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Kerry A. Emanuel

Abstract

Observations of strong convective lines in middle latitudes indicate a close association of the lines with the presence of vertical shear of the large-scale horizontal wind. Under the premise that this shear is necessary to the maintenance of mesoscale circulations accompanying the lines, it is found that the susceptibility of the large-scale momentum, temperature and moisture fields to such circulations is related to the inertial stability of the flow. Part I contains a description of a variational solution of the linear equations governing two-dimensional perturbations in a bounded, fully viscous, adiabatic and Boussinesq rotating fluid with constant vertical and horizontal shears. The principal finding of this analysis is that the horizontal length scale of the most unstable normal mode is determined primarily by the depth of the unstable domain and the slope of isentropic surfaces rather than by the diffusive properties of the fluid. The effects of moisture and the conditions under which inertial circulations are likely to develop in the atmosphere are examined in Part II and compared with observations of mesoscale convective systems.

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Kerry A. Emanuel

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Kerry A. Emanuel

Abstract

A simple model describing the slantwise ascent of a two-dimensional horizontal air tube Subject to moist symmetric instability is developed under the assumptions that the Froude number is small and that mixing is absent. It is shown that, in general, the horizontal velocities attained by the tube are comparable to those of the mean flow and that vertical velocities of up to a few meters per second are possible. The tube ascends slantwise in such a way that its buoyancy remains nearly zero, unless the environment is my very nearly moist adiabatic, in which case ascent at an angle of 45° to the vertical is preferred. Results of the analysis support the contentions of Bennetts and Hoskins and Emanual that moist symmetric instability is the cause of some mesoscale rainbands. In a companion paper, it is demonstrated that the stability of the moist baroclinic atmosphere to two-dimensional slantwise displacements of arbitrary magnitude can be approximately assessed by reversibly lifting parcel along surfaces of constant angular momentum and comparing their density with that of their environment.

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Kerry A. Emanuel

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An exact equation governing the maximum possible pressure fall in steady tropical cyclones is developed, accounting for the full effects of gaseous and condensed water on density and thermodynamics. The equation is also derived from Carnot's principle. We demonstrate the existence of critical conditions beyond which no solution for the minimum central pressure exists and speculate on the nature of hurricanes in the supercritical regime.

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Kerry A. Emanuel

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A simple linear model is developed with the idea of demonstrating the basic physical processes that serve to distinguish the dynamics of precipitating convection from those of the nonprecipitating variety. In particular, it is shown that the hypothesis advanced by Seitter and Kuo to explain the slope and propagation of squall lines in the context of a fully nonlinear numerical model operates also within a linear model. With a hierarchy of linear models, it is demonstrated that 1) precipitating convection in a basic state consisting of a resting, uniform, unstable cloud can propagate and exhibit sloping up- and down-drafts; 2) subcloud evaporation of falling precipitation leads to modifications of the aforementioned instabilities and the formation of a new mode that travels rapidly and has peak amplitude in the subcloud layer; and 3) the introduction of a shear layer at the cloud base serves to couple the subcloud layer mode mentioned here with the cloud layer and yields a deep, rapidly growing, down-shear propagating mode which, while it has no critical level, nevertheless extracts kinetic energy from the mean shear. These models predict that small vertical shear favors slow-moving shear-parallel squall lines, somewhat larger shear leads to fast-moving shear-perpendicular lines, and very large shear favors three-dimensional convection.

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Kerry A. Emanuel

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Attempts were made during two field experiments to fly instrumented aircraft along absolute momentum (M) surfaces as a means of accurately determining slantwise convective stability. The application of this technique appears to have been quite successful. We present the results of four such efforts conducted in the ascent regions of midlatitude cyclones observed during the New England Winter Storms and Genesis of Atlantic Lows Experiments. In three of the four cases the atmosphere was almost exactly neutral to slantwise ascent while being quite stable to vertical displacements. In the fourth case, the atmosphere departed from neutrality but was also substantially drier, evidently due to subsidence. We find excellent agreement between assessments of stability based on the M surface flights and on cross sections constructed from rawinsonde observations. On the basis of these results I hypothesize that slantwise convective neutrality is characteristic of the ascent regions of baroclinic cyclones and discuss the implications of this finding for the dynamics of baroclinic systems.

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Kerry A. Emanuel

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Kerry A. Emanuel

Abstract

Observations in saturated frontal regions occasionally show that the flow has become neutral to reversible slantwise displacements along pseudo-angular momentum surfaces so that the effective potential vorticity is nearly zero for further saturated displacements. A strong response to frontogenesis is indicated in these regions, as suggested by the parabolic nature of the Sawyer–Eliassen equation when the potential vorticity vanishes. Using idealized distributions of temperature and geostrophic deformation, we derive solutions of the aforementioned equation for the cross-front circulation in the case where the potential vorticity is vanishingly small for upward displacements but moderate for downward displacements. While the solutions are self-consistent, it is not known whether they are unique. They show that a strong concentrated sloping updraft occurs somewhat to the warm side of the region of maximum geostrophic compression of the isotherms. This circulation closely resembles the flow in a mesoscale precipitation band analyzed by Sanders and Bosart.

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Kerry A. Emanuel

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We present a linear model of intraseasonal oscillations produced by the interaction of an atmosphere on an equatorial Beta-plane with a fixed ocean. Convection is treated as a means of rapidly redistributing in the vertical heat acquired from the sea surface, rather than as a heat source in and of itself. The model produces a spectrum of equatorially trapped oscillating instabilities, among which is an eastward-propagating wavenumber 1 disturbance with an intrinsic phase speed in the range of 4–20 m s−1, depending on the mean zonal wind, the surface exchange coefficients, the air-sea equivalent potential temperature difference, and the difference of absolute temperature across the depth of the lower troposphere. The three-dimensional structure of this mode is in excellent agreement with observations and recent numerical experiments concerning the 30–60 day oscillation. The phase speed and growth rate of the disturbances depend only on conditions at the equator, while their meridional structure varies with meridional gradients of mean zonal wind, sea surface temperature, and the depth of the moist convective layer. Momentum fluxes by the waves may serve to maintain mean easterlies at the equator. The model also predicts nongeostrophic oscillations with generally shorter periods of around one week.

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Kerry A. Emanuel

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An expression is derived for the critical horizontal gradient of subcloud-layer θe in radiative-convective equilibrium, sufficient for the onset of thermally direct, zonally symmetric circulations. This corresponds to zero absolute vorticity at the tropopause. The expression is then generalized to nonsymmetric flows under the approximation that the corresponding radiative-convective equilibrium state is in geostrophic balance. Scale analysis shows that actual moist entropy distributions cannot be far from critical in large-scale Hadley, Walker, and monsoon circulations. The balanced component of the surface winds can be calculated from the supercriticality of the surface θe distribution, and the secondary circulation can then be estimated from the surface stress.

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