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Isaac M. Held

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.

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Isaac M. Held

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.

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Isaac M. Held

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.

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Isaac M. Held

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.

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Isaac M. Held

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.

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Isaac M. Held

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.

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Olivier Pauluis and Isaac M. Held

Abstract

In moist convection, atmospheric motions transport water vapor from the earth's surface to the regions where condensation occurs. This transport is associated with three other aspects of convection: the latent heat transport, the expansion work performed by water vapor, and the irreversible entropy production due to diffusion of water vapor and phase changes. An analysis of the thermodynamic transformations of atmospheric water yields what is referred to as the entropy budget of the water substance, providing a quantitative relationship between these three aspects of moist convection. The water vapor transport can be viewed as an imperfect heat engine that produces less mechanical work than the corresponding Carnot cycle because of diffusion of water vapor and irreversible phase changes.

The entropy budget of the water substance provides an alternative method of determining the irreversible entropy production due to phase changes and diffusion of water vapor. This method has the advantage that it does not require explicit knowledge of the relative humidity or of the molecular flux of water vapor for the estimation of the entropy production. Scaling arguments show that the expansion work of water vapor accounts for a small fraction of the work that would be produced in the absence of irreversible moist processes. It is also shown that diffusion of water vapor and irreversible phase changes can be interpreted as the irreversible counterpart to the continuous dehumidification resulting from condensation and precipitation. This leads to a description of moist convection where it acts more as an atmospheric dehumidifier than as a heat engine.

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Sumant Nigam and Isaac M. Held

Abstract

A nondivergent barotropic model on a sphere is used to study the effects of a critical latitude on stationary atmospheric waves forced by topography. Linear and “quasi-linear” calculations are performed with an idealized wavenumber 3 mountain and with realistic topography. Quasi-linear dynamics, where mean flow changes are due to momentum flux convergence, “form drag” and relation to a prescribed climatological mean flow, produces an S-shaped kink in the zonal mean absolute vorticity gradient near the critical latitude, resulting in enhanced reflection. The component of the quasi-linear solution resulting from enhanced reflection at the critical latitude is computed by taking the difference between the linear and the quasi-linear solutions. In a calculation with realistic topography and zonal flow, this reflected component is found to be dominated by a wave train emanating from the western tropical Pacific and propagating northward and then eastward across the Pacific 0cean and the North American continent. This wave train results from the reflection of the Himalayan wave train at the zero-wind latitude in the tropical winter troposphere.

The vorticity gradients in the monthly mean statistics of Oort (1983) show structure near the critical latitude similar to that produced in our quasi-linear model, suggesting that some reflection of incident Rossby waves is likely in the atmosphere, at least in the western Pacific, and that the wind structure responsible for this reflection may be created in part by the stationary Rossby waves themselves.

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Yunqing Zhang and Isaac M. Held

Abstract

A linear stochastic model is used to simulate the midlatitude storm tracks produced by an atmospheric GCM. A series of six perpetual insolation/SST GCM experiments are first performed for each month. These experiments capture the “midwinter suppression” of the Pacific storm track in a particularly clean way. The stochastic model is constructed by linearizing the GCM about its January climatology and finding damping and stirring parameters that best reproduce that model’s eddy statistics. The model is tested by examining its ability to simulate other GCM integrations when the basic state is changed to the mean flow of those models, while keeping the stirring and damping unchanged.

The stochastic model shows an impressive ability to simulate a variety of eddy statistics. It captures the midwinter suppression of the Pacific storm track qualitatively and is also capable of simulating storm track responses to El Niño. The model results are sensitive to the manner in which the model is stirred. Best results for eddy variances and fluxes are obtained by stirring the temperature and vorticity at low levels. However, a better simulation of the spatial structure of the dominant wave train as defined by covariance maps is obtained by stirring the temperature equation only, and at all levels.

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Sukyoung Lee and Isaac M. Held

Abstract

A two-layer quasi-geostrophic model forced by surface friction and radiative relaxation to a jetlike wind profile can exist in either a wave-free state or in a finite-amplitude wave state, over a substantial region of the model's parameter space. The friction on the lower layer must be much stronger than the thermal relaxation, and the upper layer must be nearly inviscid, for this behavior to be observed.

Consistent with this behavior, weakly unstable waves are found that do not stabilize the flow; instead, their growth rate increases with wave amplitude. We attempt to provide a physical explanation for this behavior in terms of 1) the competition between the stabilizing effect of the lower-layer potential vorticity fluxes and the destabilizing effect of nonlinear critical layer formation associated with the upper-layer fluxes, and 2) the tendency of surface drag to restore the vertical shear at the center of the jet by damping the surface westerlies generated by the baroclinic instability.

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