Numerical studies of transient planetary circulations in a wind-driven ocean

Summary The time-dependent primitive equations for a shallow homogeneous ocean with a free surface are solved for a bounded basin on the sphere, driven by a steady zonal wind stress and subject to lateral viscous dissipation. These are the vertically integrated equations for a free-surface model, and are integrated to 60 days from an initial state of rest by an explicit centered-difference method with zero-slip lateral boundary conditions. In a series of comparative numerical solutions it is shown that at least a 2-deg resolution is needed to resolve the western boundary currents adequately and to avoid undue distortion of the transient (Rossby waves. The -plane formulation is shown to be an adequate approximation for the mean circulation in the lower and middle latitudes, but noticeably intensifies the transports poleward of about 50 deg and both slows and distorts the transients in the central basin. The influence of the (southern) zonal boundary on the transport solutions is confined to the southernmost gyre, except in the region of the western boundary currents where its influence spreads to the northern edge of the basin by 30 days. The total boundary current transport is shown to be approximately proportional to the zonal width of the basin and independent of the basin's (uniform) depth, while the elevation of the free water surface is inversely proportional to the basin depth, in accordance with linear theory. The introduction of bottom friction has a marked damping effect on the transient Rossby waves, and also reduces the maximum boundary-current transport. The solutions throughout are approximately geostrophic and are only slightly nonlinear.The root-mean-square (rms) transport variability during the period 30 to 60 days is concentrated in the southwest portion of the basin through the reflection of the transient Rossby waves from the western shore and has a maximum corresponding to an rms current variability of about 3 cm sec^–1. The transport variabilities are about 10 percent of the mean zonal transport and more than 100 percent of the mean meridional transport over a considerable region of the western basin (outside the western boundary current regime). Some 99 percent of the total kinetic energy is associated with the zonal mean and standing zonal waves, which are also responsible for the bulk of the meridional transport of zonal angular momentum. Although the transient Rossby waves systematically produce a momentum flux convergence at the latitude of the maximum eastward current, much in the manner of their atmospheric counterparts, this is only a relatively small contribution to the zonal oceanic momentum balance; the bulk of the mean zonal stress is here balanced by a nearly stationary net pressure torque exerted against the meridional boundaries by the wind-raised water. In an ocean without such boundaries the role of the transient circulations may be somewhat more important.     

A numerical study of rotating annulus flows using a modified Galerkin method

Summary Physical phenomena fundamental to rotating, baroclinically driven flows are studied with reference to results of numerical simulation of rotating annulus flows, using a modified Galerkin Model. Both local and global effects of sources, sinks, and transports of heat and momentum are discussed. A convenient energy exchange diagram reveals detailed information that is used to analyze nonlinear equilibration and amplitude vacillation of quasi-geostrophic baroclinic eddies. Transient inertial oscillations, sidewall boundary layers, and internal boundary layers are also discussed.A detailed study of symmetric flows is made, eleven of which are tested numerically for stability with respect to three-dimensional disturbances of a given zonal wave number. Two of the four unstable cases are integrated to a numerical steady state with finite-amplitude, quasi-geostrophic baroclinic waves. With the rigid-lid geometry assumed, the average zonal velocity is zero, resulting in zero phase velocity of the waves. The structure of the thermal wave is nearly coherent in the vertical. These numerical results are consistent with laboratory observations.The eddy flow is quasi-geostrophic except in horizontal boundary layers, where the flow is driven toward low pressure. A small cross-isotherm advection is sufficient to maintain the temperature wave against diffusion and vertical advection. The eddy flow adjusts spontaneously toward the form of the fastest growing or slowest decaying disturbance representable by the truncated space resolution. The eddy flow feeds energy into the mean zonal flow in barotropic-type interactions reflected mainly by the familiar tilted trough. During equilibration, the eddy flow alters the mean zonal flow in such a way that eddy energy sources are reduced relative to energy sinks. However, this adjustment is small compared to the change of total flow, which reflects a relatively large change of eddy amplitude. This suggests that small errors in the mean zonal flow representation can lead to relatively large errors in total flow representation.In most flows studied the kinetic energy dissipation is concentrated in thin boundary layers. In spite of this thinness, the basically laminar character of these dissipative boundary layers allows accurate and economical numerical simulation through the use of characteristic functions, which is a natural refinernent of the basic Galerkin method used. (In this prototype study, only moderately characteristic functions are used, thus sacrificing numerical economy while simplifying the programming.) Similarly, the generation of potential energy, which is transformed into the kinetic energy of the flow, is accurately simulated. In most cases studied, this generation is also concentrated in thin boundary layers where thermal energy is extracted from cold fluid and added to warm fluid.Contribution number 76 of the Geophysical Fluid Dynamics Institute, Florida State University, USA.     

Baroclinic energetics and zonal plane distribution of monsoon disturbances

The adiabatic, quasi-geostraphic, 25-layer, numerical, linear model with Ekman boundary layer friction is utilised to perform the baroclinic stability analysis of the mean monsoon zonal wind profile. It is shown thec _i is a function of the resultant wavenumber alone. This relation is able to explain the effects of the lateral walls on the unstable waves.The energetics and zonal plane distribution of the short and long preferred viscous waves are computed. The upward motion of the short wave together with the warm (cold) core lies to the west of the surface trough position above (below) 850 mb. Further, it is shown that the main source of kinetic energy for the wave lies in the middle layer (850–700 mb) which is transported to the lower and upper layers. Computed is found to be in good agreement with observed values.     

Barotropic-Baroclinic instability of mean zonal wind during summer monsoon

Barotropic-Baroclinic instability of horizontally and vertically shearing mean monsoon flow during July is investigated numerically by using a 10-layer quasi-geostrophic model. The most unstable mode has a wavelength of about 3000 km and westward phase speed of about 15 m sec^–1. The most dominant energy conversion is from zonal kinetic energy to eddy kinetic energy. The structure of the most unstable mode is such that the maximum amplitude is concentrated at about 150 mb and the amplitude at the lowest layers is negligibly small. Barotropic instability of the zonal flow at 150 mb seems to be the primary excitation mechanism for the most unstable mode which is also similar to the observed westward propagating waves in the upper troposphere during the monsoon season. The results further suggest that Barotropic-Baroclinic instability of the mean monsoon flow cannot explain the occurrence of monsoon depressions which have their maximum amplitude at the lower levels and are rarely detected at 200 mb.     

Form-drag instability in a barotropic and a baroclinic atmosphere

We discuss the form-drag instability for a quasi-geostrophic channel flow. We first study the characteristics of this instability in a barotropic flow, considering in detail the influence of the meridional scale and discussing which structure of the perturbation zonal flow must be chosen in order to describe properly this instability.We then consider a continuous quasi-geostrophic channel model in which the topography enters only through the bottom boundary condition, and we discuss how in this case the effects of the form-drag are felt by the mean zonal flow through the ageostrophic mean meridional circulation. Because the meridional structure of the perturbation zonal flow cannot simply be extended from the barotropic to the continuous case, we show how to modify it properly.We then study the baroclinic model in the particular case of constant (in the vertical) basic-state zonal flow and show how this case closely resembles the barotropic, demonstrating the barotropic nature of the form-drag instability.Symbols _t is the partial derivative with respect tot. - _x is the partial derivative with respect tox. - _y is the partial derivative with respect toy. - represents the geostrophic stream function. - u is the eastward component of the geostrophic wind. - v is the northward component of the geostrophic wind. - u _a is the eastward component of the ageostrophic wind. - v _a is the northward component of the ageostrophic wind. - w is the vertical component of the wind. - f is the Coriolis parameter=2 sin f _o+y. - f _o is the Coriolis parameter evaluated at mid-latitude. - N is the Brunt-Vaisala frequency. - [A] is the zonal (x) average ofA at constantp andy. - <A> is the horizontal (x andy) average ofA at constantp     

On wave motions in a tropical spectral experiment

An attempt is made to use the barotropic vorticity equation in spectral form in order to study barotropic instability when the basic current has east-west quasi-stationary asymmetries on the scale of long waves. This is done by expressing the spectral equations in three different ways. In the first experiment a 9-component system is integrated and the long waves are allowed to propagate freely. In the second experiment the long waves are constrained to propagate slowly and in the third experiment, they are removed altogether.The motivation behind the present investigation is due to observations made in the motion fields of the tropics. These are characterized by quasi-stationary long waves and very energetically active and propagating short waves.The presence of quasi-stationary long waves seems to enhance the energy exchanges between the short waves and the mean zonal current and also allow for larger energy values for the short waves. Long term integration (90 days) shows a 6-day mode in thev time spectra at latitude 10°N and a 15-day mode in theu time spectra at individual grid points in the equatorial latitudes. Any possible connection between this peak and the observed peak of 15 days in the completely different physics of Kelvin waves is left as a conjecture.     

Analysis of various large-scale disturbances and the associated zonal mean motions in the atmosphere

Summary In this article, we present a scale analysis of planetary waves, extended long waves, and long waves. (We mean the extended long waves to be the disturbances whose east-west length is of order 10⁶ m and north-south extension 10⁷ m). We find for the extended long waves the two terms, the interaction between kinetic and available potential energy of the disturbances, and the interaction between the zonal mean available potential energy, and the eddy available potential energy, are of two orders of magnitude larger than the kinetic energy interaction between the disturbances and the associated zonal mean flow. This theoretical result concerning the relative importance of the various interaction terms may be of use in explaining the observational findings thus far available.It is also shown theoretically that the kinetic energy interaction between the planetary waves, the horizontal size of which is 10⁷ m, and the long waves, whose horizontal size is 10⁶ m, is of the same order as the interaction of kinetic energy between the zonal mean motion and the disturbances. This agrees fairly well with the observational estimates thus far obtained.     

Hemispheric simulation of the Asian summer monsoon

A three-level, -plane, filtered model is used to simulate the Northern Hemisphere summer monsoon. A time-averaged initial state, devoid of sub-planetary scale waves, is integrated through 30 days on a 5° latitude-longitude grid. Day 25 through day 30 integrations are then repeated on a 2.5° grid. The planetary-scale waves are forced by time-independent, spatially varying diabatic heating. Energy is extracted via internal and surface frictional processes. Orography is excluded to simplify synoptic-scale energy sources.During integration the model energy first increases, but stabilizes near day 10. Subsequent flow patterns closely resemble the hemisphere summer monsoon. Climatological features remain quasi-stationary. At 200 mb high pressure dominates the land area, large-scale troughs are found over the Atlantic and Pacific Oceans, the easterly jet forms south of Asia, and subtropical jets develop in the westerlies. At 800 mb subtropical highs dominate the oceans and the monsoon trough develops over the Asian land mass. The planetary scales at all levels develop a realistic cellular structure from the passage of transient synoptic-scale features, e.g., a baroclinic cyclone track develops near 55°N and westward propagating waves form in the easterlies.Barotropic redistribution of kinetic energy is examined over a low-latitude zonal strip using a Fourier wave-space. In contrast to higher latitudes where the zonal flow and both longer and shorter waves are fed by barotropic energy redistribution from the baroclinically unstable wavelengths, the low-latitude waves have a planetary-scale kinetic energy source. Wave numbers 1 and 2 maintain both the zonal flow and all shorter scales via barotropic transfers. Transient and standing wave processes are examined individually and in combination.Wave energy accumulates at wave numbers 7 and 8 at 200 mb and at wave number 11 in the lower troposphere. The 800-mb waves are thermally indirect and in the mean they give energy to the zonal flow. These characteristics agree with atmospheric observation. The energy source for these waves is the three wave barotropic transfer. The implications of examining barotropic processes in a Fourier wave-space, vice the more common approach of separating the flow into a mean plus a deviation are discussed.     

Effects of steep topography on the flow and stratification near Palmyra Atoll

Two interdisciplinary cruises aimed at relating the ecology of marine fish populations to oceanographic conditions were fielded during the late summer and late winter seasons near Palmyra Atoll (5.9°N, 162.1°W) in the Line Islands. Ocean current and hydrographic measurements revealed interaction of the flow with the steep topography. During the first cruise (August/September 1990) satellite-tracked surface drifters and acoustic Doppler current profiler (ADCP) measurements showed a strong eastward setting North Equatorial Counter Current (NECC) with maximum speeds exceeding 1 m s^–1 at 80 m depth approximately. This current turned southeastward on closer approach to Palmyra. The drifter paths exhibited excursions with zonal wavelength of approximately 250 km, meridional amplitude of 25 km and period of approximately 5 days. During the second cruise (February/March 1992), the ADCP-derived speeds of the NECC were weaker (maxima approximately 33 cm s^–1) while the relative geostrophic flow component was of magnitude similar to 1990 and the signal of zonal geostrophic currents reached much deeper to approximately 650 m depth (150 m in 1990). Doming isopycnals beneath the surface mixed layer as well as thick (10–25 m) internal mixed layers were found near Palmyra during both cruises, with slightly different positions relative to the island. The discontinuous vertical temperature profiles may have been a result of strong boundary mixing due to breaking internal waves on Palmyras steep slopes. In the immediate vicinity of the island variations in flow speed, stratification and mixing in both the alongshore and cross-isobath directions were observed. Overall, the current speeds were reduced during February/March 1992, the peak time of the 1991–1993 warm event in the tropical Pacific. While parameters of turbulent two-dimensional wake theory are suggestive of formation and shedding of eddies in the lee of the island, no direct observations of circular motions were made in either expedition.Responsible Editor: Hans Burchard     

Internal gravity wave selection in the upper troposphere and lower stratosphere observed by the MU radar: Preliminary results

Marked wavelike variations of the lower stratospheric wind observed on 7–10 May, 1985 by an MST radar in Japan (by the MU radar) are analyzed assuming that they are induced by monochromatic internal inertio-gravity waves. These variations are mainly composed of two modes (periods: 22 and 24 hours), both of which have zonal phase velocities (C _X ) slower than the mean westerly wind (). A statistical analysis of the zonal phase velocity shows thatC _X above andC _X below the tropopause jet stream, which is considered to be a vivid proof of wave selection due to the tropospheric mean flow and upward wave emission from the tropopause jet. A comparison between the MU radar results and routine meteorological observations leads to the conclusion that the marked waves appear when the jet stream takes a maximum wind speed.     

Some effects of a mean zonal thermocline gradient on planetary equatorial waves

Planetary equatorial waves are studied with the shallow water equations in the presence of a mean zonal thermocline gradient. The interactions between this gradient and waves are represented by three non-linear terms in the equations: one in the wind-forcing formulation in the x-momentum equation, and two for the advection of mass and divergence of the velocity field in the continuity equation. When the mean gradient is imposed but small, these three (linearized) terms will perturb the behavior of the equatorial waves. This paper gives a simple analytic treatment of this problem.The equatorial Kelvin mode is first solved with all three contributions, using a Wentzel-Kramers-Brillouin method. The Kelvin mode shows a spatial or/and temporal growth when the thermocline gradient is negative which is the usual situation in the equatorial Pacific ocean (deep thermocline in the west and shallow in the east). The more robust and efficient contribution comes from the advection term.The single effect of the advection of the mean zonal thermocline gradient is then studied for the Kelvin and planetary Rossby modes. The Kelvin mode remains unstable (damped), while the Rossby modes appear damped (unstable) for a negative (positive) thermocline gradient.     

Effects of the earth's rotation and the balance of zonal kinetic energy

Summary According to the symmetric formulation of the zonal kinetic energy equation, positive generations arise through countergradient transports of angular momentum. Five years of northern hemispheric upper air data are used to investigate two of the terms in the equation, which represent the effects of the transport, by the mean general circulation cells, of the angular momentum associated with the earth's rotation. These two -generation terms do not usually appear in the more traditional form of the conservation equation, and results of their evaluation have not appeared previously. It is found that positive generation largely dominates in the -term involving horizontal (meridional) transports of angular momentum, and negative generation in the -term involving vertical transport. In fall and particularly winter, both terms are responsible for very large amounts of generation of opposing sign for the whole atmosphere.The five years of data are also used to evaluate the balance of zonal kinetic energy implied by the symmetric equation in northern hemispheric polar caps of various pressure thicknesses. The vertical processes involved are not directly measured but rather are obtained from observed horizontal motions through use of continuity of mass and angular momentum requirements. Possible reasons for the lack of a perfect balance are offered, but in any case the residuals are generally not large enough to be of too much concern. Vertical eddies are found to play an important role in the balance of zonal kinetic energy. A study of the balance in the upper half of the atmosphere reveals that in spring the vertical eddies (summed for all scales) must tranport angular momentum and zonal kinetic energy upward toward the jet in order to counter the net effect of the mean cells in reducing the zonal kinetic energy in this volume. In the fall however, there is a dramatic change in the direction in which these vertical eddies act, as they now remove zonal kineticenergy from the upper half of the atmosphere in this season.The research reported in this paper was sponsored by the U.S. National Science Foundation under Grant No. GA-1310X.     

Baroclinic instability in ocean currents

Abstract

Unstable waves in a western boundary current are investigated in a full three-dimensional, numerical model. A numerical integration is carried out which traces the evolution of a growing wave on an initially uniform current with vertical shear. As indicated in earlier analytic studies based on simpler 2-layer models (Orlanski, 1969) the current is baroclinically unstable for the observed parameter range of the Gulf Stream.

Large meanders of the jet in the western boundary current are noticeable within 10 days. Finite amplitude effects, which can be investigated by the numerical model, reduce the growth rate of the disturbance by nearly an order of magnitude compared to linear theory. Comparison with observations indicate that the meanders of the Florida Current between Miami and Hatteras are probably baroclinically unstable waves.     

Numerical integration of a quasi-geostrophic atmospheric model with an asymmetric zonal current

Summary A two-level quasi-geostrophic model on a -plane, with an initial state characterized by an asymmetric zonal current was integrated numerically for a period of 14 days. Various field variables were computed and compared with the corresponding distributions obtained in two experiments with the same model and with initial states characterized by a constant zonal flow and by a flow varying sinusoidally with latitude.The research in this report has been sponsored wholly by the Air Force Cambridge Research Laboratories under Grant AF EOAR 63-108 through the European Office of Aerospace Research (OAR), US Air Force.     

A SF6 tracer study of horizontal mixing in Lake Constance

Horizontal mixing processes in the hypolimnion of the western part of Lake Constance are studied by measuring the dispersion of a sulfur hexafluoride (SF₆) tracer plume. Only 1 liter gaseous SF₆ (STP) was released at a central hypolimnic depth of 60 m in August 1990. Over a period of 3 months the horizontal dispersion of the tracer plume was measured by 19 surveys using a new, vertically integrating sampling device. The observed horizontal dispersion is marked by strong storm-induced stirring events. Nevertheless mean turbulent diffusion coefficients for the whole period can be computed. They rise about linear from 0.7 10⁵ cm²/s to 3.0 10⁵ cm²/s with the distance from the western end of the lake. For the hypolimnion of Überlingersee, a sill-separated basin in the western part of Lake Constance, a simple budget model gives an exchange time of 67 ± 6 days with the main basin (Obersee).     

Three-dimensional structure of mesoscale eddies in the western tropical Pacific as revealed by a high-resolution ocean simulation

The three-dimensional structure of mesoscale eddies in the western tropical Pacific(6°S–20°N, 120°E–150°E)is investigated using a high-resolution ocean model simulation. Eddy detection and eddy tracking algorithms are applied to simulated horizontal velocity vectors, and the anticyclonic and cyclonic eddies identified are composited to obtain their three-dimensional structures. The mean lifetime of all long-lived eddies is about 52 days, and their mean diameter is 147 km. Two typical characteristics of mesoscale eddies are revealed and possible dynamic explanations are analyzed. One typical characteristic is that surface eddies are generally separated from subthermocline eddies along the bifurcation latitude(~13°N) of the North Equatorial Current in the western tropical Pacific, which may be associated with different eddy energy sources and vertical eddy energy fluxes in subtropical and tropical gyres. Surface eddies have maximum swirl velocities of 8–9 cm s~(-1) and can extend to about 1500 m depth. Subthermocline eddies occur below 200 m, with their cores at about 400–600 m depth, and their maximum swirl velocities can reach 10 cm s~(-1). The other typical characteristic is that the meridional velocity component of the eddy is much larger than the zonal component. This characteristic might be due to more zonal eddy pairs(two eddies at the same latitude),which is also supported by the zonal wavelength(about 200 km) in the high-frequency meridional velocity component of the horizontal velocity.     

Atmosphere and Earth's rotation

The theoretical aspects of the transfer of angular momentum between atmosphere and Earth are treated with particular emphasis on analytical solutions. This is made possible by the consequent usage of spherical harmonics of low degree and by the development of large-scale atmospheric dynamics in terms of orthogonal wave modes as solutions of Laplace's tidal equations.An outline of the theory of atmospheric ultralong planetary waves is given leading to analytical expressions for the meridional and height structure of such waves. The properties of the atmospheric boundary layer, where the exchange of atmospheric angular momentum with the solid Earth takes place, are briefly reviewed. The characteristic coupling time is the Ekman spin-down time of about one week.The axial component of the atmospheric angular momentum (AAM), consisting of a pressure loading component and a zonal wind component, can be described by only two spherical functions of latitude : the zonal harmonicP ₂ ⁰ (), responsible for pressure loading, and the spherical functionP ₁ ¹ () simulating supperrotation of the zonal wind. All other wind and pressure components merely redistributeAAM internally such that their contributions toAAM disappear if averaged over the globe. It is shown that both spherical harmonics belong to the meridional structure functions of the gravest symmetric Rossby-Haurwitz wave (0, –1)^*. This wave describes retrograde rotation of the atmosphere within the tropics (the tropical easterlies), while the gravest symmetric external wave mode (0, –2) is responsible for the westerlies at midlatitudes. Applying appropriate lower boundary conditions and assuming that secular angular momentum exchange between solid Earth and atmosphere disappears, the sum of both waves leads to an analytical solution of the zonal mean flow which roughly simulates the observed zonal wind structure as a function of latitude and height. This formalism is used as a basis for a quantitative discussion of the seasonal variations of theAAM within the troposphere and middle atmosphere.Atmospheric excitation of polar motion is due to pressure loading configurations, which contain the antisymmetric functionP ₂ ¹ () exp(i) of zonal wavenumberm=1, while the winds must have a superrotation component in a coordinate system with the polar axis within the equator. The Rossby-Haurwitz wave (1, –3)^* can simulate well the atmospheric excitation of the observed polar motion of all periods from the Chandler wobble down to normal modes with periods of about 10 days. Its superrotation component disappears so that only pressure loading contributes to polar motion.The solar gravitational semidiurnal tidal force acting on the thermally driven atmospheric solar semidiurnal tidal wave can accelerate the rotation rat of the Earth by about 0.2 ms per century. It is speculated that the viscous-like friction of the geomagnetic field at the boundary between magnetosphere and solar wind may be responsible for the westward drift of the dipole component of the internal geomagnetic field. Electromagnetic or mechanical coupling between outer core and mantle may then contribute to a decrease of the Earth's rotation rate.     

Possible modulation of migrating diurnal tide by latitudinal gradient of zonal wind observed by SABER/TIMED

Temperature data from SABER/TIMED and Empirical Orthogonal Function(EOF) analysis are taken to examine possible modulations of the temperature migrating diurnal tide(DW1) by latitudinal gradients of zonal mean zonal wind(■). The result shows that z increases with altitudes and displays clearly seasonal and interannual variability. In the upper mesosphere and lower thermosphere(MLT), at the latitudes between 20°N and 20°S, when ■ strengthens(weakens) at equinoxes(solstices) the DW1 amplitude increases(decreases) simultaneously. Stronger maximum in March-April equinox occurs in both z and the DW1 amplitude. Besides, a quasi-biennial oscillation of DW1 is also found to be synchronous with ■. The resembling spatial-temporal features suggest that ■ in the upper tropic MLT probably plays an important role in modulating semiannual, annual, and quasi-biennial oscillations in DW1 at the same latitude and altitude. In addition, ■ in the mesosphere possibly affects the propagation of DW1 and produces SAO of DW1 in the lower thermosphere. Thus, SAO of DW1 in the upper MLT may be a combined effect of ■ both in the mesosphere and in the upper MLT, which models studies should determine in the future.     

Some laboratory model experiments on the mechanism of two-dimensional momentum transfer in the atmosphere

Summary Investigating the jetstream formation in the upper troposphere, it becomes evident that two-dimensional transfer processes are, to a high degree, responsible for the accumulation of kinetic energy and momentum in those upper tropospheric regions. To shed light on these processes a series of barotropic model experiments has been carried out using a special dynamic procedure for vortex generation. In a large, rotating, cylindrical vessel (filled with water, rotation rate ₀) three smaller cylinders have been fitted eccentrically. Their rotation relative to the vessel (rotation rate _i ,i=1, 2, 3) produces a sharply limited narrow region around each of them, where a nearly two-dimensional relative motion can be observed. Beyond this region — we call it friction zone — there is no motion. Now if we impose some perturbation on this steady mean flow (e.g. by setting _i = 0) the zonal current breaks down into a definite number of vortices which show a random distribution. The dynamic behaviour of these nearly two-dimensional vortices can then be studied.The main results are: I) After the sudden breakdown of the friction zones the most intensive eddies, which are cyclonic, drift more or less directly towards the centre to be organized there into a larger vortex. This development is strongly influenced by the -effect and the ratio = _i /₀, which controls the supply of rotational energy. II) If there exists a steady zonal basic current, the vortices will be more and more deformed when approaching and penetrating the zonal flow until they are wholly incorporated.     

Some general results for normal mode instability on a sphere

Abstract

The stability properties are described for two general types of zonal mean flows: solid body rotation and a mid-latitude jet. Growth rates are plotted versus zonal wavenumber and mean flow vertical shear in both cases. The structure of the most unstable modes is described and some physical interpretation given.