Bibliography - Stephen T Garner

1. Garner, Stephen T., Isaac Held, Thomas R Knutson, and Joseph J Sirutis, in press: The roles of wind shear and thermodynamic stability in past and projected changes of Atlantic tropical-cyclone activity. Journal of Climate. 2/09.
   [ Abstract ]

   Atlantic tropical-cyclone activity has trended upward in recent decades. The increase coincides with favorable changes in local sea-surface temperature and other environmental indices, principally vertical shear and thermodynamic stability. The relative importance of these environmental factors has not been firmly established. A recent study using a high-resolution dynamical downscaling model has captured both the trend and interannual variations in Atlantic storm frequency with considerable fidelity. In the present work, this downscaling framework is used to assess the importance of the large-scale thermodynamic environment relative to other factors influencing Atlantic tropical storms. Separate assessments are done for the recent multi-decadal trend (1980 to 2006) and a model-projected global-warming environment for the late 21st century. For the multi-decadal trend, changes in the seasonal-mean thermodynamic environment (sea-surface temperature and atmospheric temperature profile at fixed relative humidity) account for most of the observed increase in tropical-cyclone frequency, with other seasonal-mean changes (including vertical shear) having a smaller combined effect. In contrast, the model’s projected reduction in Atlantic tropical-cyclone activity in the warm-climate scenario appears driven mostly by increased seasonal-mean vertical shear in the western Atlantic and Caribbean, rather than changes in the SST and thermodynamic profile.

2. Knutson, Thomas R., Joseph J Sirutis, Stephen T Garner, G A Vecchi, and Isaac Held, 2008: Simulated reduction in Atlantic hurricane frequency under twenty-first-century warming conditions. Nature Geoscience, 1(6), 359-364.
   [ Abstract PDF ]

   Increasing sea surface temperatures in the tropical Atlantic Ocean and measures of Atlantic hurricane activity have been reported to be strongly correlated since at least 1950 (refs 1, 2, 3, 4, 5), raising concerns that future greenhouse-gas-induced warming6 could lead to pronounced increases in hurricane activity. Models that explicitly simulate hurricanes are needed to study the influence of warming ocean temperatures on Atlantic hurricane activity, complementing empirical approaches. Our regional climate model of the Atlantic basin reproduces the observed rise in hurricane counts between 1980 and 2006, along with much of the interannual variability, when forced with observed sea surface temperatures and atmospheric conditions7. Here we assess, in our model system7, the changes in large-scale climate that are projected to occur by the end of the twenty-first century by an ensemble of global climate models8, and find that Atlantic hurricane and tropical storm frequencies are reduced. At the same time, near-storm rainfall rates increase substantially. Our results do not support the notion of large increasing trends in either tropical storm or hurricane frequency driven by increases in atmospheric greenhouse-gas concentrations.

3. Garner, Stephen T., D M W Frierson, Isaac Held, O M Pauluis, and Geoffrey K Vallis, June 2007: Resolving convection in a global hypohydrostatic model. Journal of the Atmospheric Sciences, 64(6), doi:10.1175/JAS3929.1.
   [ Abstract ]

   Convection cannot be explicitly resolved in general circulation models given their typical grid size of 50 km or larger. However, by multiplying the vertical acceleration in the equation of motion by a constant larger than unity, the horizontal scale of convection can be increased at will, without necessarily affecting the larger-scale flow. The resulting hypohydrostatic system has been recognized for some time as a way to improve numerical stability on grids that cannot well resolve nonhydrostatic gravity waves. More recent studies have explored its potential for better representing convection in relatively coarse models. The recent studies have tested the rescaling idea in the context of regional models. Here the authors present global aquaplanet simulations with a low-resolution, nonhydrostatic model free of convective parameterization, and describe the effect on the global climate of very large rescaling of the vertical acceleration. As the convection expands to resolved scales, a deepening of the troposphere, a weakening of the Hadley cell, and a moistening of the lower troposphere is found, compared to solutions in which the moist convection is essentially hydrostatic. The growth rate of convective instability is reduced and the convective life cycle is lengthened relative to synoptic phenomena. This problematic side effect is noted in earlier studies and examined further here.

4. Knutson, Thomas R., Joseph J Sirutis, Stephen T Garner, Isaac Held, and Robert E Tuleya, 2007: Simulation of the Recent Multidecadal Increase of Atlantic Hurricane Activity Using an 18-km-Grid Regional Model. Bulletin of the American Meteorological Society, 88(10), doi:10.1175/BAMS-88-10-1549.
   [ Abstract ]

   In this study, a new modeling framework for simulating Atlantic hurricane activity is introduced. The model is an 18-km-grid nonhydrostatic regional model, run over observed specified SSTs and nudged toward observed time-varying large-scale atmospheric conditions (Atlantic domain wavenumbers 0–2) derived from the National Centers for Environmental Prediction (NCEP) reanalyses. Using this “perfect large-scale model” approach for 27 recent August–October seasons (1980–2006), it is found that the model successfully reproduces the observed multidecadal increase in numbers of Atlantic hurricanes and several other tropical cyclone (TC) indices over this period. The correlation of simulated versus observed hurricane activity by year varies from 0.87 for basin-wide hurricane counts to 0.41 for U.S. landfalling hurricanes. For tropical storm count, accumulated cyclone energy, and TC power dissipation indices the correlation is 0.75, for major hurricanes the correlation is 0.69, and for U.S. landfalling tropical storms, the correlation is 0.57. The model occasionally simulates hurricanes intensities of up to category 4 (942 mb) in terms of central pressure, although the surface winds (< 47 m s^-1 ) do not exceed category-2 intensity. On interannual time scales, the model reproduces the observed ENSO-Atlantic hurricane covariation reasonably well. Some notable aspects of the highly contrasting 2005 and 2006 seasons are well reproduced, although the simulated activity during the 2006 core season was excessive. The authors conclude that the model appears to be a useful tool for exploring mechanisms of hurricane variability in the Atlantic (e.g., shear versus potential intensity contributions). The model may be capable of making useful simulations/projections of pre-1980 or twentieth-century Atlantic hurricane activity. However, the reliability of these projections will depend on obtaining reliable large-scale atmospheric and SST conditions from sources external to the model.

5. Phillips, V T., Leo J Donner, and Stephen T Garner, February 2007: Nucleation processes in deep convection simulated by a cloud-system-resolving model with double moment bulk microphysics. Journal of the Atmospheric Sciences, 64(3), doi:10.1175/JAS3869.1.
   [ Abstract ]

   A novel type of limited double-moment scheme for bulk microphysics is presented here for cloud-system-resolving models (CSRMs). It predicts the average size of cloud droplets and crystals, which is important for representing the radiative impact of clouds on the climate system. In this new scheme, there are interactive components for ice nuclei (IN) and cloud condensation nuclei (CCN). For cloud ice, the processes of primary ice nucleation, Hallett–Mossop (HM) multiplication of ice particles (secondary ice production), and homogeneous freezing of aerosols and droplets provide the source of ice number. The preferential evaporation of smaller droplets during homogeneous freezing of cloud liquid is represented for the first time. Primary and secondary (i.e., in cloud) droplet nucleation are also represented, by predicting the supersaturation as a function of the vertical velocity and local properties of cloud liquid. A linearized scheme predicts the supersaturation, explicitly predicting rates of condensation and vapor deposition onto liquid (cloud liquid, rain) and ice (cloud ice, snow, graupel) species. The predicted supersaturation becomes the input for most nucleation processes, including homogeneous aerosol freezing and secondary droplet activation. Comparison of the scheme with available aircraft and satellite data is performed for two cases of deep convection over the tropical western Pacific Ocean. Sensitivity tests are performed with respect to a range of nucleation processes. The HM process of ice particle multiplication has an important impact on the domain-wide ice concentration in the lower half of the mixed-phase region, especially when a lack of upper-level cirrus suppresses homogeneous freezing. Homogeneous freezing of droplets and, especially, aerosols is found to be the key control on number and sizes of cloud particles in the simulated cloud ensemble. Preferential evaporation of smaller droplets during homogeneous freezing produces a major impact on ice concentrations aloft. Aerosols originating from the remote free troposphere become activated in deep convective updrafts and produce most of the supercooled cloud droplets that freeze homogeneously aloft. Homogeneous aerosol freezing is found to occur only in widespread regions of weak ascent while homogeneous droplet freezing is restricted to deep convective updrafts. This means that homogeneous aerosol freezing can produce many more crystals than homogeneous droplet freezing, if conditions in the upper troposphere are favorable. These competing mechanisms of homogeneous freezing determine the overall response of the ice concentration to environmental CCN concentrations in the simulated cloud ensemble. The corresponding sensitivity with respect to environmental IN concentrations is much lower. Nevertheless, when extremely high concentrations of IN are applied, that are typical for plumes of desert dust, the supercooled cloud liquid is completely eliminated in the upper half of the mixed phase region. This shuts down the process of homogeneous droplet freezing.

6. Pauluis, O M., and Stephen T Garner, 2006: Sensitivity of radiative–convective equilibrium simulations to horizontal resolution. Journal of the Atmospheric Sciences, 63(7), doi:10.1175/JAS3705.1.
   [ Abstract ]

   This paper investigates the impacts of horizontal resolution on the statistical behavior of convection. An idealized radiative–convective equilibrium is simulated for model resolutions ranging between 2 and 50 km. The simulations are compared based upon the analysis of the mean state, the energy and water vapor transport, and the probability distribution functions for various quantities. It is shown that, at a coarse resolution, the model is unable to capture the mixing associated with shallow clouds. This results in a dry bias in the lower troposphere, and in an excessive amount of water clouds. Despite this deficiency, the coarse resolution simulations are able to reproduce reasonably well the statistical properties of deep convective towers. This is particularly apparent in the cloud ice and vertical velocity distributions that exhibit a very robust behavior. A theoretical scaling for the vertical velocity as function of the grid resolution is derived based upon the behavior of an idealized air bubble. It is shown that the vertical velocity of an ascending air parcel is determined by its aspect ratio, with a wide, flat parcel rising at a much slower pace than a narrow one. This theoretical scaling law exhibits a similar sensitivity to that of the numerical simulations. It is used to renormalize the probability distribution functions for vertical velocity, which show a very good agreement for resolutions up to 16 km. This new scaling law offers a way to improve direct simulations of deep convection in coarse resolution models.

7. Garner, Stephen T., 2005: A topographic drag closure built on an analytical base flux. Journal of the Atmospheric Sciences, 62(7), doi:10.1175/JAS3496.1.
   [ Abstract ]

   Topographic drag schemes depend on grid-scale representations of the average height, width, and orientation of the subgrid topography. Until now, these representations have been based on a combination of statistics and dimensional analysis. However, under certain physical assumptions, linear analysis provides the exact amplitude and orientation of the drag for arbitrary topography. The author proposes a computationally practical closure based on this analysis. Also proposed is a nonlinear correction for nonpropagating base flux. This is patterned after existing schemes but is better constrained to match the linear solution because it assumes a correlation between mountain height and width. When the correction is interpreted as a formula for the transition to saturation in the wave train, it also provides a way of estimating the vertical distribution of the momentum forcing. The explicit subgrid height distribution causes a natural broadening of the layers experiencing the forcing . Linear drag due to simple oscillating flow over topography, which is relevant to ocean tides, has almost the same form as for the stationary atmospheric problem. However, dimensional analysis suggests that the nonpropagating drag in this situation is mostly due to topographic length scales that are small enough to keep the steady-state assumption satisfied.

8. Arbic, B K., Stephen T Garner, Robert W Hallberg, and H L Simmons, 2004: The accuracy of surface elevations in forward global barotropic and baroclinic tide models. Deep-Sea Research, Part II, 51(25-26), 3069-3101.
   [ Abstract PDF ]

   This paper examines the accuracy of surface elevations in a forward global numerical model of 10 tidal constituents. Both one-layer and two-layer simulations are performed. As far as the authors are aware, the two-layer simulations and the simulations in a companion paper (Deep-Sea Research II, 51 (2004) 3043) represent the first published global numerical solutions for baroclinic tides. Self-consistent forward solutions for the global tide are achieved with a convergent iteration procedure for the self-attraction and loading term. Energies are too large, and elevation accuracies are poor, unless substantial abyssal drag is present. Reasonably accurate tidal elevations can be obtained with a spatially uniform bulk drag cd or horizontal viscosity KH, but only if these are inordinately large. More plausible schemes concentrate drag over rough topography. The topographic drag scheme used here is based on an exact analytical solution for arbitrary small-amplitude terrain, and supplemented by dimensional analysis to account for drag due to flow-splitting and low-level turbulence as well as that due to breaking of radiating waves. The scheme is augmented by a multiplicative factor tuned to minimize elevation discrepancies with respect to the TOPEX/POSEIDON (T/P)-constrained GOT99.2 model. The multiplicative factor may account for undersampled small spatial scales in bathymetric datasets. An optimally tuned multi-constituent one-layer simulation has an RMS elevation discrepancy of 9.54 cm with respect to GOT99.2, in waters deeper than 1000 m and over latitudes covered by T/P (66N to 66S). The surface elevation discrepancy decreases to 8.90 cm (92 percent of the height variance captured) in the optimally tuned two-layer solution. The improvement in accuracy is not due to the direct surface elevation signature of internal tides, which is of small amplitude, but to a shift in the barotropic tide induced by baroclinicity. Elevations are also more accurate in the two-layer model when pelagic tide gauges are used as the benchmark, and when the T/P-constrained TPXO6.2 model is used as a benchmark in deep waters south of 66S. For Antarctic diurnal tides, the improvement in forward model elevation accuracy with baroclinicity is substantial. The optimal multiplicative factor in the two-layer case is nearly the same as in the one-layer case, against initial expectations that the explicit resolution of low-mode conversion would allow less parameterized drag. In the optimally tuned two-layer M2 solution, local values of the ratio of temporally averaged squared upper layer speed to squared lower layer speed often exceed 10.

9. Schneider, T, Isaac Held, and Stephen T Garner, 2003: Boundary effects in potential vorticity dynamics. Journal of the Atmospheric Sciences, 60(8), 1024-1040.
   [ Abstract PDF ]

   Many aspects of geophysical flows can be described compactly in terms of potential vorticity dynamics. Since potential temperature can fluctuate at boundaries, however, the boundary conditions for potential vorticity dynamics are inhomogeneous, which complicates considerations of potential vorticity dynamics when boundary effects are dynamically significant. A formulation of potential vorticity dynamics is presented that encompasses boundary effects. It is shown that, for arbitrary flows, the generalization of the potential vorticity concept to a sum of the conventional interior potential vorticity and a singular surface potential vorticity allows one to replace the inhomogeneous boundary conditions for potential vorticity dynamics by simpler homogeneous boundary conditions (of constant potential temperature). Functional forms of the surface potential vorticity are derived from field equations in which the potential vorticity and a potential vorticity flux appear as sources of flow quantities in the same way in which an electric charge and an electric current appear as sources of fields in electrodynamics. For the generalized potential vorticity of flows that need be neither balanced nor hydrostatic and that can be influenced by diabatic processes and friction, a conservation law holds that is similar to the conservation law for the conventional interior potential vorticity. The conservation law for generalized potential vorticity contains, in the quasigeostrophic limit, the well-known dual relationship between fluctuations of potential temperature at boundaries and fluctuations of potential vorticity in the interior of quasigeostrophic flows. A nongeostrophic effect described by the conservation law is the induction of generalized potential vorticity by baroclinicity at boundaries, an effect that plays a role, for example, in mesoscale flows past topographic obstacles. Based on the generalized potential vorticity concept, a theory is outlined of how a wake with lee vortices can form in weakly dissipative flows past a mountain. Theoretical considerations and an analysis of a simulation show that a wake with lee vortices can form by separation of a generalized potential vorticity sheet from the mountain surface, similar to the separation of a friction-induced vorticity sheet from an obstacle, except that the generalized potential vorticity sheet can be induced by baroclinicity at the surface.

10. Garner, Stephen T., 1999: Blocking and frontogenesis by two-dimensional terrain in baroclinic flow. Part I: Numerical experiments. Journal of the Atmospheric Sciences, 56(11), 1495-1508.
    [ Abstract PDF ]

    The shallow atmospheric fronts that develop in the early winter along the east coast of North America have been attributed, in various modeling and observational studies, to the land-sea contrasts in both surface heating and friction. However, typical synoptic conditions are such that these "coastal" fronts could also be a type of upstream influence by the Appalachian Mountain chain. Generalized models have suggested that relatively cold air can become trapped on the windward side of a mountain range during episodes of warm advection without a local contribution from differential surface fluxes. Such a process was proposed decades ago in a study of observations along the coast of Norway. Could coastal frontogenesis be primarily a consequence of a mountain circulation acting on the large-scale temperature gradient? A two-dimensional, terrain-following numerical model is used to find conditions under which orography may be sufficient to cause blocking and upstream frontogenesis in a baroclinic environment. The idealized basic flow is taken to have constant vertical shear parallel to a topographic ridge and a constant perpendicular wind that advects warm or cold temperatures toward the ridge. Land-sea contrasts are omitted. In the observed cases, the mountain is "narrow" in the sense that the Rossby number is large. This by itself increases the barrier effect, but the experiments show that large-scale warm advection is still crucial for blocking. For realistic choices of ambient static stability and baroclinicity, the flow can be blocked by a range like the northern Appalachians if the undisturbed incident wind speed is around 10 m s-1. Cold advection weakens the barrier effect. The long-term behavior of the front in strongly blocked cases is described and compared to observations. Because of the background rotation and large-scale temperature advection, blocked solutions cannot become steady in the assumed environment. However, the interface between blocked and unblocked fluid can settle into a balanced configuration in some cases. A simple argument suggests that, in the absence of dissipation, the frontal slope should be similar to that of the ambient "absolute momentum" surfaces.

11. Garner, Stephen T., 1999: Blocking and frontogenesis by two-dimensional terrain in baroclinic flow. Part II: Analysis of flow stagnation mechanisms. Journal of the Atmospheric Sciences, 56(11), 1509-1523.
    [ Abstract PDF ]

    Numerical solutions presented in a companion paper show that two-dimensional mesoscale terrain becomes a much stronger barrier to a continuously stratified flow when the flow contains warm advection. Here it is shown that this baroclinic enhancement is a strictly nonlinear phenomenon. The linear analysis indicates a weakening of the upstream response in warm advection. However, a weakly nonlinear analysis shows that baroclinicity facilitates blocking in warm advection by strengthening the nonlinearity in the cross-mountain momentum equation in such a way as to amplify the vertical shear on the windward flank of the ridge. This is enough to send the flow past the blocking threshold even when conditions over the mountain are too linear to produce wave breaking. A more intuitive mechanism whereby the upstream static stability is increased by the nonlinearity in the temperature equation is found to be much less important.

12. Balasubramanian, G, and Stephen T Garner, 1997: The equilibrium of short baroclinic waves. Journal of the Atmospheric Sciences, 54(24), 2850-2871.
    [ Abstract PDF ]

    The life cycles of short baroclinic waves are investigated with the intention of completing a simple classification of nonlinear equilibration scenarios. Short waves become important in moist environments as latent heating reduces the scale of maximum baroclinic instability. Long-wave life cycles (wavenumber 6) were previously found to depend on details of the low-level momentum fluxes established during the earliest stages of development. These fluxes also serve as a focal point for the present study. For a realistic, zonally symmetric jet on the sphere, the normal-mode life cycle of a short wave (wavenumber 8) under both dry and moist conditions is described. Latent heating intensifies the low pressure system and frontal zones but does not alter the broader details of the life cycle. The normal modes have predominantly equatorward momentum fluxes, in contrast to the mainly poleward momentum fluxes of long waves. The short waves are more meridionally confined. The equatorward momentum fluxes direct the waves toward cyclonic breaking. The feedback with the zonal-mean wind, the so-called barotropic governor, is less effective than in the standard long-wave life cycle, which ends in anticyclonic breaking. However, in contrast to long-wave life cycles that are "engineered" to produce equatorward momentum fluxes, relatively little potential vorticity and surface temperature anomaly roll up into isolated vortices. Therefore, the short wave undergoes protracted barotropic decay leading to complete zonalization. Short waves also have a brief period of baroclinic decay due to cold advection over the surface cyclones. Eliassen-Palm cross sections for the short-wave life cycles show the usual combination of upward and meridional propagation of wave activity. However, the meridional propagation is mainly toward the pole and there is a consequent zonal-mean deceleration at high latitudes. These details are included in the proposed classification of equilibration scenarios.

13. Balasubramanian, G, and Stephen T Garner, 1997: The role of momentum fluxes in shaping the life cycle of a baroclinic wave. Journal of the Atmospheric Sciences, 54(4), 510-533.
    [ Abstract PDF ]

    The wide disparities in baroclinic wave development between spherical and Cartesian geometry are investigated with the purpose of assessing the role of the eddy momentum fluxes. Differences are already significant at the linear stage, as momentum fluxes are predominantly poleward in spherical geometry and predominantly equatorward in Cartesian geometry. More important, the low-level flux convergence is displaced poleward on the sphere and equatorward on the plane. On the sphere, these circumstances lead to rapid poleward movement of the low-level zonal-mean jet. The anticyclonic horizontal shear region expands as the jet feeds back on the momentum flux. The wave breaks anticyclonically and quickly zonalizes. In the Cartesian life cycle, the equatorward displacement of the flux convergence is counteracted by the mean meridional circulation and there is consequently a weaker feedback with the horizontal shear. The wave breaks, in this case cyclonically, but then takes much longer to zonalize. On the sphere, the angular velocity gradient in uniform westerly or easterly flow adds a separate mechanism for converting eddy kinetic energy to zonal mean, further hastening the zonalization process. It is possible to change the sign of the eddy momentum flux and the sense of the breaking in either geometry by slightly changing the basic flow. For example, cyclonic roll-up on the sphere can be obtained by adding weak cyclonic barotropic shear, as highlighted in a recently published study. Similarly, the addition of anticyclonic barotropic shear in a Cartesian simulation leads to anticyclonic wave breaking. An easterly jet on the sphere allows cyclonic breaking, but the wave still zonalizes rapidly, as in the case of a westerly jet. The persistence of the nonlinear eddies in these diverse experiments is not well correlated with the minimum value of the refractive index for Rossby waves, as suggested in the referenced study. It is proposed that the longevity of residual vortices after wave breaking is determined not by the sign of the vorticity or the breadth of the waveguide, but by the sign of the momentum flux and the geometry of the model.

14. Garner, Stephen T., 1995: Permanent and transient upstream effects in nonlinear stratified flow over a ridge. Journal of the Atmospheric Sciences, 52(2), 227-246.
    [ Abstract PDF ]

    The "high drag" state of stratified flow over isolated terrain is still an impediment to theoretical and experimental estimation of topographic wave drag and mean-flow modification. Linear theory misses the transition to the asymmetrical configuration that produces the enhanced drag. Steady-state nonlinear models rely on an ad hoc upstream condition like Long's hypothesis and can, as a result, be inconsistent with the flow established naturally by transients, especially if blocking is involved. Numerical solutions of the stratified initial value problem have left considerable uncertainty about the upstream alteration, especially as regards its permanence. A time-dependent numerical model with open boundaries is used in an effort to distinguish between permanent and transient upstream flow changes and to relate these to developments near the mountain. A nonrotating atmosphere with initially uniform wind and static stability is assumed. It is found that permanent alterations are primarily due to an initial surge not directly related to wave breaking. Indeed, there are no obvious parameter thresholds in the time-mean upstream state until "orographic adjustment" (deep blocking) commences. Wave breaking, in addition to establishing the downstream shooting flow, generates a persistent, quasi-periodic, upstream transience, which apparently involves the ducting properties of the downslope mixed region. This transience is slow enough to be easily confused with permanent changes. To understand the inflow alteration and transience, the energy and momentum budgets are examined in regions near the mountain. High drag conditions require permanent changes in flow force difference across the mountain and, consequently, an ongoing horizontal flux of energy and negative momentum. The source of the upstream transience is localized at the head of the mixed region. Blocking allows the total drag to exceed the saturation value by more than an order of magnitude. The implication for nonlinear steady-state models and wave drag parameterization are discussed.

15. Held, Isaac, R T Pierrehumbert, Stephen T Garner, and K L Swanson, 1995: Surface quasi-geostrophic dynamics. Journal of Fluid Mechanics, 282, 1-20.
    [ Abstract PDF ]

    The dynamics of quasi-geostrophic flow with uniform potential vorticity reduces to the evolution of buoyancy, or potential temperature, on horizontal boundaries. There is a formal resemblance to two-dimensional flow, with surface temperature playing the role of vorticity, but a different relationship between the flow and the advected scalar creates several distinctive features. A series of examples are described which highlight some of these features: the evolution of an eliptical vortex; the start-up vortex shed by flow over a mountain; the instability of temperature filaments; the `edge wave' critical layer; and mixing in an overturning edge wave. Characteristics of the direct cascade of the tracer variance to small scales in homogeneous turbulence, as well as the inverse energy cascade, are also described. In addition to its geophysical relevance, the ubiquitous generation of secondary instabilities and the possibility of finite-time collapse make this system a potentially important, numerically tractable, testbed for turbulence theories.

16. Garner, Stephen T., N Nakamura, and Isaac Held, 1992: Nonlinear equilibration of two-dimensional eady waves: a new perspective. Journal of the Atmospheric Sciences, 49(21), 1984-1996.
    [ Abstract PDF ]

    The equilibration of two-dimensional baroclinic waves differs fundamentally from equilibration in three dimensions because two-dimensional eddies cannot develop meridional temperature or velocity structure. It was shown in an earlier paper that frontogenesis together with diffusive mixing in a two-dimensional Eady wave brings positive potential vorticity (PV) anomalies deep into the atmosphere from both boundaries and allows the disturbance to settle into a steady state without meridional gradients. Here we depart from the earlier explanation of this equilibration and associate the PVintrusions with essentially the same kind of vortex "roll-up" that characterizes the evolution of barotropic shear layers. To avoid subgrid turbulence parameterizations and computational diffusion, the analogy is developed using Eady's generalized baroclinic instability problem. Eady's generalized model has two semi-infinite regions of large PV surrounding a layer of relatively small PV. Without boundaries, frontal collapse, or strong diffusion the model still produces equilibrated states, with structure similar to the vortex streets that emerge from unstable barotropic shear layers. The similarity is greatest when the baroclinic development is viewed in isentropic coordinates. The contrast between the present equilibrated solutions, which exhibit no vertical tilt, and Blumen's diffusive frontogenesis model, which allows the wave to retain its phase tilt, is briefly discussed. The equilibration of two-dimensional baroclinic waves differs fundamentally from equilibration in three dimensions because two-dimensional eddies cannot develop meridional temperature or velocity structure. It was shown in an earlier paper that frontogenesis together with diffusive mixing in a two-dimensional Eady wave brings positive potential vorticity (PV) anomalies deep into the atmosphere from both boundaries and allows the disturbance to settle into a steady state without meridional gradients. Here we depart from the earlier explanation of this equilibration and associate the PVintrusions with essentially the same kind of vortex "roll-up" that characterizes the evolution of barotropic shear layers. To avoid subgrid turbulence parameterizations and computational diffusion, the analogy is developed using Eady's generalized baroclinic instability problem. Eady's generalized model has two semi-infinite regions of large PV surrounding a layer of relatively small PV. Without boundaries, frontal collapse, or strong diffusion the model still produces equilibrated states, with structure similar to the vortex streets that emerge from unstable barotropic shear layers. The similarity is greatest when the baroclinic development is viewed in isentropic coordinates. The contrast between the present equilibrated solutions, which exhibit no vertical tilt, and Blumen's diffusive frontogenesis model, which allows the wave to retain its phase tilt, is briefly discussed.

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