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- Author or Editor: Christopher C. Walker x

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## Abstract

The nonlinear behavior of planetary waves excited by midlatitude topography is considered in an atmospheric GCM. The GCM is run at standard resolution (T42) and includes all of the complexity normally associated with a GCM. Only two simplifications are made to the model. First, it is run in perpetual January mode, so that the solar radiation takes the diurnally varying value associated with 15 January. Second, the lower boundary is simplified so that it is entirely ocean with zonally symmetric SSTs. Planetary waves are excited by Gaussian-shaped topography centered at 45°N, 90°W. As in earlier studies, the excited wave train propagates toward low latitudes where, for sufficiently large forcing amplitude (i.e., height of topography), the wave will break. Several different experiments are run with different mountain heights. Each experiment is run for a total of 4015 days.

The response of the model depends on the height of the mountain. For the small-amplitude mountain (500 m), the wave is dissipated at low latitudes near its critical latitude. For large-amplitude mountains (2000, 3000, and 4000 m), wave breaking and nonlinear reflection out of the wave breaking region is observed. The spatial character of the reflected wave train is similar to that detected in earlier studies with more idealized models.

## Abstract

The nonlinear behavior of planetary waves excited by midlatitude topography is considered in an atmospheric GCM. The GCM is run at standard resolution (T42) and includes all of the complexity normally associated with a GCM. Only two simplifications are made to the model. First, it is run in perpetual January mode, so that the solar radiation takes the diurnally varying value associated with 15 January. Second, the lower boundary is simplified so that it is entirely ocean with zonally symmetric SSTs. Planetary waves are excited by Gaussian-shaped topography centered at 45°N, 90°W. As in earlier studies, the excited wave train propagates toward low latitudes where, for sufficiently large forcing amplitude (i.e., height of topography), the wave will break. Several different experiments are run with different mountain heights. Each experiment is run for a total of 4015 days.

The response of the model depends on the height of the mountain. For the small-amplitude mountain (500 m), the wave is dissipated at low latitudes near its critical latitude. For large-amplitude mountains (2000, 3000, and 4000 m), wave breaking and nonlinear reflection out of the wave breaking region is observed. The spatial character of the reflected wave train is similar to that detected in earlier studies with more idealized models.

## Abstract

The nonlinear behavior of quasi-stationary planetary waves excited by midlatitude orographic forcing is considered in a three-dimensional primitive equation model that includes a representation of the Hadley circulation. The Hadley circulation is forced by Newtonian cooling to a zonally symmetric reference temperature and vertical diffusion on the zonally symmetric component of the flow. To quantify the effect of the Hadley circulation on wave propagation, breaking, and nonlinear reflection, an initial state with no meridional flow, but with the same zonal flow as the Hadley state, is also considered. In order to allow the propagation of large-scale waves over extended periods, Rayleigh friction is applied at low levels to delay the onset of baroclinic instability.

As in the absence of a Hadley circulation, the waves in the Hadley state propagate toward low latitudes where the background flow is weak and the waves are therefore likely to break. Potential vorticity fields on isentropic surfaces are used to diagnose wave breaking. Nonlinear pseudomomentum conservation relations are used to quantify the absorption–reflection behavior of the wave breaking region. In the presence of a Hadley circulation representative of winter conditions, the nonlinear reflection requires more forcing to get established, but a reflected wave train is still present in the numerical simulations, both for a longitudinally symmetric forcing and for the more realistic case of an isolated forcing. The effect of the thermal damping on the waves is more severe in the current three-dimensional simulations than in the shallow water case considered in an earlier study. Both the directly forced wave train and the reflected wave train are quite barotropic in character; however, in the shallow water case one is essentially assuming an infinite vertical scale.

## Abstract

The nonlinear behavior of quasi-stationary planetary waves excited by midlatitude orographic forcing is considered in a three-dimensional primitive equation model that includes a representation of the Hadley circulation. The Hadley circulation is forced by Newtonian cooling to a zonally symmetric reference temperature and vertical diffusion on the zonally symmetric component of the flow. To quantify the effect of the Hadley circulation on wave propagation, breaking, and nonlinear reflection, an initial state with no meridional flow, but with the same zonal flow as the Hadley state, is also considered. In order to allow the propagation of large-scale waves over extended periods, Rayleigh friction is applied at low levels to delay the onset of baroclinic instability.

As in the absence of a Hadley circulation, the waves in the Hadley state propagate toward low latitudes where the background flow is weak and the waves are therefore likely to break. Potential vorticity fields on isentropic surfaces are used to diagnose wave breaking. Nonlinear pseudomomentum conservation relations are used to quantify the absorption–reflection behavior of the wave breaking region. In the presence of a Hadley circulation representative of winter conditions, the nonlinear reflection requires more forcing to get established, but a reflected wave train is still present in the numerical simulations, both for a longitudinally symmetric forcing and for the more realistic case of an isolated forcing. The effect of the thermal damping on the waves is more severe in the current three-dimensional simulations than in the shallow water case considered in an earlier study. Both the directly forced wave train and the reflected wave train are quite barotropic in character; however, in the shallow water case one is essentially assuming an infinite vertical scale.

## Abstract

An idealized GCM is used to investigate how the strength and meridional extent of the Hadley circulation depend on the planet radius, rotation rate, and thermal driving. Over wide parameter ranges, the strength and meridional extent of the Hadley circulation display clear scaling relations with regime transitions, which are not predicted by existing theories of axisymmetric Hadley circulations. For example, the scaling of the strength as a function of the radiative-equilibrium equator-to-pole temperature contrast exhibits a regime transition corresponding to a regime transition in scaling laws of baroclinic eddy fluxes. The scaling of the strength of the cross-equatorial Hadley cell as a function of the latitude of maximum radiative-equilibrium temperature exhibits a regime transition from a regime in which eddy momentum fluxes strongly influence the strength to a regime in which the influence of eddy momentum fluxes is weak.

Over a wide range of flow parameters, albeit not always, the Hadley circulation strength is directly related to the eddy momentum flux divergence at the latitude of the streamfunction extremum. Simulations with hemispherically symmetric thermal driving span circulations with local Rossby numbers in the horizontal upper branch of the Hadley circulation between 0.1 and 0.8, indicating that neither nonlinear nearly inviscid theories, valid for Ro → 1, nor linear theories, valid for Ro → 0, of axisymmetric Hadley circulations can be expected to be generally adequate. Nonlinear theories of axisymmetric Hadley circulations may account for aspects of the circulation when the maximum radiative-equilibrium temperature is displaced sufficiently far away from the equator, which results in cross-equatorial Hadley cells with nearly angular momentum-conserving upper branches.

The dependence of the Hadley circulation on eddy fluxes, which are themselves dependent on extratropical circulation characteristics such as meridional temperature gradients, suggests that tropical circulations depend on the extratropical climate.

## Abstract

An idealized GCM is used to investigate how the strength and meridional extent of the Hadley circulation depend on the planet radius, rotation rate, and thermal driving. Over wide parameter ranges, the strength and meridional extent of the Hadley circulation display clear scaling relations with regime transitions, which are not predicted by existing theories of axisymmetric Hadley circulations. For example, the scaling of the strength as a function of the radiative-equilibrium equator-to-pole temperature contrast exhibits a regime transition corresponding to a regime transition in scaling laws of baroclinic eddy fluxes. The scaling of the strength of the cross-equatorial Hadley cell as a function of the latitude of maximum radiative-equilibrium temperature exhibits a regime transition from a regime in which eddy momentum fluxes strongly influence the strength to a regime in which the influence of eddy momentum fluxes is weak.

Over a wide range of flow parameters, albeit not always, the Hadley circulation strength is directly related to the eddy momentum flux divergence at the latitude of the streamfunction extremum. Simulations with hemispherically symmetric thermal driving span circulations with local Rossby numbers in the horizontal upper branch of the Hadley circulation between 0.1 and 0.8, indicating that neither nonlinear nearly inviscid theories, valid for Ro → 1, nor linear theories, valid for Ro → 0, of axisymmetric Hadley circulations can be expected to be generally adequate. Nonlinear theories of axisymmetric Hadley circulations may account for aspects of the circulation when the maximum radiative-equilibrium temperature is displaced sufficiently far away from the equator, which results in cross-equatorial Hadley cells with nearly angular momentum-conserving upper branches.

The dependence of the Hadley circulation on eddy fluxes, which are themselves dependent on extratropical circulation characteristics such as meridional temperature gradients, suggests that tropical circulations depend on the extratropical climate.

## Abstract

In simulations of a wide range of circulations with an idealized general circulation model, clear scaling laws of dry atmospheric macroturbulence emerge that are consistent with nonlinear eddy–eddy interactions being weak. The simulations span several decades of eddy energies and include Earth-like circulations and circulations with multiple jets and belts of surface westerlies in each hemisphere. In the simulations, the eddy available potential energy and the barotropic and baroclinic eddy kinetic energy scale linearly with each other, with the ratio of the baroclinic eddy kinetic energy to the barotropic eddy kinetic energy and eddy available potential energy decreasing with increasing planetary radius and rotation rate. Mean values of the meridional eddy flux of surface potential temperature and of the vertically integrated convergence of the meridional eddy flux of zonal momentum generally scale with functions of the eddy energies and the energy-containing eddy length scale, with a few exceptions in simulations with statically near-neutral or neutral extratropical thermal stratifications. Eddy energies scale with the mean available potential energy and with a function of the supercriticality, a measure of the near-surface slope of isentropes. Strongly baroclinic circulations form an extended regime in which eddy energies scale linearly with the mean available potential energy. Mean values of the eddy flux of surface potential temperature and of the vertically integrated eddy momentum flux convergence scale similarly with the mean available potential energy and other mean fields.

The scaling laws for the dependence of eddy fields on mean fields exhibit a regime transition between a regime in which the extratropical thermal stratification and tropopause height are controlled by radiation and convection and a regime in which baroclinic entropy fluxes modify the extratropical thermal stratification and tropopause height. At the regime transition, for example, the dependence of the eddy flux of surface potential temperature and the dependence of the vertically integrated eddy momentum flux convergence on mean fields changes—a result with implications for climate stability and for the general circulation of an atmosphere, including its tropical Hadley circulation.

## Abstract

In simulations of a wide range of circulations with an idealized general circulation model, clear scaling laws of dry atmospheric macroturbulence emerge that are consistent with nonlinear eddy–eddy interactions being weak. The simulations span several decades of eddy energies and include Earth-like circulations and circulations with multiple jets and belts of surface westerlies in each hemisphere. In the simulations, the eddy available potential energy and the barotropic and baroclinic eddy kinetic energy scale linearly with each other, with the ratio of the baroclinic eddy kinetic energy to the barotropic eddy kinetic energy and eddy available potential energy decreasing with increasing planetary radius and rotation rate. Mean values of the meridional eddy flux of surface potential temperature and of the vertically integrated convergence of the meridional eddy flux of zonal momentum generally scale with functions of the eddy energies and the energy-containing eddy length scale, with a few exceptions in simulations with statically near-neutral or neutral extratropical thermal stratifications. Eddy energies scale with the mean available potential energy and with a function of the supercriticality, a measure of the near-surface slope of isentropes. Strongly baroclinic circulations form an extended regime in which eddy energies scale linearly with the mean available potential energy. Mean values of the eddy flux of surface potential temperature and of the vertically integrated eddy momentum flux convergence scale similarly with the mean available potential energy and other mean fields.

The scaling laws for the dependence of eddy fields on mean fields exhibit a regime transition between a regime in which the extratropical thermal stratification and tropopause height are controlled by radiation and convection and a regime in which baroclinic entropy fluxes modify the extratropical thermal stratification and tropopause height. At the regime transition, for example, the dependence of the eddy flux of surface potential temperature and the dependence of the vertically integrated eddy momentum flux convergence on mean fields changes—a result with implications for climate stability and for the general circulation of an atmosphere, including its tropical Hadley circulation.

## Abstract

It is generally held that atmospheric macroturbulence can be strongly nonlinear. Yet weakly nonlinear models successfully account for scales and structures of baroclinic eddies in Earth's atmosphere. Here a theory and simulations with an idealized GCM are presented that suggest weakly nonlinear models are so successful because atmospheric macroturbulence organizes itself into critical states of weak nonlinear eddy–eddy interactions. By modifying the thermal structure of the extratropical atmosphere such that its supercriticality remains limited, macroturbulence inhibits nonlinear eddy–eddy interactions and the concomitant inverse energy cascade from the length scales of baroclinic instability to larger scales. For small meridional surface temperature gradients, the extratropical thermal stratification and tropopause height are set by radiation and convection, and the supercriticality is less than one; for sufficiently large meridional surface temperature gradients, the extratropical thermal stratification and tropopause height are modified by baroclinic eddies such that the supercriticality does not significantly exceed one. In either case, the scale of the energy-containing eddies is similar to the scale of the linearly most unstable baroclinic waves, and eddy kinetic and available potential energies are equipartitioned. The theory and simulations point to fundamental constraints on the thermal structures and global circulations of the atmospheres of Earth and other planets, for example, by providing limits on the tropopause height and estimates for eddy scales, eddy energies, and jet separation scales.

## Abstract

It is generally held that atmospheric macroturbulence can be strongly nonlinear. Yet weakly nonlinear models successfully account for scales and structures of baroclinic eddies in Earth's atmosphere. Here a theory and simulations with an idealized GCM are presented that suggest weakly nonlinear models are so successful because atmospheric macroturbulence organizes itself into critical states of weak nonlinear eddy–eddy interactions. By modifying the thermal structure of the extratropical atmosphere such that its supercriticality remains limited, macroturbulence inhibits nonlinear eddy–eddy interactions and the concomitant inverse energy cascade from the length scales of baroclinic instability to larger scales. For small meridional surface temperature gradients, the extratropical thermal stratification and tropopause height are set by radiation and convection, and the supercriticality is less than one; for sufficiently large meridional surface temperature gradients, the extratropical thermal stratification and tropopause height are modified by baroclinic eddies such that the supercriticality does not significantly exceed one. In either case, the scale of the energy-containing eddies is similar to the scale of the linearly most unstable baroclinic waves, and eddy kinetic and available potential energies are equipartitioned. The theory and simulations point to fundamental constraints on the thermal structures and global circulations of the atmospheres of Earth and other planets, for example, by providing limits on the tropopause height and estimates for eddy scales, eddy energies, and jet separation scales.