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## Abstract

A homogeneous fluid is bounded above and below by horizontal plane surfaces in rapid rotation about a vertical axis. An obstacle is attached to one of the surfaces, and at large distances from the obstacle the relative velocity is steady and horizontal. Solutions are obtained as power series expansions in the Rossby number, uniformly valid as the Taylor number approaches infinity.

If the height of the obstacle is greater than the Rossby number times the depth, a stagnant region (Taylor column) forms over the obstacle. Outside this region there is a net circulation in a direction opposite the rotation. The shape of the stagnant region and the circulation are uniquely determined as part of the solution.

Possible geophysical applications are discussed, and it is shown that stratification renders Taylor columns unlikely on earth, but that the Great Red Spot of Jupiter may be an example of this phenomenon, as Hide has suggested.

## Abstract

A homogeneous fluid is bounded above and below by horizontal plane surfaces in rapid rotation about a vertical axis. An obstacle is attached to one of the surfaces, and at large distances from the obstacle the relative velocity is steady and horizontal. Solutions are obtained as power series expansions in the Rossby number, uniformly valid as the Taylor number approaches infinity.

If the height of the obstacle is greater than the Rossby number times the depth, a stagnant region (Taylor column) forms over the obstacle. Outside this region there is a net circulation in a direction opposite the rotation. The shape of the stagnant region and the circulation are uniquely determined as part of the solution.

Possible geophysical applications are discussed, and it is shown that stratification renders Taylor columns unlikely on earth, but that the Great Red Spot of Jupiter may be an example of this phenomenon, as Hide has suggested.

## Abstract

Radiative-convective equilibrium models of planetary atmospheres are discussed for the case when the infrared opacity is due to a vapor in equilibrium with its liquid or solid phase. For a grey gas, or for a gas which absorbs at all infrared wavelengths, equilibrium is impossible when the solar constant exceeds a critical value. Equilibrium therefore requires that the condensed phase evaporates into the atmosphere.

Moist adiabatic and pseudoadiabatic atmospheres in which the condensing vapor is a major atmospheric constituent are considered. This situation would apply if the solar constant were supercritical with respect to an abundant substance such as water. It is shown that the condensing gas would be a major constituent at all levels in such an atmosphere. Photodissociation of water in the primordial Venus atmosphere is discussed in this context.

## Abstract

Radiative-convective equilibrium models of planetary atmospheres are discussed for the case when the infrared opacity is due to a vapor in equilibrium with its liquid or solid phase. For a grey gas, or for a gas which absorbs at all infrared wavelengths, equilibrium is impossible when the solar constant exceeds a critical value. Equilibrium therefore requires that the condensed phase evaporates into the atmosphere.

Moist adiabatic and pseudoadiabatic atmospheres in which the condensing vapor is a major atmospheric constituent are considered. This situation would apply if the solar constant were supercritical with respect to an abundant substance such as water. It is shown that the condensing gas would be a major constituent at all levels in such an atmosphere. Photodissociation of water in the primordial Venus atmosphere is discussed in this context.

## Abstract

Expressions are derived for the potential energy of a fluid whose density depends on three variables: temperature, pressure, and salinity. The thermal expansion coefficient is a function of depth, and the application is to thermobaric convection in the oceans. Energy conservation, with conversion between kinetic and potential energies during adiabatic, inviscid motion, exists for the Boussinesq and anelastic approximations but not for all approximate systems of equations. In the Boussinesq/anelastic system, which is a linearization of the thermodynamic variables, the expressions for potential energy involve thermodynamic potentials for salinity and potential temperature. Thermobaric instability can occur with warm salty water either above or below cold freshwater. In both cases the fluid may be unstable to large perturbations even though it is stable to small perturbations. The energy per mass of this finite-amplitude instability varies as the square of the layer thickness. With a 4-K temperature difference and a 0.6-psu salinity difference across a layer that is 4000 m thick, the stored potential energy is ∼0.3 m^{2} s^{−2}, which is comparable to the kinetic energy of the major ocean currents. This potential could be released as kinetic energy in a single large event. Thermobaric effects cause parcels moving adiabatically to follow different neutral trajectories. A cold fresh parcel that is less dense than a warm salty parcel near the surface may be more dense at depth. Examples are given in which two isopycnal trajectories cross at one place and differ in depth by 1000 m or more at another.

## Abstract

Expressions are derived for the potential energy of a fluid whose density depends on three variables: temperature, pressure, and salinity. The thermal expansion coefficient is a function of depth, and the application is to thermobaric convection in the oceans. Energy conservation, with conversion between kinetic and potential energies during adiabatic, inviscid motion, exists for the Boussinesq and anelastic approximations but not for all approximate systems of equations. In the Boussinesq/anelastic system, which is a linearization of the thermodynamic variables, the expressions for potential energy involve thermodynamic potentials for salinity and potential temperature. Thermobaric instability can occur with warm salty water either above or below cold freshwater. In both cases the fluid may be unstable to large perturbations even though it is stable to small perturbations. The energy per mass of this finite-amplitude instability varies as the square of the layer thickness. With a 4-K temperature difference and a 0.6-psu salinity difference across a layer that is 4000 m thick, the stored potential energy is ∼0.3 m^{2} s^{−2}, which is comparable to the kinetic energy of the major ocean currents. This potential could be released as kinetic energy in a single large event. Thermobaric effects cause parcels moving adiabatically to follow different neutral trajectories. A cold fresh parcel that is less dense than a warm salty parcel near the surface may be more dense at depth. Examples are given in which two isopycnal trajectories cross at one place and differ in depth by 1000 m or more at another.

## Abstract

A nonlinear numerical model of long-lived Jovian vortices has been constructed. We assume that the measured zonal velocity profile ū(*y*) extends into the adiabatic interior, but that the eddies and large oval structures are confined to a shallow stably stratified upper layer. Each vortex is stationary with respect to the shear flow ū(*y*) at a critical latitude *y*
_{c}, that is close to the latitude of the vortex center, in agreement with observed flows on Jupiter. Our model differs from the solitary wave model of Maxworthy and Redekopp in that the stratification is not large in our model (the radius of deformation is less than the latitudinal scale of the shear flow), and therefore stationary linear wave solutions, neutral or amplified, do not exist. The solutions obtained are strongly nonlinear in contrast to the solitary wave solutions which are the weakly nonlinear extensions of ultralong linear waves. Both stable and unstable vortices are found in the numerical experiments. When two stable vortices collide, they merge after a short transient phase to form a larger stable vortex. This merging, rather than the non-interaction behavior predicted by the solitary wave theory, is more in agreement with observations of Jovian vortices. We suggest that the long-lived Jovian vortices maintain themselves against dissipation by adsorbing smaller vortices which are produced by convection.

## Abstract

A nonlinear numerical model of long-lived Jovian vortices has been constructed. We assume that the measured zonal velocity profile ū(*y*) extends into the adiabatic interior, but that the eddies and large oval structures are confined to a shallow stably stratified upper layer. Each vortex is stationary with respect to the shear flow ū(*y*) at a critical latitude *y*
_{c}, that is close to the latitude of the vortex center, in agreement with observed flows on Jupiter. Our model differs from the solitary wave model of Maxworthy and Redekopp in that the stratification is not large in our model (the radius of deformation is less than the latitudinal scale of the shear flow), and therefore stationary linear wave solutions, neutral or amplified, do not exist. The solutions obtained are strongly nonlinear in contrast to the solitary wave solutions which are the weakly nonlinear extensions of ultralong linear waves. Both stable and unstable vortices are found in the numerical experiments. When two stable vortices collide, they merge after a short transient phase to form a larger stable vortex. This merging, rather than the non-interaction behavior predicted by the solitary wave theory, is more in agreement with observations of Jovian vortices. We suggest that the long-lived Jovian vortices maintain themselves against dissipation by adsorbing smaller vortices which are produced by convection.

## Abstract

A linearized primitive equation (LPE) model is developed to study thermal tides in the atmosphere of Venus. The LPE model describes diurnal and semidiurnal oscillations of a cyclostrophically balanced atmosphere in which zonal velocity varies with altitude and latitude. The numerical algorithm follows Staniforth and Daley. The solar thermal forcing is increased algebraically in time to separate the forced tidal response from free atmospheric oscillations. Parameters of the basic state and forcing agree with *Pioneer Venus* observations. Results of the model are compared with the solar-fixed component of brightness temperature variations measured by Taylor *et al*. and Elson using data from the *Pioneer Venus* orbiter infrared radiometer (OIR). The comparison is made by convolving the computed model radiances with the weighting functions of the OIR channels. Agreement between LPE model results and OIR observations is excellent. Two interesting features of the OIR data are accounted for, namely, the slow variation of phase with altitude and the dominance of the semidiurnal oscillation over the diurnal oscillation. Success of the LPE model opens the way for calculating tidal transports of heat and momentum and assessing the role of tides in maintaining the Venus super-rotation.

## Abstract

A linearized primitive equation (LPE) model is developed to study thermal tides in the atmosphere of Venus. The LPE model describes diurnal and semidiurnal oscillations of a cyclostrophically balanced atmosphere in which zonal velocity varies with altitude and latitude. The numerical algorithm follows Staniforth and Daley. The solar thermal forcing is increased algebraically in time to separate the forced tidal response from free atmospheric oscillations. Parameters of the basic state and forcing agree with *Pioneer Venus* observations. Results of the model are compared with the solar-fixed component of brightness temperature variations measured by Taylor *et al*. and Elson using data from the *Pioneer Venus* orbiter infrared radiometer (OIR). The comparison is made by convolving the computed model radiances with the weighting functions of the OIR channels. Agreement between LPE model results and OIR observations is excellent. Two interesting features of the OIR data are accounted for, namely, the slow variation of phase with altitude and the dominance of the semidiurnal oscillation over the diurnal oscillation. Success of the LPE model opens the way for calculating tidal transports of heat and momentum and assessing the role of tides in maintaining the Venus super-rotation.

## Abstract

On many planets there is a continuous heat supply to the surface and a continuous emission of infrared radiation to space by the atmosphere. Since the heat source is located at higher pressure than the heat sink, the system is capable of doing mechanical work. Atmospheric convection is a natural heat engine that might operate in this system. Based on the heat engine framework, a simple theory is presented for atmospheric convection that predicts the buoyancy, the vertical velocity, and the fractional area covered by either dry or moist convection in a state of statistical equilibrium. During one cycle of the convective heat engine, heat is taken from the surface layer (the hot source) and a portion of it is rejected to the free troposphere (the cold sink) from where it is radiated to space. The balance is transformed into mechanical work. The mechanical work is expended in the maintenance of the convective motions against mechanical dissipation. Ultimately, the energy dissipated by mechanical friction is transformed into heat. Then, a fraction of the dissipated energy is radiated to space while the remaining portion is recycled by the convecting air parcels. Increases in the fraction of energy dissipated at warmer temperature, at the expense of decreases in the fraction of energy dissipated at colder temperatures, lead to increases in the apparent efficiency of the convective heat engine. The volume integral of the work produced by the convective heat engine gives a measure of the statistical equilibrium amount of convective available potential energy (CAPE) that must be present in the planet's atmosphere so that the convective motions can be maintained against viscous dissipation. This integral is a fundamental global number qualifying the state of the planet in statistical equilibrium conditions. For the earth's present climate, the heat engine framework predicts a CAPE value of the order of 1000 J kg^{−1} for the tropical atmosphere. This value is in agreement with observations. It also follows from our results that the total amount of CAPE present in a convecting atmosphere should increase with increases in the global surface temperature (or the atmosphere's opacity to infrared radiation).

## Abstract

On many planets there is a continuous heat supply to the surface and a continuous emission of infrared radiation to space by the atmosphere. Since the heat source is located at higher pressure than the heat sink, the system is capable of doing mechanical work. Atmospheric convection is a natural heat engine that might operate in this system. Based on the heat engine framework, a simple theory is presented for atmospheric convection that predicts the buoyancy, the vertical velocity, and the fractional area covered by either dry or moist convection in a state of statistical equilibrium. During one cycle of the convective heat engine, heat is taken from the surface layer (the hot source) and a portion of it is rejected to the free troposphere (the cold sink) from where it is radiated to space. The balance is transformed into mechanical work. The mechanical work is expended in the maintenance of the convective motions against mechanical dissipation. Ultimately, the energy dissipated by mechanical friction is transformed into heat. Then, a fraction of the dissipated energy is radiated to space while the remaining portion is recycled by the convecting air parcels. Increases in the fraction of energy dissipated at warmer temperature, at the expense of decreases in the fraction of energy dissipated at colder temperatures, lead to increases in the apparent efficiency of the convective heat engine. The volume integral of the work produced by the convective heat engine gives a measure of the statistical equilibrium amount of convective available potential energy (CAPE) that must be present in the planet's atmosphere so that the convective motions can be maintained against viscous dissipation. This integral is a fundamental global number qualifying the state of the planet in statistical equilibrium conditions. For the earth's present climate, the heat engine framework predicts a CAPE value of the order of 1000 J kg^{−1} for the tropical atmosphere. This value is in agreement with observations. It also follows from our results that the total amount of CAPE present in a convecting atmosphere should increase with increases in the global surface temperature (or the atmosphere's opacity to infrared radiation).

## Abstract

Radio scintillations in Pioneer Venus radio Occultation data are simulated assuming that the index of refraction fluctuations in Venus's atmosphere responsible for the scintillations are directly caused by gravity wave fluctuations. The gravity waves are created by a global convection layer between 50- and 55-km attitude in Venus's atmosphere and propagate vertically. The authors compare the simulated scintillations with data from Pioneer Venus.

These gravity waves can explain the spectral shape and amplitude of the radio scintilations. The shape at high frequencies is controlled by wave breaking, which yields a saturated spectrum. The amplitude is subject to parameters such as the intensity of the convection, the angle between the zonal winds and the beam path, and the zonal wind profile at polar latitudes. To match the observed amplitude of the scintillations, the velocity variations of the energy-bearing eddies in the convection must be at least 2 m s^{−1}. This value is consistent with the Venus balloon results of Sagdeev et al. and is in the middle of the range considered by Leroy and Ingersoll in their study of convectively generated gravity waves. The later study, combined with the lower bound on velocity from the present study, then yields lower bounds on the vertical fluxes of momentum and energy in the Venus atmosphere.

## Abstract

Radio scintillations in Pioneer Venus radio Occultation data are simulated assuming that the index of refraction fluctuations in Venus's atmosphere responsible for the scintillations are directly caused by gravity wave fluctuations. The gravity waves are created by a global convection layer between 50- and 55-km attitude in Venus's atmosphere and propagate vertically. The authors compare the simulated scintillations with data from Pioneer Venus.

These gravity waves can explain the spectral shape and amplitude of the radio scintilations. The shape at high frequencies is controlled by wave breaking, which yields a saturated spectrum. The amplitude is subject to parameters such as the intensity of the convection, the angle between the zonal winds and the beam path, and the zonal wind profile at polar latitudes. To match the observed amplitude of the scintillations, the velocity variations of the energy-bearing eddies in the convection must be at least 2 m s^{−1}. This value is consistent with the Venus balloon results of Sagdeev et al. and is in the middle of the range considered by Leroy and Ingersoll in their study of convectively generated gravity waves. The later study, combined with the lower bound on velocity from the present study, then yields lower bounds on the vertical fluxes of momentum and energy in the Venus atmosphere.

## Abstract

The observed zonal motion of Jupiter's atmosphere near the cloud tops is investigated assuming geostrophic balance and a systematic temperature difference between light and dark bands. Excellent agreement is obtained between observed velocities and those predicted from the thermal wind relation with the temperature and rotation rate of the deep atmosphere independent of latitude. The light bands are found to be warmer than the dark bands. This model is inconsistent with a monotonic variation of insolation as the only energy source for the flow.

The barotropic stability criterion is also applied to the observed motion, and it appears that the necessary criterion for instability is approached but not exceeded in mid-latitude regions.

## Abstract

The observed zonal motion of Jupiter's atmosphere near the cloud tops is investigated assuming geostrophic balance and a systematic temperature difference between light and dark bands. Excellent agreement is obtained between observed velocities and those predicted from the thermal wind relation with the temperature and rotation rate of the deep atmosphere independent of latitude. The light bands are found to be warmer than the dark bands. This model is inconsistent with a monotonic variation of insolation as the only energy source for the flow.

The barotropic stability criterion is also applied to the observed motion, and it appears that the necessary criterion for instability is approached but not exceeded in mid-latitude regions.

## Abstract

A shallow water model with realistic topography and idealized zonal wind forcing is used to investigate orographically forced modes in the Martian atmosphere. Locally, the model produces barotropic modes with periods within the broad range of periods observed at the sites of *Viking Lander I* and *II* (VILI and VL2) during the fall and spring seasons. Its variability at those sites is dominated by an oscillation of 3 Martian solar days (sols) in the region of VL1 and by a 6-sol oscillation in that of VL2. These oscillations are forced by the zonal asymmetries of the Martian mountain field. Their robustness with respect to changes of the fundamental model parameters is examined. Since the exhibited periods occur for a barotropic forcing field that is highly idealized, it is difficult to say whether they have much to do with the real Mars, but their resemblance to some of the periodicities present in the observed Martian climatology deserves further investigation.

The spatial variability associated with the orographically forced oscillations is studied by means of extended empirical orthogonal function (EEOF) analysis. The 3-sol VL1 oscillation corresponds to a tropical, eastward traveling, zonal wavenumber one pattern. The 6-sol VL2 oscillation is characterized by two midlatitude, eastward traveling, mixed zonal wavenumber one and two and zonal wavenumber three and four patterns, with respective periods near 6.1 and 5.5 sols. The corresponding phase speeds are in agreement with some of the conclusions drawn from the lander observations. A linear stability analysis of the zonally asymmetric climatology reveals that the two most unstable modes are associated with periods near 3 and 6 sols; with the corresponding eigen-vectors showing patterns consistent with the results of the EEOF analyses.

## Abstract

A shallow water model with realistic topography and idealized zonal wind forcing is used to investigate orographically forced modes in the Martian atmosphere. Locally, the model produces barotropic modes with periods within the broad range of periods observed at the sites of *Viking Lander I* and *II* (VILI and VL2) during the fall and spring seasons. Its variability at those sites is dominated by an oscillation of 3 Martian solar days (sols) in the region of VL1 and by a 6-sol oscillation in that of VL2. These oscillations are forced by the zonal asymmetries of the Martian mountain field. Their robustness with respect to changes of the fundamental model parameters is examined. Since the exhibited periods occur for a barotropic forcing field that is highly idealized, it is difficult to say whether they have much to do with the real Mars, but their resemblance to some of the periodicities present in the observed Martian climatology deserves further investigation.

The spatial variability associated with the orographically forced oscillations is studied by means of extended empirical orthogonal function (EEOF) analysis. The 3-sol VL1 oscillation corresponds to a tropical, eastward traveling, zonal wavenumber one pattern. The 6-sol VL2 oscillation is characterized by two midlatitude, eastward traveling, mixed zonal wavenumber one and two and zonal wavenumber three and four patterns, with respective periods near 6.1 and 5.5 sols. The corresponding phase speeds are in agreement with some of the conclusions drawn from the lander observations. A linear stability analysis of the zonally asymmetric climatology reveals that the two most unstable modes are associated with periods near 3 and 6 sols; with the corresponding eigen-vectors showing patterns consistent with the results of the EEOF analyses.

## Abstract

We examine the evolution of baroclinic vortices in a time-dependent, nonlinear numerical model of a Jovian atmosphere. The model uses a normal-mode expansion in the vertical, using the barotropic and first two baroclinic modes. Results for the stability of baroclinic vortices on an *f* plane in the absence of a mean zonal flow are similar to results of Earth vortex models, although the presence of a fluid interior on the Jovian planets shifts the stability boundaries to smaller length scales. The presence of a barotropic mean zonal flow in the interior stabilizes vortices against instability and significantly modifies the finite amplitude form of baroclinic instabilities. The effect of a zonal flow on a form of barotropic instability produces periodic oscillations in the latitude and longitude of the vortex as observed at the level of the cloud tops. This instability may explain some, but not all, observations of longitudinal oscillations of vortices on the outer planets. Oscillations in aspect ratio and orientation of stable vortices in a zonal shear flow are observed in this baroclinic model, as in simpler twodimensional models. Such oscillations are also observed in the atmospheres of Jupiter and Neptune. The meridional propagation and decay of vortices on a *β* plane is inhibited by the presence of a mean zonal flow. The direction of propagation of a vortex relative to the mean zonal flow depends upon the sign of the meridional potential vorticity gradient; combined with observations of vortex drift rates, this may provide a constraint on model assumption for the flow in the deep interior of the Jovian planets.

## Abstract

We examine the evolution of baroclinic vortices in a time-dependent, nonlinear numerical model of a Jovian atmosphere. The model uses a normal-mode expansion in the vertical, using the barotropic and first two baroclinic modes. Results for the stability of baroclinic vortices on an *f* plane in the absence of a mean zonal flow are similar to results of Earth vortex models, although the presence of a fluid interior on the Jovian planets shifts the stability boundaries to smaller length scales. The presence of a barotropic mean zonal flow in the interior stabilizes vortices against instability and significantly modifies the finite amplitude form of baroclinic instabilities. The effect of a zonal flow on a form of barotropic instability produces periodic oscillations in the latitude and longitude of the vortex as observed at the level of the cloud tops. This instability may explain some, but not all, observations of longitudinal oscillations of vortices on the outer planets. Oscillations in aspect ratio and orientation of stable vortices in a zonal shear flow are observed in this baroclinic model, as in simpler twodimensional models. Such oscillations are also observed in the atmospheres of Jupiter and Neptune. The meridional propagation and decay of vortices on a *β* plane is inhibited by the presence of a mean zonal flow. The direction of propagation of a vortex relative to the mean zonal flow depends upon the sign of the meridional potential vorticity gradient; combined with observations of vortex drift rates, this may provide a constraint on model assumption for the flow in the deep interior of the Jovian planets.