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## Abstract

The emission of internal gravity waves from a layer of dry convection embedded within a stable atmosphere with static stability and zonal winds varying in height is calculated. This theory is applied to Venus to investigate whether these waves can help support the westward maximum of angular momentum of Venus's middle atmosphere. The emission mechanism is similar to that suggested for driving the gravity modes of the Sun and relates the amplitude and spectrum of the waves to the amplitude and spectrum of the convection. Waves are damped by several mechanisms: wavebreaking in the stable atmosphere, critical layer absorption, reabsorption by the convection, and wave radiation to space. The authors use plane parallel geometry without rotation and assume sinusoidal wave fluctuations in the horizontal dimensions. The vertical dependence is determined using the WKBJ approximation.

It is found that convectively generated gravity waves do not exert an acceleration where the westward winds are greatest. Instead, they deposit westward momentum in a 1-km thick layer just above the convection. Other waves deposit eastward momentum far above the westward wind maximum where decelerations can exceed 20 m s^{−1} day^{−1}, comparable to deceleration amplitudes in Earth's mesosphere. Although the momentum fluxes by gravity waves are substantial, the vertical profile of acceleration does not match what is required for supporting Venus's atmospheric superrotation.

## Abstract

The emission of internal gravity waves from a layer of dry convection embedded within a stable atmosphere with static stability and zonal winds varying in height is calculated. This theory is applied to Venus to investigate whether these waves can help support the westward maximum of angular momentum of Venus's middle atmosphere. The emission mechanism is similar to that suggested for driving the gravity modes of the Sun and relates the amplitude and spectrum of the waves to the amplitude and spectrum of the convection. Waves are damped by several mechanisms: wavebreaking in the stable atmosphere, critical layer absorption, reabsorption by the convection, and wave radiation to space. The authors use plane parallel geometry without rotation and assume sinusoidal wave fluctuations in the horizontal dimensions. The vertical dependence is determined using the WKBJ approximation.

It is found that convectively generated gravity waves do not exert an acceleration where the westward winds are greatest. Instead, they deposit westward momentum in a 1-km thick layer just above the convection. Other waves deposit eastward momentum far above the westward wind maximum where decelerations can exceed 20 m s^{−1} day^{−1}, comparable to deceleration amplitudes in Earth's mesosphere. Although the momentum fluxes by gravity waves are substantial, the vertical profile of acceleration does not match what is required for supporting Venus's atmospheric superrotation.

## Abstract

Layer thickness variations in Jupiter's atmosphere are investigated by treating potential vorticity as a conserved tracer. Starting with the horizontal velocity field measured from *Voyager* images, fluid trajectories around the Great Red Spot (GRS) and White Oval BC are calculated. The flow is assumed to be frictionless, adiabatic, hydrostatic, and steady in the reference frame of the vortex. Absolute vorticity is followed along each trajectory; its magnitude is assumed to vary directly as the thickness, which is defined as the mass per unit area between potential temperature surfaces. To the accuracy of the observations. the inferred thickness is a separable function of trajectory and latitude. The latitude dependence has positive curvature near the GRS and BC. The relative variations of thickness with respect to latitude are generally larger than the relative variations of Coriolis parameter with respect to latitude—the beta effect. The data are a useful diagnostic which will help differentiate between models, of Jovian vortices. The present analysis employs a quasi-geostrophic model in which a thin upper weather layer, which contains the vortex, is supported hydrostatically by a much deeper lower layer. In this model, the upper free surface does not contribute to the observed variation of thickness along trajectories. Such variations are due exclusively to bottom topography—flow of the deep lower layer relative to the vortex. The observation are used to infer the form of the deep zonal velocity profile vs. latitude. The magnitude of the profile depends on the unknown static stability. The principal result is the existence of horizontal shear in the deep layer zonal velocity profile, i.e., the lower layer is not in solid body rotation and does not act like a flat solid surface. In this respect the data support the hypothesis of Ingersoll and Cuong concerning motions in the deep layer. However at some latitudes the data violate Ingersoll and Cuong's criterion governing the compactness of the vortices. At these latitudes the topography allows standing Rossby waves (wakes) extending far downstream to the west. Observed wavelike features, the filamentary regions, are possibly formed by this mechanism.

## Abstract

Layer thickness variations in Jupiter's atmosphere are investigated by treating potential vorticity as a conserved tracer. Starting with the horizontal velocity field measured from *Voyager* images, fluid trajectories around the Great Red Spot (GRS) and White Oval BC are calculated. The flow is assumed to be frictionless, adiabatic, hydrostatic, and steady in the reference frame of the vortex. Absolute vorticity is followed along each trajectory; its magnitude is assumed to vary directly as the thickness, which is defined as the mass per unit area between potential temperature surfaces. To the accuracy of the observations. the inferred thickness is a separable function of trajectory and latitude. The latitude dependence has positive curvature near the GRS and BC. The relative variations of thickness with respect to latitude are generally larger than the relative variations of Coriolis parameter with respect to latitude—the beta effect. The data are a useful diagnostic which will help differentiate between models, of Jovian vortices. The present analysis employs a quasi-geostrophic model in which a thin upper weather layer, which contains the vortex, is supported hydrostatically by a much deeper lower layer. In this model, the upper free surface does not contribute to the observed variation of thickness along trajectories. Such variations are due exclusively to bottom topography—flow of the deep lower layer relative to the vortex. The observation are used to infer the form of the deep zonal velocity profile vs. latitude. The magnitude of the profile depends on the unknown static stability. The principal result is the existence of horizontal shear in the deep layer zonal velocity profile, i.e., the lower layer is not in solid body rotation and does not act like a flat solid surface. In this respect the data support the hypothesis of Ingersoll and Cuong concerning motions in the deep layer. However at some latitudes the data violate Ingersoll and Cuong's criterion governing the compactness of the vortices. At these latitudes the topography allows standing Rossby waves (wakes) extending far downstream to the west. Observed wavelike features, the filamentary regions, are possibly formed by this mechanism.

## Abstract

We propose a nonlinear, quasi-geostrophic, baroclinic model of Jovian atmospheric dynamics, in which vertical variations of velocity are represented by a truncated sum over a complete set of orthogonal functions obtained by a separation of variables of the linearized quasi-geostrophic potential vorticity equation. A set of equations for the time variation of the mode amplitudes in the nonlinear case is then derived. We show that for a planet with a neutrally stable, fluid interior instead of a solid lower boundary, the baroclinic mode represents motions in the interior, and is not affected by the baroclinic modes. One consequence of this is that a normal-mode model with one baroclinic mode is dynamically equivalent to a one layer model with solid lower topography. We also show that for motions in Jupiter's cloudy lower troposphere, the stratosphere behaves nearly as a rigid lid, so that the normal-mode model is applicable to Jupiter. We test the accuracy of the normal-mode model for Jupiter using two simple problem forced, vertically propagating Rossby waves, using two and three baroclinic modes and baroclinic instability, using two baroclinic modes. We find that the normal-road model provide qualitatively correct results, even with only a very limited number of vertical degrees of freedom.

## Abstract

We propose a nonlinear, quasi-geostrophic, baroclinic model of Jovian atmospheric dynamics, in which vertical variations of velocity are represented by a truncated sum over a complete set of orthogonal functions obtained by a separation of variables of the linearized quasi-geostrophic potential vorticity equation. A set of equations for the time variation of the mode amplitudes in the nonlinear case is then derived. We show that for a planet with a neutrally stable, fluid interior instead of a solid lower boundary, the baroclinic mode represents motions in the interior, and is not affected by the baroclinic modes. One consequence of this is that a normal-mode model with one baroclinic mode is dynamically equivalent to a one layer model with solid lower topography. We also show that for motions in Jupiter's cloudy lower troposphere, the stratosphere behaves nearly as a rigid lid, so that the normal-mode model is applicable to Jupiter. We test the accuracy of the normal-mode model for Jupiter using two simple problem forced, vertically propagating Rossby waves, using two and three baroclinic modes and baroclinic instability, using two baroclinic modes. We find that the normal-road model provide qualitatively correct results, even with only a very limited number of vertical degrees of freedom.

## Abstract

Most current models of Jupiter's Great Red Spot (GRS) are cast in terms of a two-layer model, where a thin upper weather layer, which contains the vortex, overlies a much deeper layer, which is meant to represent the neutrally stratified deep atmosphere. Any motions in the deep layer are assumed to be zonal and steady. This two-layer model is dynamically equivalent to a one-layer model with meridionally varying solid bottom topography, called the reduced-gravity model. Specifying the motions, or lack thereof, in the lower layer of the two-layer model is equivalent to specifying the bottom topography, and hence the far-field potential vorticity, in the reduced-gravity model. Current models of the GRS start by guessing the deep motions and then proceed to study vortices using the implied bottom topography. Here, using the GRS cloud-top velocity data, we derive the bottom topography, up to a constant that depends on the unknown radius of deformation (or equivalently, the product of the reduced gravity and the mean thickness of the upper layer). The bottom topography is inferred from three quantities derived from the velocity data—Bernoulli streamfunction, kinetic energy per unit mass, and absolute vorticity—all of which are functions only of horizontal position in the reference frame of the vortex. Far from the vortex, potential vorticity versus latitude is calculated from the observed cloud-top zonal velocity and the derived bottom topography. The results show that the deep atmosphere is in differential motion and that the far-field potential vorticity gradient changes sign at several latitudes. Numerical shallow water experiments are performed, using both the derived bottom topography and the bottom topographies prescribed by current models. The results of three published studies are reproduced in our numerical experiments. Each of these models is successful in maintaining a long-lived, isolated vortex, but only the present model yields absolute vorticity profiles along streamlines that agree with those observed for the GRS by Dowling and Ingersoll. In all the models, large vortices form by merging with smaller vortices. In the present, observationally based model, and in one other published model, the smaller vortices arise spontaneously because the observed cloud-top zonal velocity profile is unstable. These two models require an additional momentum source to maintain the upper-layer zonal velocity profile. In the other two models, the bottom topography stabilizes the zonal velocity profile. If dissipation is present, the latter two models require an additional source of smaller vortices to maintain the larger one. A crucial unanswered question for the present model, and for Jupiter itself, is how the cloud-top zonal velocity profile is maintained in its present unstable state.

## Abstract

Most current models of Jupiter's Great Red Spot (GRS) are cast in terms of a two-layer model, where a thin upper weather layer, which contains the vortex, overlies a much deeper layer, which is meant to represent the neutrally stratified deep atmosphere. Any motions in the deep layer are assumed to be zonal and steady. This two-layer model is dynamically equivalent to a one-layer model with meridionally varying solid bottom topography, called the reduced-gravity model. Specifying the motions, or lack thereof, in the lower layer of the two-layer model is equivalent to specifying the bottom topography, and hence the far-field potential vorticity, in the reduced-gravity model. Current models of the GRS start by guessing the deep motions and then proceed to study vortices using the implied bottom topography. Here, using the GRS cloud-top velocity data, we derive the bottom topography, up to a constant that depends on the unknown radius of deformation (or equivalently, the product of the reduced gravity and the mean thickness of the upper layer). The bottom topography is inferred from three quantities derived from the velocity data—Bernoulli streamfunction, kinetic energy per unit mass, and absolute vorticity—all of which are functions only of horizontal position in the reference frame of the vortex. Far from the vortex, potential vorticity versus latitude is calculated from the observed cloud-top zonal velocity and the derived bottom topography. The results show that the deep atmosphere is in differential motion and that the far-field potential vorticity gradient changes sign at several latitudes. Numerical shallow water experiments are performed, using both the derived bottom topography and the bottom topographies prescribed by current models. The results of three published studies are reproduced in our numerical experiments. Each of these models is successful in maintaining a long-lived, isolated vortex, but only the present model yields absolute vorticity profiles along streamlines that agree with those observed for the GRS by Dowling and Ingersoll. In all the models, large vortices form by merging with smaller vortices. In the present, observationally based model, and in one other published model, the smaller vortices arise spontaneously because the observed cloud-top zonal velocity profile is unstable. These two models require an additional momentum source to maintain the upper-layer zonal velocity profile. In the other two models, the bottom topography stabilizes the zonal velocity profile. If dissipation is present, the latter two models require an additional source of smaller vortices to maintain the larger one. A crucial unanswered question for the present model, and for Jupiter itself, is how the cloud-top zonal velocity profile is maintained in its present unstable state.

## Abstract

The Madden–Julian oscillation (MJO) is the dominant mode of intraseasonal variability in the tropics. Despite its primary importance, a generally accepted theory that accounts for fundamental features of the MJO, including its propagation speed, planetary horizontal scale, multiscale features, and quadrupole structures, remains elusive. In this study, the authors use a shallow-water model to simulate the MJO. In this model, convection is parameterized as a short-duration localized mass source and is triggered when the layer thickness falls below a critical value. Radiation is parameterized as a steady uniform mass sink. The following MJO-like signals are observed in the simulations: 1) slow eastward-propagating large-scale disturbances, which show up as low-frequency, low-wavenumber features with eastward propagation in the spectral domain, 2) multiscale structures in the time–longitude (Hovmöller) domain, and 3) quadrupole vortex structures in the longitude–latitude (map view) domain. The authors propose that the simulated MJO signal is an interference pattern of westward and eastward inertia–gravity (WIG and EIG) waves. Its propagation speed is half of the speed difference between the WIG and EIG waves. The horizontal scale of its large-scale envelope is determined by the bandwidth of the excited waves, and the bandwidth is controlled by the number density of convection events. In this model, convection events trigger other convection events, thereby aggregating into large-scale structures, but there is no feedback of the large-scale structures onto the convection events. The results suggest that the MJO is not so much a low-frequency wave, in which convection acts as a quasi-equilibrium adjustment, but is more a pattern of high-frequency waves that interact directly with the convection.

## Abstract

The Madden–Julian oscillation (MJO) is the dominant mode of intraseasonal variability in the tropics. Despite its primary importance, a generally accepted theory that accounts for fundamental features of the MJO, including its propagation speed, planetary horizontal scale, multiscale features, and quadrupole structures, remains elusive. In this study, the authors use a shallow-water model to simulate the MJO. In this model, convection is parameterized as a short-duration localized mass source and is triggered when the layer thickness falls below a critical value. Radiation is parameterized as a steady uniform mass sink. The following MJO-like signals are observed in the simulations: 1) slow eastward-propagating large-scale disturbances, which show up as low-frequency, low-wavenumber features with eastward propagation in the spectral domain, 2) multiscale structures in the time–longitude (Hovmöller) domain, and 3) quadrupole vortex structures in the longitude–latitude (map view) domain. The authors propose that the simulated MJO signal is an interference pattern of westward and eastward inertia–gravity (WIG and EIG) waves. Its propagation speed is half of the speed difference between the WIG and EIG waves. The horizontal scale of its large-scale envelope is determined by the bandwidth of the excited waves, and the bandwidth is controlled by the number density of convection events. In this model, convection events trigger other convection events, thereby aggregating into large-scale structures, but there is no feedback of the large-scale structures onto the convection events. The results suggest that the MJO is not so much a low-frequency wave, in which convection acts as a quasi-equilibrium adjustment, but is more a pattern of high-frequency waves that interact directly with the convection.

## Abstract

The Madden–Julian oscillation (MJO), also known as the intraseasonal oscillation (ISO), is a planetary-scale mode of variation in the tropical Indian and western Pacific Oceans. Basic questions about the MJO are why it propagates eastward at ∼5 m s^{−1}, why it lasts for intraseasonal time scales, and how it interacts with the fine structure that is embedded in it. This study will test the hypothesis that the MJO is not a wave but a wave packet—the interference pattern produced by a narrow frequency band of mixed Rossby–gravity (MRG) waves. As such, the MJO would propagate with the MRG group velocity, which is eastward at ∼5 m s^{−1}. Simulation with a 3D model shows that MRG waves can be forced independently by relatively short-lived, eastward- and westward-moving disturbances, and the MRG wave packet can last long enough to form the intraseasonal variability. This hypothesis is consistent with the view that the MJO is episodic, with an irregular time interval between events rather than a periodic oscillation. The packet is defined as the horizontally smoothed variance of the MRG wave—the rectified MRG wave, which has features in common with the MJO. The two-dimensional Fourier analysis of the NOAA outgoing longwave radiation (OLR) dataset herein indicates that there is a statistically significant correlation between the MJO amplitude and wave packets of MRG waves but not equatorial Rossby waves or Kelvin waves, which are derived from the Matsuno shallow water theory. However, the biggest absolute value of the correlation coefficient is only 0.21, indicating that the wave packet hypothesis explains only a small fraction of the variance of the MJO in the OLR data.

## Abstract

The Madden–Julian oscillation (MJO), also known as the intraseasonal oscillation (ISO), is a planetary-scale mode of variation in the tropical Indian and western Pacific Oceans. Basic questions about the MJO are why it propagates eastward at ∼5 m s^{−1}, why it lasts for intraseasonal time scales, and how it interacts with the fine structure that is embedded in it. This study will test the hypothesis that the MJO is not a wave but a wave packet—the interference pattern produced by a narrow frequency band of mixed Rossby–gravity (MRG) waves. As such, the MJO would propagate with the MRG group velocity, which is eastward at ∼5 m s^{−1}. Simulation with a 3D model shows that MRG waves can be forced independently by relatively short-lived, eastward- and westward-moving disturbances, and the MRG wave packet can last long enough to form the intraseasonal variability. This hypothesis is consistent with the view that the MJO is episodic, with an irregular time interval between events rather than a periodic oscillation. The packet is defined as the horizontally smoothed variance of the MRG wave—the rectified MRG wave, which has features in common with the MJO. The two-dimensional Fourier analysis of the NOAA outgoing longwave radiation (OLR) dataset herein indicates that there is a statistically significant correlation between the MJO amplitude and wave packets of MRG waves but not equatorial Rossby waves or Kelvin waves, which are derived from the Matsuno shallow water theory. However, the biggest absolute value of the correlation coefficient is only 0.21, indicating that the wave packet hypothesis explains only a small fraction of the variance of the MJO in the OLR data.

## Abstract

Exactly solving the absolute minimum potential energy state (Lorenz reference state) is a difficult problem because of the nonlinear nature of the equation of state of seawater. This problem has been solved recently but the algorithm comes at a high computational cost. As the first part of this study, the authors develop an algorithm that is ~10^{3}–10^{5} times faster, making it useful for energy diagnosis in ocean models. The second part of this study shows that the global patterns of Lorenz available potential energy (APE) density are distinct from those of eddy kinetic energy (EKE). This is because the Lorenz APE density is based on the entire domainwide parcel rearrangement, while mesoscale eddies, if related to baroclinic instability, are typically generated through local parcel rearrangement approximately around the eddy size. Inspired by this contrast, this study develops a locally defined APE framework: the eddy size–constrained APE density based on the strong constraint that the parcel rearrangement/displacement to achieve the minimum potential energy state should not exceed the local eddy size horizontally. This concept typically identifies baroclinically unstable regions. It is shown to be helpful to detect individual eddies/vortices and local EKE patterns, for example, around the Southern Ocean fronts and subtropical western boundary currents. This is consistent with the physical picture that mesoscale eddies are associated with a strong signature in both the velocity field (i.e., EKE) and the stratification (i.e., local APE). The new APE concept may be useful in parameterizing mesoscale eddies in ocean models.

## Abstract

Exactly solving the absolute minimum potential energy state (Lorenz reference state) is a difficult problem because of the nonlinear nature of the equation of state of seawater. This problem has been solved recently but the algorithm comes at a high computational cost. As the first part of this study, the authors develop an algorithm that is ~10^{3}–10^{5} times faster, making it useful for energy diagnosis in ocean models. The second part of this study shows that the global patterns of Lorenz available potential energy (APE) density are distinct from those of eddy kinetic energy (EKE). This is because the Lorenz APE density is based on the entire domainwide parcel rearrangement, while mesoscale eddies, if related to baroclinic instability, are typically generated through local parcel rearrangement approximately around the eddy size. Inspired by this contrast, this study develops a locally defined APE framework: the eddy size–constrained APE density based on the strong constraint that the parcel rearrangement/displacement to achieve the minimum potential energy state should not exceed the local eddy size horizontally. This concept typically identifies baroclinically unstable regions. It is shown to be helpful to detect individual eddies/vortices and local EKE patterns, for example, around the Southern Ocean fronts and subtropical western boundary currents. This is consistent with the physical picture that mesoscale eddies are associated with a strong signature in both the velocity field (i.e., EKE) and the stratification (i.e., local APE). The new APE concept may be useful in parameterizing mesoscale eddies in ocean models.

## Abstract

Previous observations and simulations suggest that an approximate 3°–5°C warming occurred at intermediate depths in the North Atlantic over several millennia during Heinrich stadial 1 (HS1), which induces warm salty water (WSW) lying beneath surface cold freshwater. This arrangement eventually generates ocean convective available potential energy (OCAPE), the maximum potential energy releasable by adiabatic vertical parcel rearrangements in an ocean column. The authors find that basin-scale OCAPE starts to appear in the North Atlantic (~67.5°–73.5°N) and builds up over decades at the end of HS1 with a magnitude of about 0.05 J kg^{−1}. OCAPE provides a key kinetic energy source for thermobaric cabbeling convection (TCC). Using a high-resolution TCC-resolved regional model, it is found that this decadal-scale accumulation of OCAPE ultimately overshoots its intrinsic threshold and is released abruptly (~1 month) into kinetic energy of TCC, with further intensification from cabbeling. TCC has convective plumes with approximately 0.2–1-km horizontal scales and large vertical displacements (~1 km), which make TCC difficult to be resolved or parameterized by current general circulation models. The simulation herein indicates that these local TCC events are spread quickly throughout the OCAPE-contained basin by internal wave perturbations. Their convective plumes have large vertical velocities (~8–15 cm s^{−1}) and bring the WSW to the surface, causing an approximate 2°C sea surface warming for the whole basin (~700 km) within a month. This exposes a huge heat reservoir to the atmosphere, which helps to explain the abrupt Bølling–Allerød warming.

## Abstract

Previous observations and simulations suggest that an approximate 3°–5°C warming occurred at intermediate depths in the North Atlantic over several millennia during Heinrich stadial 1 (HS1), which induces warm salty water (WSW) lying beneath surface cold freshwater. This arrangement eventually generates ocean convective available potential energy (OCAPE), the maximum potential energy releasable by adiabatic vertical parcel rearrangements in an ocean column. The authors find that basin-scale OCAPE starts to appear in the North Atlantic (~67.5°–73.5°N) and builds up over decades at the end of HS1 with a magnitude of about 0.05 J kg^{−1}. OCAPE provides a key kinetic energy source for thermobaric cabbeling convection (TCC). Using a high-resolution TCC-resolved regional model, it is found that this decadal-scale accumulation of OCAPE ultimately overshoots its intrinsic threshold and is released abruptly (~1 month) into kinetic energy of TCC, with further intensification from cabbeling. TCC has convective plumes with approximately 0.2–1-km horizontal scales and large vertical displacements (~1 km), which make TCC difficult to be resolved or parameterized by current general circulation models. The simulation herein indicates that these local TCC events are spread quickly throughout the OCAPE-contained basin by internal wave perturbations. Their convective plumes have large vertical velocities (~8–15 cm s^{−1}) and bring the WSW to the surface, causing an approximate 2°C sea surface warming for the whole basin (~700 km) within a month. This exposes a huge heat reservoir to the atmosphere, which helps to explain the abrupt Bølling–Allerød warming.

## Abstract

A new formula is derived for calculating the moist adiabatic temperature profile of an atmosphere consisting of ideal gases with multiple condensing species. This expression unifies various formulas published in the literature and can be generalized to account for chemical reactions. Unlike previous methods, it converges to machine precision independent of mesh size. It accounts for any ratio of condensable vapors to dry gas, from zero to infinity, and for variable heat capacities as a function of temperature. Because the derivation is generic, the new formula is not only applicable to planetary atmospheres in the solar system but also to hot Jupiters and brown dwarfs in which a variety of alkali metals, silicates, and exotic materials condense. It is demonstrated that even though the vapors are ideal gases, they interact in their effects on the moist adiabatic lapse rate. Finally, the authors apply the new thermodynamic model to study the effects of downdrafts on the distribution of minor constituents and the thermal profile in the *Galileo* probe hot spot. The authors find that the *Galileo* probe measurements can be interpreted as a strong downdraft that displaces an air parcel from the 1-bar to the 4-bar level (1 bar = 100 000 Pa).

## Abstract

A new formula is derived for calculating the moist adiabatic temperature profile of an atmosphere consisting of ideal gases with multiple condensing species. This expression unifies various formulas published in the literature and can be generalized to account for chemical reactions. Unlike previous methods, it converges to machine precision independent of mesh size. It accounts for any ratio of condensable vapors to dry gas, from zero to infinity, and for variable heat capacities as a function of temperature. Because the derivation is generic, the new formula is not only applicable to planetary atmospheres in the solar system but also to hot Jupiters and brown dwarfs in which a variety of alkali metals, silicates, and exotic materials condense. It is demonstrated that even though the vapors are ideal gases, they interact in their effects on the moist adiabatic lapse rate. Finally, the authors apply the new thermodynamic model to study the effects of downdrafts on the distribution of minor constituents and the thermal profile in the *Galileo* probe hot spot. The authors find that the *Galileo* probe measurements can be interpreted as a strong downdraft that displaces an air parcel from the 1-bar to the 4-bar level (1 bar = 100 000 Pa).

## Abstract

Thermobaric convection (type II convection) and thermobaric cabbeling (type III convection) might substantially contribute to vertical mixing, vertical heat transport, and deep-water formation in the World Ocean. However, the extent of this contribution remains poorly constrained. The concept of ocean convective available potential energy (OCAPE), the thermobaric energy source for type II and type III convection, is introduced to improve the diagnosis and prediction of these convection events. OCAPE is analogous to atmospheric CAPE, which is a key energy source for atmospheric moist convection and has long been used to forecast moist convection. OCAPE is the potential energy (PE) stored in an ocean column arising from thermobaricity, defined as the difference between the PE of the ocean column and its minimum possible PE under adiabatic vertical parcel rearrangements. An ocean column may be stably stratified and still have nonzero OCAPE. The authors present an efficient strategy for computing OCAPE accurately for any given column of seawater. They further derive analytical expressions for OCAPE for approximately two-layer ocean columns that are widely observed in polar oceans. This elucidates the dependence of OCAPE on key physical parameters. Hydrographic profiles from the winter Weddell Sea are shown to contain OCAPE (0.001–0.01 J kg^{−1}), and scaling analysis suggests that OCAPE may be substantially enhanced by wintertime surface buoyancy loss. The release of this OCAPE may substantially contribute to the kinetic energy of deep convection in polar oceans.

## Abstract

Thermobaric convection (type II convection) and thermobaric cabbeling (type III convection) might substantially contribute to vertical mixing, vertical heat transport, and deep-water formation in the World Ocean. However, the extent of this contribution remains poorly constrained. The concept of ocean convective available potential energy (OCAPE), the thermobaric energy source for type II and type III convection, is introduced to improve the diagnosis and prediction of these convection events. OCAPE is analogous to atmospheric CAPE, which is a key energy source for atmospheric moist convection and has long been used to forecast moist convection. OCAPE is the potential energy (PE) stored in an ocean column arising from thermobaricity, defined as the difference between the PE of the ocean column and its minimum possible PE under adiabatic vertical parcel rearrangements. An ocean column may be stably stratified and still have nonzero OCAPE. The authors present an efficient strategy for computing OCAPE accurately for any given column of seawater. They further derive analytical expressions for OCAPE for approximately two-layer ocean columns that are widely observed in polar oceans. This elucidates the dependence of OCAPE on key physical parameters. Hydrographic profiles from the winter Weddell Sea are shown to contain OCAPE (0.001–0.01 J kg^{−1}), and scaling analysis suggests that OCAPE may be substantially enhanced by wintertime surface buoyancy loss. The release of this OCAPE may substantially contribute to the kinetic energy of deep convection in polar oceans.