, if the vortex does not cross the front, it can drift fairly rapidly along it. The merger of a vortex doublet (two like-signed vortices) below a surface jet is possible whatever the relative position of this doublet with respect to the jet axis. Nevertheless, doublets initially located below the front, will undergo stronger shear and merger efficiency will be diminished. The merged vortex will be circled at the surface by a large meander of the jet. Finally, eastward jet-dipole interaction experiments are performed with various orientations of the vortex dipoles. Eastward propagating dipoles below the jet follow it without deformation. Southeastward drifting dipoles finally join the previous evolution. Southward and southwestward directed dipoles cross the surface jet southeastward. The presence of meanders initially on the jet does not prevent its crossing by a single vortex. Characteristics of the surface jet meanders are also described for a possible remote detection of this process.     

Interaction between a surface quasi-geostrophic buoyancy filament and an internal vortex

This paper focuses on the nonlinear interaction between a surface quasi-geostrophic buoyancy filament and an internal vortex. We first revisit the stability of an isolated buoyancy filament. The buoyancy profile considered is continuous and leads to a continuous velocity field, albeit one with infinite shear just outside its edge. The stability properties of an isolated filament help to interpret the unsteady interaction with a sub-surface (internal) vortex studied next. We find that, in all cases, the filament breaks into billows, analogous in form to those occurring in Kelvin–Helmholtz shear instability. For intense buoyancy filaments, the vortex itself may undergo strong deformations, including being split into several pieces. Generally, the nonlinear interaction causes both the filament and the vortex to lose their respective “self”-energies to the energy of interaction. The flow evolution depends sensitively on whether the vertical vorticity of the filament and the vortex have the same or opposite signs – termed “cooperative” and “adverse” shear respectively. In cooperative shear, the filament rolls up into a coherent surface eddy above a vortex initially placed below it, whereas in adverse shear, buoyancy is expelled above the vortex. Although sufficiently great shear induced by the buoyancy filament may split the vortex in both cases, adverse shear is significantly more destructive.     

Analyses of zonal atmospheric excitation functions and their correlation with polar motion excitation functions

The atmospheric influence on the Earths, rotation can be described by the effective atmospheric angular momentum (EAAM) functions. In this study we focus on the analysis of short period variations of the equatorial components of the zonal EAAM excitation functions ₁ and ₂ and their influence on similar variations of polar motion. The global objective analysis data of the Japanese Meteorological Agency for the period 1986–1992 were used to compute the EAAM excitation functions in different latitude belts. Time- and latitude-variable amplitude spectra of variations of these functions with periods shorter than 150 days, containing pressure, pressure with the inverted barometric correction, and wind terms were computed. The spectra show distinct latitude and time variations of the prograde and retrograde oscillations which reach their maxima mainly in mid-latitudes. Prograde and retrograde oscillations with periods of about 40–60 days and about 110–120 days are seen in the spectra of pressure terms of the equatorial components of the zonal EAAM excitation functions. Additionally, correlation coefficients and cross-spectra between variations of the geodetic polar motion and equatorial components of the zonal EAAM excitation functions were computed to identify the latitude belts of the globe over which atmospheric circulation changes are correlated mostly with short period variations of the polar motion excitation functions. The correlation coefficients vary in time and latitude and reach maximum values in the northern latitudes from 50°N to 60°N. In the cross-spectra between the polar motion excitation functions and pressure terms of the zonal EAAM excitation functions there are peaks of common prograde oscillations with the periods around 20, 30, 40–50, 60 and 80–150 days and of common retrograde oscillations around 20, 30, 40 and 50–70 days.Paper presented at the IERS Workshop in Paris, March 1994     

Numerical computation of the tidally induced Lagrangian residual current in a model bay

With a depth-averaged numerical model, the tidally induced Lagrangian residual current in a model bay was studied. To correctly reflect the long-term mass transport, it is appropriate to use the Lagrangian residual velocity (LRV) rather than the Eulerian residual velocity (ERV) or the Eulerian residual transport velocity (ETV) to describe the residual current. The parameter κ, which is defined as the ratio of the typical tidal amplitude at the open boundary to the mean water depth, is considered to be the indicator of the nonlinear effect in the system. It is found that the feasibility of making the mass transport velocity (MTV) approximate the LRV is strongly dependent on κ. The error between the MTV and the LRV tends to increase with a growing κ. An additional error will come from the various initial tidal phases due to the Lagrangian drift velocity (LDV) when κ is no longer small. According to the residual vorticity equation based on the MTV, the Coriolis effect is found to influence the residual vorticity mainly through the curl of the tidal stress. A significant difference in the flow pattern indicates that the LRV is sensitive to the bottom friction in different forms.     

On the stability properties of the nongeostrophic disturbances in a barotropic zonal current

Summary The stability properties of the nongeostrophic disturbances are studied in a barotropic zonal current. The growth rate of the nongeostrophic disturbances is increased and the instability is generally shifted towards shorter wavelengths. Even in the structure of the nongeostrophic disturbances large differences are found as compared to geostrophic disturbances.On leave from Physical Research Laboratory, Ahmedabad, India.     

纬向非均匀基流对大气长波调整的作用

大气长波的发展和演变影响着大气的可预报性,并对提高天气预报和气候预测水平有重要的意义.在影响大气长波演变的因子中,除波与波非线性相互作用外,基流的作用也非常重要.本文利用非均匀基本场下Rossby波运动方程,通过数值求解,分析了基本场结构和初始场对Rossby波演变的影响,揭示了纬向非均匀基本场对长波调整的作用.研究结果表明:基流纬向非均匀时,线性Rossby波也会出现长波调整现象,基流随纬向变化是长波发生调整的又一个重要机制;大气长波调整对波动的初始振幅不敏感,但基本场振幅影响着长波调整能否出现和出现的时间;基本场纬向平均西风基流的大小除影响波动传播的速度和方向外,还影响长波调整出现的时间和规律;长波调整的出现还与基本场和初始场的结构有关,不同基本场时,波动是否发生调整、向高波数还是向低波数调整都决定于基本场结构,相同基本场时,不同初始结构的波动也有着不同的演变过程.     

A comparison of numerical simulations of eddy generation performed with a two- and a three-layer quasi-geostrophic model of oceanic mesoscale eddies

Abstract

The generation of eddies by a large-scale flow over mesoscale topography is studied with the help of two- and three-layer nonlinear quasi-geostrophic models of the open ocean. The equations are integrated forward in time with no eddies present initially. For a given time, the displacement of the interface between layers two and three (ζ) tends to a well-defined limit (function of the horizontal spatial coordinates) as ρ ₃ - ρ ₂ → 0 (ρ_r is the density of layer r). Even for values of α[= (ρ ₃ - ρ ₂)/(ρ ₂ - ρ ₁)] ^as small as 0.01 the potential energy due to ζ is not negligible and it can reach, in some cases, a considerable fraction of the total eddy energy.     

The effect of aerosols on the temperatures of a zonal average climate model

The effect of atmospheric aerosols on the temperatures of a zonal average climate model is investigated. This is done by introducing into the climate model the results of extensive calculations of the effect of aerosols on the partitioning of solar radiation. Calculations are performed for a non-absorbing and a sloghtly absorbing aerosol, for average and for heavy aerosol amounts. The results indicate that the presence of atmospheric aerosols causes a cooling of the earth's surface and atmosphere, at all latitudes, with aerosol amounts, especially for the absorbing aerosols. The results are compared with some of the previous estimates of aerosol effects on climate.     

Numerical simulation of the electric field and zonal current in the Earth’s ionosphere: The dynamo field and equatorial electrojet

The work is devoted to the numerical simulation of the dynamo electric field and its effects in the Earth’s ionosphere within the scope of the thermosphere-ionosphere-protonosphere global self-consistent model developed at WD IZMIRAN. The new electric field calculation block, which was used to obtain results of the self-consistent calculations of the electric field potential generated by the dynamo effect of the thermospheric winds (the dynamo field) and the equatorial electrojet for March 22, 1987, is briefly described in this work. A comparison of the obtained results with the experimental data showed a satisfactory agreement. Moreover, the proposed model was used to calculate the diurnal variations in the ionospheric parameters for Jicamarca equatorial station under the same conditions with the help of the new block of the electric field. The results of these calculations are also presented and discussed in this work. It has been indicated that the new model satisfactorily describes the specific features of electric field distribution at the geomagnetic equator and the well-known phenomenon of equatorial electrojet.     

Baroclinic nonlinear exchanges of energy and potential enstrophy in the quasi-geostrophic two-layer model

Abstract

Merilees and Warn's (1975) nonlinear interaction analysis of two-dimensional nondivergent flow is extended to examine the quasi-geostrophic two-layer model. Two sets of triads exist in this model (Salmon, 1978). The purely barotropic triads are the same as the triads examined by Merilees and Warn. Baroclinic-barotropic triads are found to exchange more energy or potential enstrophy with smaller or larger scales depending on the scale of motion as compared with the internal Rossby deformation radius and the relative wavenumber position of baroclinic and barotropic components.     

Numerical modeling of the atmospheric boundary layer over a hilly landscape

Summary A model for calculating the wind, turbulent exchange coefficients and a modification of the initial temperature over a hilly terrain is described. The paper mainly deals with a numerical realization of the model equations. Some features of the splitting method are discussed in detail. A special version of the splitting method suitable for solving the atmospheric boundary layer is described.

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A note on the necessary condition for baroclinic instability of monsoon zonal current

Analytic expressions are derived for the minimum easterly and westerly jet strengths necessary for baroclinic instability, in terms of their half-widths and location. For this purpose the necessary condition for an internal jet is utilized and the jets and static stability are represented by simple mathematical functions. Dependency of the minimum jet strengths to their half-width and location are discussed.