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- Author or Editor: Isaac M. Held x
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Abstract
Some of the advances of the past century in our understanding of the general circulation of the atmosphere are described, starting with a brief summary of some of the key developments from the first half of the twentieth century, but with a primary focus on the period beginning with the midcentury breakthrough in baroclinic instability and quasigeostrophic dynamics. In addition to baroclinic instability, topics touched upon include the following: stationary wave theory, the role played by the two-layer model, scaling arguments for the eddy heat flux, the subtlety of large-scale eddy momentum fluxes, the Eliassen–Palm flux and the transformed Eulerian mean formulation, the structure of storm tracks, and the controls on the Hadley cell.
Abstract
Some of the advances of the past century in our understanding of the general circulation of the atmosphere are described, starting with a brief summary of some of the key developments from the first half of the twentieth century, but with a primary focus on the period beginning with the midcentury breakthrough in baroclinic instability and quasigeostrophic dynamics. In addition to baroclinic instability, topics touched upon include the following: stationary wave theory, the role played by the two-layer model, scaling arguments for the eddy heat flux, the subtlety of large-scale eddy momentum fluxes, the Eliassen–Palm flux and the transformed Eulerian mean formulation, the structure of storm tracks, and the controls on the Hadley cell.
Abstract
Linear modes on shear flows are not orthogonal in the sense of energy; if two modes are present, the eddy energy is not equal to the sum of the eddy energy in the separate modes. However, linear modes are orthogonal in the sense of pseudomomentum (or pseudoenergy). Two applications of this result to planetary waves in horizontal and vertical sheer are discussed. 1) The qualitative character of the evolution of a disturbance to a stable meridional sheer flow, as described by the barotropic vorticity equation, depends critically on whether the disturbance projects primarily onto discrete modes or onto continuum modes that cascade enstrophy to small meridional scales. It is demonstrated that the pseudomomentum and pseudoenergy orthogonality relations provide a natural framework for examining the relative excitation of discrete and continuum modes. 2) Using the quasi-geostrophic potential vorticity equation, it is shown that pseudomomentum orthogonality provides a simple explanation for how quasi-stationary neutral external modes of large amplitude can be excited by a small initial disturbance.
Abstract
Linear modes on shear flows are not orthogonal in the sense of energy; if two modes are present, the eddy energy is not equal to the sum of the eddy energy in the separate modes. However, linear modes are orthogonal in the sense of pseudomomentum (or pseudoenergy). Two applications of this result to planetary waves in horizontal and vertical sheer are discussed. 1) The qualitative character of the evolution of a disturbance to a stable meridional sheer flow, as described by the barotropic vorticity equation, depends critically on whether the disturbance projects primarily onto discrete modes or onto continuum modes that cascade enstrophy to small meridional scales. It is demonstrated that the pseudomomentum and pseudoenergy orthogonality relations provide a natural framework for examining the relative excitation of discrete and continuum modes. 2) Using the quasi-geostrophic potential vorticity equation, it is shown that pseudomomentum orthogonality provides a simple explanation for how quasi-stationary neutral external modes of large amplitude can be excited by a small initial disturbance.
Abstract
Some results due to Kuo concerning momentum fluxes in barotropic flows are generalized so as to apply to quasi-geostrophic flows on a beta-plane. It is shown that linear, amplifying waves on an arbitrary zonal flow cause a net transport of westerly momentum out of that part of the fluid in which Raleigh's stability criterion (as generalized by Charney and Stern, and by Pedlosky) is satisfied locally. Also, it is shown that if quasi-geostrophic eddies are introduced by some “external” agent into a region in which the zonal flow satisfies the stability criterion, then westerly momentum will flow into this region.
Abstract
Some results due to Kuo concerning momentum fluxes in barotropic flows are generalized so as to apply to quasi-geostrophic flows on a beta-plane. It is shown that linear, amplifying waves on an arbitrary zonal flow cause a net transport of westerly momentum out of that part of the fluid in which Raleigh's stability criterion (as generalized by Charney and Stern, and by Pedlosky) is satisfied locally. Also, it is shown that if quasi-geostrophic eddies are introduced by some “external” agent into a region in which the zonal flow satisfies the stability criterion, then westerly momentum will flow into this region.
Abstract
The mass transport in the shallow, wind-driven, overturning cells in the tropical oceans is constrained to be close to the mass transport in the atmospheric Hadley cell, assuming that zonally integrated wind stresses on land are relatively small. Therefore, the ratio of the poleward energy transport in low latitudes in the two media is determined by the ratio of the atmospheric gross static stability to that of the ocean. A qualitative discussion of the gross stability of each medium suggests that the resulting ratio of oceanic to atmospheric energy transport, averaged over the Hadley cell, is roughly equal to the ratio of the heat capacity of water to that of air at constant pressure, multiplied by the ratio of the moist- to the dry-adiabatic lapse rates near the surface. The ratio of oceanic to atmospheric energy transport should be larger than this value near the equator and smaller than this value near the poleward boundary of the Hadley cell.
Abstract
The mass transport in the shallow, wind-driven, overturning cells in the tropical oceans is constrained to be close to the mass transport in the atmospheric Hadley cell, assuming that zonally integrated wind stresses on land are relatively small. Therefore, the ratio of the poleward energy transport in low latitudes in the two media is determined by the ratio of the atmospheric gross static stability to that of the ocean. A qualitative discussion of the gross stability of each medium suggests that the resulting ratio of oceanic to atmospheric energy transport, averaged over the Hadley cell, is roughly equal to the ratio of the heat capacity of water to that of air at constant pressure, multiplied by the ratio of the moist- to the dry-adiabatic lapse rates near the surface. The ratio of oceanic to atmospheric energy transport should be larger than this value near the equator and smaller than this value near the poleward boundary of the Hadley cell.
Abstract
There exists an infinite set of quadratic conserved quantities for linear quasi-geostrophic waves in horizontal and vertical shear, the first two members of the set corresponding to the pseudomomentum and pseudo-energy conservation laws that lead to the Rayleigh-Kuo (or Charney-Stern) and the Fjortoft stability criteria. This infinite hierarchy of conservation laws follows from the conservation of the pseudomomentum in each eigenmode of the shear flow.
Abstract
There exists an infinite set of quadratic conserved quantities for linear quasi-geostrophic waves in horizontal and vertical shear, the first two members of the set corresponding to the pseudomomentum and pseudo-energy conservation laws that lead to the Rayleigh-Kuo (or Charney-Stern) and the Fjortoft stability criteria. This infinite hierarchy of conservation laws follows from the conservation of the pseudomomentum in each eigenmode of the shear flow.
Abstract
Linear, quasi-geostrophic waves destabilized by a surface temperature gradient produce eddy potential vorticity fluxes which characteristically extend above the surface to a height where the vertical shear ∂u¯/∂z, static stability N 2 and potential vorticity gradient ∂q/∂y of the zonal flow are evaluated at the surface. Utilizing this result and a simple scaling analysis, we argue that the time averaged, vertically integrated, poleward eddy heat flux is proportional to the fifth power of the meridional temperature gradient when h 0 is much less than the scale height of the atmosphere.
Abstract
Linear, quasi-geostrophic waves destabilized by a surface temperature gradient produce eddy potential vorticity fluxes which characteristically extend above the surface to a height where the vertical shear ∂u¯/∂z, static stability N 2 and potential vorticity gradient ∂q/∂y of the zonal flow are evaluated at the surface. Utilizing this result and a simple scaling analysis, we argue that the time averaged, vertically integrated, poleward eddy heat flux is proportional to the fifth power of the meridional temperature gradient when h 0 is much less than the scale height of the atmosphere.
Abstract
The sensitivity of both moist and dry versions of a two-level primitive equation atmospheric model to variations in the solar constant is analyzed. The models have fixed surface albedos, fixed cloudiness and a zero heat flux lower boundary condition, and are forced with annual mean solar fluxes. An attempt is made to understand the response of the static stability in these model atmospheres and the importance of these changes in stability for the climatic responses of other parts of the system.
In the moist model, the static stability increases in low latitudes but decreases in high latitudes as the solar constant increases, resulting in considerable latitudinal structure in the sensitivity of surface temperatures and zonal winds. In the dry model the stability decreases at all latitudes as the solar constant increases. It is argued that this decrease in stability in the dry model, through its effect on isentropic slopes and the supercriticality of the flow, is responsible for the observed large increases in eddy energies and fluxes. Parameterization schemes for the eddy heat flux are critically examined in light of these results.
Abstract
The sensitivity of both moist and dry versions of a two-level primitive equation atmospheric model to variations in the solar constant is analyzed. The models have fixed surface albedos, fixed cloudiness and a zero heat flux lower boundary condition, and are forced with annual mean solar fluxes. An attempt is made to understand the response of the static stability in these model atmospheres and the importance of these changes in stability for the climatic responses of other parts of the system.
In the moist model, the static stability increases in low latitudes but decreases in high latitudes as the solar constant increases, resulting in considerable latitudinal structure in the sensitivity of surface temperatures and zonal winds. In the dry model the stability decreases at all latitudes as the solar constant increases. It is argued that this decrease in stability in the dry model, through its effect on isentropic slopes and the supercriticality of the flow, is responsible for the observed large increases in eddy energies and fluxes. Parameterization schemes for the eddy heat flux are critically examined in light of these results.
The problem of creating truly convincing numerical simulations of our Earth's climate will remain a challenge for the next generation of climate scientists. Hopefully, the ever increasing power of computers will make this task somewhat less frustrating than it is at present. But, increasing computational power also raises issues as to how we would like to see climate modeling and the study of climate dynamics evolve in the twenty-first century. One of the key issues we will need to address is the widening gap between simulation and understanding.
The problem of creating truly convincing numerical simulations of our Earth's climate will remain a challenge for the next generation of climate scientists. Hopefully, the ever increasing power of computers will make this task somewhat less frustrating than it is at present. But, increasing computational power also raises issues as to how we would like to see climate modeling and the study of climate dynamics evolve in the twenty-first century. One of the key issues we will need to address is the widening gap between simulation and understanding.
Predictions of future climate change raise a variety of issues in large-scale atmospheric and oceanic dynamics. Several of these are reviewed in this essay, including the sensitivity of the circulation of the Atlantic Ocean to increasing freshwater input at high latitudes; the possibility of greenhouse cooling in the southern oceans; the sensitivity of monsoonal circulations to differential warming of the two hemispheres; the response of midlatitude storms to changing temperature gradients and increasing water vapor in the atmosphere; and the possible importance of positive feedback between the mean winds and eddy-induced heating in the polar stratosphere.
Predictions of future climate change raise a variety of issues in large-scale atmospheric and oceanic dynamics. Several of these are reviewed in this essay, including the sensitivity of the circulation of the Atlantic Ocean to increasing freshwater input at high latitudes; the possibility of greenhouse cooling in the southern oceans; the sensitivity of monsoonal circulations to differential warming of the two hemispheres; the response of midlatitude storms to changing temperature gradients and increasing water vapor in the atmosphere; and the possible importance of positive feedback between the mean winds and eddy-induced heating in the polar stratosphere.
Abstract
Abrupt transitions to strongly superrotating states have been found in some idealized models of the troposphere. These transitions are thought to be caused by feedbacks between the eddy momentum flux convergence in low latitudes and the strength of the equatorial flow. The behavior of an axisymmetric shallow-water model with an applied tropical torque is studied here to determine if an abrupt transition can be realized without eddy feedbacks. The upper-tropospheric layer is relaxed to a radiative equilibrium thickness, exchanging mass and thus momentum with the nonmoving lower layer. For low values of the applied torque, the circulation is earthlike; however, for larger values, an abrupt transition to a strongly superrotating state can occur. In some cases, the system remains superrotating as the torque is subsequently decreased. A simple analytical model is used to better understand the system. The bifurcation is caused by a feedback between the applied torque and the strength of the Hadley cell. As the torque increases, the strength of the cell decreases, reducing the damping caused by momentum transfer from the lower layer.
Abstract
Abrupt transitions to strongly superrotating states have been found in some idealized models of the troposphere. These transitions are thought to be caused by feedbacks between the eddy momentum flux convergence in low latitudes and the strength of the equatorial flow. The behavior of an axisymmetric shallow-water model with an applied tropical torque is studied here to determine if an abrupt transition can be realized without eddy feedbacks. The upper-tropospheric layer is relaxed to a radiative equilibrium thickness, exchanging mass and thus momentum with the nonmoving lower layer. For low values of the applied torque, the circulation is earthlike; however, for larger values, an abrupt transition to a strongly superrotating state can occur. In some cases, the system remains superrotating as the torque is subsequently decreased. A simple analytical model is used to better understand the system. The bifurcation is caused by a feedback between the applied torque and the strength of the Hadley cell. As the torque increases, the strength of the cell decreases, reducing the damping caused by momentum transfer from the lower layer.
