# Publications

## DISSIPATIVE DESTABILIZATION OF EXTERNAL ROSSBY WAVES.

Journal of the Atmospheric Sciences **43** (1986) 388-396

External Rossby waves in vertical shear can be destabilized by thermal damping. They can also be destabilized by damping of potential vorticity if this damping is larger in the lower than in the upper troposphere. Results are described in detail for Charney's model. Implications for the effects of diabatic heating and mixing due to smaller scale transients on equivalent barotropic stationary or quasi-stationary long waves are discussed. It is pointed out that energy or potential enstrophy budgets may indicate that transients are damping the long waves while, in fact, their presence is destabilizing these waves.

## Problems and Prospects in Long and Medium Range Weather Forecasting

Journal of Fluid Mechanics **163** (1986) 498-500

## Remarks on a paper by Aref and Flinchem

JOURNAL OF FLUID MECHANICS **163** (1986) 21-26

## THE EFFECT OF LOCAL BAROCLINIC INSTABILITY ON ZONAL INHOMOGENEITIES OF VORTICITY AND TEMPERATURE

ADVANCES IN GEOPHYSICS **29** (1986) 165-182

## Regimes of axisymmetric flow in an internally heated rotating fluid

Journal of Fluid Mechanics **168** (1986) 255-289

A boundary-layer scale analysis is presented for steady, zonally symmetric flow in a Cartesian channel of rectangular cross-section, subject to uniform internal heating, and cooling at the lateral boundaries, using an approach based on that of Hignett, Ibbetson & Killworth for a related system. Six main flow regimes are identified, depending chiefly upon the magnitude of the parameter P defined as the square of the ratio of the (non-rotating) thermal-boundary-layer thickness scale to that of the Ekman layers adjacent to the horizontal boundaries. For P ≪ A1/6ε1/2 [formula omitted] 1, where A is the Rayleigh number and e the channel aspect ratio), the flow consists of an advectively dominated interior, characterized by a balance between vertical advection and internal heat generation, diffusively dominated thermal boundary layers adjacent to the sidewalls, and horizontal, viscously dominated Ekman layers (for non-zero rotation rate). If P ≪ 1, the flow is only weakly modified by rotation, but as P increases through unity, rotation tends to inhibit heat transfer and thickens the thermal boundary layers. Provided P [formula omitted] ε2 σ-2, (where σ is the Prandtl number), the zonal flow is predominantly geostrophic, though not given by the conventional thermal-wind scale (based on the total thermal contrast AT) unless P [formula omitted] 1. The results of the scale analysis are compared with laboratory measurements and numerical simulations of steady flow in a rotating, cylindrical annulus subject to (radially non-uniform) internal heating and sidewall cooling. Over the range of parameters accessible in the laboratory, the azimuthal velocity scale and thermal contrast were found to vary with rotation and heating rates in the way predicted from the scale analysis for the Cartesian system. Above a certain critical value of P (for the geometry used here Pcrit ≈ 1), the baroclinic wave regime was found to occur, corresponding to where rotational constraints first begin to influence significantly the heat transfer of the axisymmetric flow. The numerical simulations are compared with the laboratory measurements, and used to extend the ranges of rotation rate and aspect ratio over which the scale analysis could be verified. Good agreement was found for the dependence of globally averaged flow parameters on P, and the dynamical characteristics of each regime were further verified using explicit calculations of the balance of terms in the basic equations from the numerical model. Further applications of the scaling technique to other, related systems are also discussed, together with a consideration of its generalization to systems of geophysical interest. © 1986, Cambridge University Press. All rights reserved.

## Super‐rotation and diffusion of axial angular momentum: I. ‘Speed limits’ for axisymmetric flow in a rotating cylindrical fluid annulus

Quarterly Journal of the Royal Meteorological Society **112** (1986) 231-251

‘Super‐rotation’ can be defined with respect to the limitations on the magnitude of specific angular momentum, m, in an inviscid fluid. In a viscous fluid, a steady, super‐rotating axisymmetric flow is shown to require diffusion of m against its gradient ∇m in the meridional plane. The conditions under which m can be diffused in an incompressible fluid by molecular viscosity against ∇m in a cylindrical system are shown to be consistent with the normal properties of isotropic Newtonian viscosity (i.e. appropriate for the laminar flow of a viscous liquid in the laboratory) when cylindrical curvature is fully represented. A series of numerical simulations of thermally‐driven axisymmetric circulations in a cylindrical fluid annulus, subject to various mechanical boundary conditions, is then presented. The role of diffusion in the angular momentum budget of the simulations is examined by diagnosing m, its diffusive flux F (due to molecular viscosity) and divergence ∇·F from the final equilibrium (steady) flow. Up‐gradient diffusion (with respect to ∇m) is found to be particularly important for flows in a system with stress‐free top and side boundaries and a non‐slip base. Similar up‐gradient diffusion can also result in angular momentum expulsion effects in a system confined entirely by stress‐free boundaries. The characteristic dynamics of super‐rotation in a viscous fluid, and the associated limitations upon its magnitude and dependence upon the external conditions and fluid properties, are then explored in a scale analysis for the cylindrical annulus with a non‐slip base (based on a scheme due to Hignett, Ibbetson and Killworth). The most rapid super‐rotation (with zonal Rossby number > 1) is found to be favoured at moderate rotation rates, with strong cylindrical curvature, and a large meridional aspect ratio and Prandtl number. The results of the scale analysis are verified by means of further numerical experiments. Copyright © 1986 Royal Meteorological Society

## Super‐rotation and diffusion of axial angular momentum: II. A review of quasi‐axisymmetric models of planetary atmospheres

Quarterly Journal of the Royal Meteorological Society **112** (1986) 253-272

The role of angular momentum quasi‐conservation in generating and maintaining axisymmetric flows characterized by a net global and/or local super‐rotation is reviewed. The conditions under which angular momentum per unit mass, m, can be diffused by Newtonian viscosity against its mean gradient in the meridional plane in a compressible, spherical fluid shell are explored in detail, and integral constraints on the form of the diffusive flux of m are derived for a steady flow. The implications of the results for simple models of planetary and stellar atmospheres are explored, with particular reference to the analogy between molecular and ‘eddy’ viscosity (as represented in mixing‐length theory), and various mixing hypotheses for eddy transfer properties. The results are relevant to zonally‐averaged models of the circulation of planetary and stellar atmospheres since, in the absence of molecular viscosity, the Eliassen—Palm flux of m must obey similar integral constraints to those applicable to the viscous flux in a purely axisymmetric system. Despite the non‐Newtonian character of realistic eddies in a baroclinic atmosphere, therefore, studies of simple axisymmetric systems with viscous diffusion can shed some useful insight into ways in which atmospheres, such as those of the earth, Venus, Titan, the Jovian planets and the sun, may acquire significant components of super‐rotation and prograde differential rotation, especially (though not exclusively) near the equator. Copyright © 1986 Royal Meteorological Society

## Stable, baroclinic eddies on Jupiter and Saturn: A laboratory analog and some observational tests

Icarus **65** (1986) 304-334

Laboratory experiments (and corresponding numerical simulations) on free thermal convection in a rotating fluid, subject to horizontal differential heating and cooling, are examined in the light of recent observations of the longest-lived eddies on Jupiter and Saturn (including Jupiter's Great Red Spot and White Ovals). Both laboratory and atmospheric systems are shown to be capable of satisfying scaling requirements for mutual dynamical similarity, within the uncertainties of the Jovian observations. By employing a suitable distribution of heat sources and sinks in the laboratory, a pattern of zonally averaged flow analogous to a laterally sheared belt or zone on Jupiter can be obtained at upper levels. Baroclinic eddies may develop in such a flow, whose properties are remarkably similar in structure and appearance to the long-lived features on the major planets. Difficulties in determining from global energy budget studies the essential processes maintaining and dissipating stable eddies are discussed with reference to the laboratory and atmospheric systems. Such difficulties do not arise when considering the potential vorticity budget for the flow. Inviscid, unforced "free mode" (i.e., nonadvecting) solution to a suitable potential vorticity equation are first-order components of most recent models of the Jovian eddies (including the baroclinic eddy analog described herein). Small departures from such a "free mode" in a realistic flow arise as a result of the dynamically crucial processes maintaining and dissipating it, with baroclinic eddies in the laboratory corresponding largely to a residual balance between thermal forcing (via internal heating) and viscous dissipation. On Jupiter, diabatically forced and transient eddy-driven flows are shown to differ primarily in the implied role of transient eddies in transporting potential vorticity q across closed geostrophic streamlines in the time mean. The feasibility of using observations of naturally occurring chemical tracers to infer aspects of the transport of q on Jupiter are discussed with a view to testing models of the long-lived eddies using data from the Galileo mission. © 1986.

## STRATIFIED SEMIGEOSTROPHIC FLOW OVER TWO-DIMENSIONAL TOPOGRAPHY IN AN UNBOUNDED ATMOSPHERE

JOURNAL OF THE ATMOSPHERIC SCIENCES **42** (1985) 523-526

## A THEORETICAL-MODEL OF OROGRAPHICALLY MODIFIED CYCLOGENESIS

JOURNAL OF THE ATMOSPHERIC SCIENCES **42** (1985) 1244-1258

## UPSTREAM EFFECTS OF MESOSCALE MOUNTAINS

JOURNAL OF THE ATMOSPHERIC SCIENCES **42** (1985) 977-1003

## STATIONARY EXTERNAL ROSSBY WAVES IN VERTICAL SHEAR

JOURNAL OF THE ATMOSPHERIC SCIENCES **42** (1985) 865-883

## Finite-amplitude, neutral baroclinic eddies and mean flows in an internally heated rotating fluid: 1. Numerical simulations and quasi-geostrophic 'free modes'

Dynamics of Atmospheres and Oceans **9** (1985) 135-207

A series of numerical simulations of steady wave flows in a rotating fluid annulus, subject to internal heating and various thermal boundary conditions, is examined to characterise their structures, energetics and potential vorticity transport properties. The last of these characteristics, together with more conventional scaling considerations, indicate the possibility of applying quasi-geostrophic theory to the interior flow in a formulation similar to the inviscid, adiabatic models of Kuo and White. The analytical model of White, describing finite amplitude, neutral baroclinic eddies and mean flows as illustrations of the Charney-Drazin non-acceleration theorem, is then extended to include uniform diabatic heating and the effects of different forms of lateral shear in the background mean zonal flow. Like the solutions discussed by White, those obtained in the present paper consist of steady, internal jet, mean zonal flows, and baroclinic and barotropic Rossby wave components, all having the same three-dimensional wavenumber. Provided the diabatic heating is proportional to the stratification of the background flow, measured by the square of the Brunt-Vaisälä frequency N, the potential vorticity equation remains homogeneous. All the solutions are then characterised by zero net transfer of potential vorticity despite the possibility of non-zero eddy fluxes of heat or momentum and non-trivial Lorenz energy cycles. A series of particular three-component solutions (which, like some of the solutions discussed by White, do not obey conventional lateral boundary conditions) is examined as possible theoretical analogues of the steady waves observed in the numerical simulations of the laboratory flows, and is found to agree encouragingly well in the spatial variations of their mean flows, eddy stream function (pressure) and eddy fluxes of heat and momentum. Potential vorticity fluxes in the numerical simulations are relatively small (though crucially non-zero), supporting the possible analogy with the analytical model and exposing some limitations of the latter in not accounting for weak dissipation and forcing processes present in the laboratory flows. Further implications of the results are discussed, including possible analogies between the laboratory experiments and certain features in planetary atmospheres and oceans. © 1985.

## LOCAL AND GLOBAL BAROCLINIC INSTABILITY OF ZONALLY VARYING FLOW

JOURNAL OF THE ATMOSPHERIC SCIENCES **41** (1984) 2141-2162

## LINEAR RESULTS ON THE BARRIER EFFECTS OF MESOSCALE MOUNTAINS

JOURNAL OF THE ATMOSPHERIC SCIENCES **41** (1984) 1356-1367

## FORCED COHERENT STRUCTURES AND LOCAL MULTIPLE EQUILIBRIA IN A BAROTROPIC ATMOSPHERE

JOURNAL OF THE ATMOSPHERIC SCIENCES **41** (1984) 246-257

## FORMATION OF SHEAR LAYERS UPSTREAM OF THE ALPS

RIVISTA DI METEOROLOGIA AERONAUTICA **44** (1984) 237-248

## An isolated baroclinic eddy as a laboratory analogue of the Great Red Spot on Jupiter

Nature **308** (1984) 45-48

We have recently presented evidence1 supporting the hypothesis2 that the long-lived large oval atmospheric eddies on Jupiter and Saturn, including Jupiter's anticyclonic Great Red Spot (GRS) and White Ovals and the cyclonic 'barges', are manifestations of 'slantwise' or 'sloping' convection in a rotating fluid, implying that they are involved in the horizontal transport of heat towards or away from the edges of the atmospheric zones or belts in which they occur, and that their kinetic energy derives directly from the action of gravity on the density field associated with horizontal gradients of temperature. These eddies would then be dynamically similar to the highly stable closed 'baroclinic' eddies produced in certain laboratory experiments on thermal convection in a rotating fluid subject to internal heating or cooling1,3. We now present laboratory findings that bear on the interpretation of the isolated nature of the GRS, including the crucial demonstration that a single intense stable baroclinic disturbance that is strongly localized in azimuth can form readily when the impressed conditions are close to the transition from axisymmetric to non-axisymmetric flow. © 1984 Nature Publishing Group.

## Long-lived eddies in the laboratory and in the atmospheres of Jupiter and Saturn

Nature **302** (1983) 126-129

The Great Red Spot (GRS), the three White Ovals, and other long-lived anticyclonic eddies in Jupiter's atmosphere might be dynamically similar 1 to the closed, stable baroclinic eddies that were first discovered in laboratory studies of thermal convection in a rotating fluid subject to internal heating and sidewall cooling2,3. We outline here results of new laboratory and numerical experiments on the structure, energetics and stability of such eddies, which strongly support the suggestion that these laboratory and atmospheric flows (including similar eddies found on Saturn 4) might all be manifestations of the same dynamical process - 'sloping' or 'slantwise' convection. Included in our numerical experiments are cases with internal cooling and sidewall heating, in which stable baroclinic eddies with a cyclonic peripheral jet stream at upper levels surrounding a region of slow descent have been produced and studied. We suggest that these cyclonic eddies are dynamically similar to the 'barges' observed in Jupiter's Tropical and Temperate Belts5. © 1983 Nature Publishing Group.