Boussinesq and Anelastic Approximations Revisited: Potential Energy Release during Thermobaric Instability

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

Dynamics of planetary atmospheres

The overall goal is to illuminate the mechanisms that control weather and climate on the Earth and other planets. Each planet presents its own puzzling behavior - the stability of jets and vortices in Jupiter's otherwise turbulent atmosphere, the superrotation of the Venus atmosphere, the interplay of dust, polar volatiles, and climate change in Mars, the supersonic meteorology of Io, and the counterintuitive equator-to-pole temperature gradients on the outer planets. The data sets are generally those obtained from spacecraft - cloud-tracked winds, radiometrically inferred temperatures, and the results of in situ observations where appropriate. The approach includes both data analysis and modeling, ranging from analytic modeling to time-dependent numerical modeling of atmospheric dynamics. The latter approach involves the use of supercomputers such as the San Diego Cray. Progress is generally made when a model with a small number of free parameters either fits a data set that has a large number of independent observations or applies to several planets at once

Testing the Hypothesis that the MJO is a Mixed Rossby-Gravity Wave Packet

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

The atmospheres of Mars and Venus

Of all the planets which may exist in the Universe, only nine have been studied by man. As a result, one cannot classify planets with the same confidence that one has in classifying stars; there is no theory of planetary evolution comparable in development to the theory of stellar evolution. Nevertheless, many of the goals of planetary science and stellar astronomy are the same: to classify objects according to their most fundamental properties in order to understand their present physical state and their evolution. From this point of view, the terrestrial planets comprise a group which can usefully be considered together. By comparing the similarities and differences between them, we may hope to gain insight into the evolution of the entire group

The Runaway Greenhouse: A History of Water on Venus

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

High-Frequency Orographically Forced Variability in a Single-Layer Model of the Martian Atmosphere

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 reproduces well the climatology at the sites of Viking Lander I and II (VLl and VL2) as inferred from the Viking Lander fall and spring observations. Its variability at those sites is dominated by a 3-sol (Martian solar day) oscillation in the region of VLl and by a 6-sol oscillation in that of VL2. These oscillations are forced by the zonal asymmetries of the Martian mountain field. It is suggested that they contribute to the observed variability by reinforcing the baroclinic oscillations with nearby periods identified in observational studies. The spatial variability associated with the orographically forced oscillations is studied by means of extended empirical orthogonal function 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 arc in agreement with the conclusions drawn from the VL2 observations

The weather of other planets

Recent observations from spacecraft and from powerful Earth-based telescopes are providing new information concerning the atmospheres and climatic conditions of other members of the solar system

Convective Instabilities in Plane Couette Flow

The stability to infinitesimal disturbances of plane Couette flow is considered in the presence of a negative vertical temperature gradient. The fluid is contained between horizontal planes which are maintained at different temperatures. The flow becomes unstable at the critical Rayleigh number for convection without shear. Below this critical Rayleigh number, the flow is stable in the limit of large and small Reynolds numbers. Numerical solutions at finite Reynolds numbers are given for stationary and traveling disturbances at Prandtl numbers equal to ten and infinity. For these cases, the flow appears stable at subcritical Rayleigh numbers, for all Reynolds numbers

Mars: The case against permanent CO_2 frost caps

Leighton and Murray have argued that there is a polar reservoir of solid CO_2 on Mars that lasts throughout the year and whose vapor pressure determines the mean partial pressure of CO_2 in the atmosphere. This model is discussed in the light of recent data, and several difficulties emerge. First, such a system might be unstable, owing to the tendency of poleward heat transport to increase with atmospheric pressure. Second, the annual retreat of the CO_2 frost cover would be slower according to the model than that observed. Moreover, the observations seem to indicate that the residual polar cap that lasts throughout the year is composed of water ice rather than CO_2. Finally, observations of water vapor in the atmosphere appear to be inconsistent with a permanent CO_2 cold trap in continuous existence for many years. These difficulties hold also for a CO_2 reservoir buried by water ice and for a hydrated CO_2 clathrate. If Leighton and Murray's model does not apply, several alternatives remain. First, the total accumulated CO_2 may simply be equal to that observed in the atmosphere. Second, there may be a buried reservoir of CO_2 that is not in vapor equilibrium with the atmosphere. Third, adsorption of CO_2 and water in the Mars regolith may control the amounts of these compounds observed in the atmosphere at present. Unfortunately, not one of these alternatives provides a satisfactory quantitative theory for the present CO_2 partial pressure in the atmosphere

Polarization Measurements Of Mars And Mercury: Rayleigh Scattering In The Martian Atmosphere

Ground-based polarimetric data taken near maximum elongation are presented. These data are analyzed on the assumption of an optically thin, Rayleigh-scattering atmosphere, and a surface whose polarization varies inversely as surface albedo. For Mars, the best fit to the data yields an estimate of surface pressure in the range 4-7.5 mb, if CO_2 is the principal constituent. There is no need to postulate the existence of fine dust in the Martian atmosphere. For Mercury, the best fit to the data yields an upper limit on Rayleigh scattering equal to 0.001 of the Earth's atmosphere