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The numerical study presented here focuses on baroclinic processes that contribute to tropical cyclone (TC) propagation. A three-dimensional, semispectral, primitive equation model of baroclinic vortex was developed to study TC motion. In a tilted vortex, interaction between upper- and lower-level vorticity anomalies leads to vortex propagation relative to the steering flow. On a, β plane, with no environmental flow, the vortex is tilted toward the south and the interaction between the layers reduces the westward movement of the vortex. The vortex tilting can also occur due to the vertical shear in the environmental wind. On an f plane, the interaction between the layers causes the northward movement of the vortex in westerly linear shear, and southward movement in easterly linear shear, with a meridional velocity of about 1 m s−1. Ibis velocity increases with increasing vortex intensity and vertical motion.

The paper examines the role of the development of outflow-layer instabilities on the motion of tropical cyclones. The influence of barotropic instability is examined by comparing the time changes in the storm tracks with the frequencies of free, unstable barotropic modes. For intense vortices barotropic instability is shown to contribute to the slow (periods of a few days) trochoidal motion of a cyclone. The development of instability depends on the horizontal distribution and frequency of environmental forcing. The strongest response occurs when the frequency of the forcing matches the frequency of an unstable mode.

We propose a quasi-balance dynamical system of equations for slowly evolving, large-scale motions in the tropics. Unlike other balance schemes, equatorially trapped Kelvin waves are included. Following the lead of Gill, this system is based on the neglect of the meridional acceleration (the so-called long-wave approximation). Consistent budgets for kinetic energy and potential vorticity are derived, with those quantities appropriately redefined. Unlike the quasi-geostrophic system, vertical advection of potential vorticity as well as of potential temperature is relevant. A primary circulation is defined, involving the zonal wind, geopotential, and potential temperature, such that potential vorticity depends on latitudinal and vertical gradients of the primary circulation. A residual secondary circulation is governed by an elliptic equation for a streamfunction in the meridional plane. The invertibility principle is affected by the Kelvin waves with zero potential vorticity. The eigenfrequencies f...

The barotropic instability of basic states with downstream and asymmetric cross-stream variations is investigated using the linearized, non-divergent barotropic vorticity equation in a periodic beta channel. A single expression for streamfunction defines the basic state; the variations are introduced by parameter changes. Eigenvalue and time integration methods are employed to determine the instabilities. When downstream variation is present, the maximum amplitude of the unstable streamfunction is always located downstream from the location of maximum latitudinal shear. This occurs because the disturbance propagates through a range of longitudes where the flow is locally barotropically unstable. The instability is sensitive to the degree of downstream variation. When there is strong variation there is more concentration of streamfunction amplitude in the regions downstream of the jet maximum, smaller disturbance scales and smaller growth rates than when the flow is more parallel. The smaller grow...

The movement of a set of Lagrangian parcels in the two-dimensional pressure field associated with a tropical convective line is considered. The results are compared with observational characteristics of GATE quasi-two-dimensional convective lines. It is shown that for the composite, slow-moving GATE convective line it is necessary to account for horizontal pressure gradients in order to obtain realistic momentum flux. The role of vertical pressure gradients and initial conditions for an air parcel's movement is studied. Based on the results, some suggestions concerning proper formulation of parameterization of the convective momentum flux are made.

A revised version Of Raymond's wave-CISK model is used to study the propagation of mesoscale modes. The sensitivity of unstable modes to variations in basic state stability and wind show (characteristics of the eastern Atlantic during GATE), as well as parameterized cumulus heating is examined. Unstable, modes exist for mesoscale wavelengths, which are sensitive to the details of the cumulus heating parameters as well as the structure of the large-scale wind shell. In many cases, the most unstable mode has a two-dimensional structure.

A version of Holton's numerical model of the stratospheric sudden warming is found to be very sensitive to the assumed initial mean zonal wind distribution. In tests with three initial wind profiles, in only one case can we simulate a wavenumber 1 warming involving flow reversal over a deep layer of the polar atmosphere and substantial warming (i.e., a major warming). In the other two cases, flow reversal is noted in restricted areas and warming is less intense. Examination of Eliassen-Palm cross sections and of Matsuno's refractive index squared throughout each integration reveals how the different warnings develop, and why they differ. Examination of refractive index squared in the atmosphere at the time of enhanced wave propagation out of the troposphere may be valuable aid in predicting the likelihood of a warming. Some characteristics of an “ideal” mean zonal wind profile (with which a major warming can develop) are discussed.

The tropical response to a localized thermal forcing with approximately 45-day period is investigated for several models of increasing complexity consisting of two equivalent shallow water systems and two fully stratified systems. The fully stratified models appear to be able to reproduce a number of observed features of the tropical 40-50 day oscillation including the modulation of the subtropical jet and the eastward and poleward propagation of zonal wind anomalies.

A two level, global, spectral model using pressure as a vertical coordinate was developed. The system of equations describing the model is nonlinear and quasi-geostrophic (linear balance). Static stability is variable in the model. A moisture budget is calculated in the lower layer only. Convective adjustment is used to avoid supercritical temperature lapse rates. The mechanical forcing of topography is introduced as a vertical velocity at the lower boundary. Solar forcing is specified assuming a daily mean zenith angle. The differential diabatic heating between land and sea is parameterized. On land and sea ice surfaces, a steady state thermal energy equation is solved to calculate the surface temperature. On the oceans, the sea surface temperature is specified as the climatological average for January. The model is used to simulate the January, February and March circulations. Previously announced in STAR as N83-14822

Through the use of a zonal balance model we investigate the response of the mean meridional circulation to a specified diabatic forcing for both resting and nonresting zonal flows. The use of a potential latitude coordinate and transformed meridional circulation components results in a simplified meridional circulation equation in which the variable coefficients are the normalized potential vorticity and inertial stability. Solutions of this equation illustrate how latent heat release away from the equator forces a winter hemisphere Hadley cell that is more intense than the summer hemisphere cell. This asymmetric response is due primarily to the anisotropy associated with the spatial variation of the inertial stability field. Despite the sensitivity of the meridional circulation to the location and breadth of the forcing, the low latitude thermodynamic response is for the most part insensitive as long as the total latent heat release remains the same. Numerical solutions of the zonal balance mode...

The wave-CISK problem is investigated in a linearized context with two significant departures from previous models: 1) the cumulus heating parameterization is made thermodynamically consistent by requiring that cumulus heating exactly equal the latent heat of moisture converged in the wave; and 2) cumulus friction is included in the model. The parameterization of vertical transport of horizontal momentum by cumulus clouds follows the formulation of Schneider and Lindzen (1976); with a constant mean zonal wind, cumulus friction is proportional to the mean cloud mass flux. Results from the model of Stevens et at. (1977) are presented for various scales of motion. For magnitudes of cloud mass flux typical of the ITCZ, no wave-CISK modes appear on the synoptic scale of several thousand kilometers. As the horizontal scales of these long-period waves are decreased, the disturbances become frictionally controlled, neutral wave-CISK modes. When the mean cloud mass flux is reduced by a factor of 2, instab...

We present a detailed analysis of a mesoscale circulation phenomenon that appeared on satellite images as a group of propagating cloud wavelets. These wavelets developed on the anticyclonic side of a strong, upper-level subtropical jet in a region of negative potential vorticity (P). During their lifetime, the wavelets were located over the North American synoptic sounding network; the meteorological conditions surrounding their occurrence are examined. We investigate the various physical mechanisms that may have been responsible for generating the observed cloud wavelets. In consideration of the time scale of the wavelets and their proximity to the region where P < 0, inertial instability appears to be the most likely dynamical mechanism for explaining their existence. Using hourly satellite images, we determined that the wavelets propagated downstream at a phase speed 25 m s−1 slower than the maximum wind speed of the jet with life cycles of 4–5 h, horizontal wavelengths of ∼400 km, and periods...

We investigate the temporal and spatial characteristics of unstable normal modes in a horizontally sheared flow on a sphere using the shallow water equations. Both inertial and barotropic instabilities are identified in cases where the appropriate necessary conditions are satisfied. A primary focus is determining what conditions favor asymmetric modes of inertial instability rather than symmetric modes. With the Bickley jet profile, the region of instability [f(f + &xi) ≤ 0] is confined to the anticyclonic side of the jet in a limited region. We find that symmetric instability is preferred only for modes of very small vertical wide, for which the pressure gradient force is secondary. Relatively small dissipation is needed to stabilize these modes. With deeper vertical scales, asymmetric instabilities are preferred in which the zonal scale of the instability is comparable to the width of the unstable region. This study extends previous results for linear shear on an equatorial beta plane to the mi...

Obserations of longitudinally-averaged zonal flows in the atmosphere and ocean tend to display north–south symmetry about the equator, with a characteristic wind maximum or minimum, and therefore little horizontal wind shear locally near the equator. It is shown that this configuration is required for balanced flow on a sphere to be inertially stable. If dissipation can be neglected, any horizontal wind shear at the equator will cause inertial instability to develop. effectively eliminating the horizontal shear. It follows that the potential vorticity (q) must vanish at the equator for the symmetric circulation to be stable; and that it must increase to the north and decrease to the south. Balanced cross-equatorial flow can occur only if there is a north–south gradient in the torque or the diabatic heating at the equator. These conclusions are obtained under the assumption of a balanced zonal flow; i.e., acceleration and dissipation are explicitly neglected in the meridional momentum equation. Th...

The spherical geometry of the earth is replaced by polar cylindrical geometry, with a plane tangential to the earth at the pole. The resulting frequency and structure of free motions in an isothermal, adiabatic atmosphere with a resting basic state is studied in both geometries. The solutions for ν (meridional wind) may be written as a single Bessel function if certain approximations are made. For positive equivalent depths, the geometrical approximation is best when the Lamb parameter ϵ≳ 10, so that Rossby waves are well modeled, while fast moving gravity waves are not well approximated. The impact of setting f to a constant value when undifferentiated, as in the usual midlatitude beta-plane approximation, is examined. It is found that the value of f is as important in determining how well the model behaves as are the geometrical and other approximations.

The term Walker Circulation is used to refer to the zonal overturning across the equatorial Pacific driven by enhanced convection over the Indonesian region. In this work, an attempt is made to simulate the Walker Circulation using a linear model that includes a cumulus friction parameterization. The work of Geisler is extended by including a realistic mean zonal wind field obtained from the FGGE dataset and a prescribed mean Hadley cell that is computed from an analytical streamfunction. The model is forced by a stationary tropical heat source. The sensitivity of the model circulation to changes in the basic state is examined. Model results show that the inclusion of a nonzero mean zonal wind field tends to enhance the extratropical response in the winter hemisphere. Including a cumulus friction parameterization tends to damp the zonal wind response near the heating center and also lower the level of zero zonal wind in the model Walker Circulation. Including a mean Hadley cell in the basic state...

The linear, zonally symmetric modes of the basic state of a Hadley cell are examined. It is found that the inclusion of the divergent basic state leads to the formation of a new class of slowly oscillating modes, some of which have periods in the range of 40-50 days. The modes have many features in common with the observed tropical 40-50-day oscillation; however, an explanation for the observed fluctuations in convective cloudiness remains a topic for future work.

Measuremenits of the momentum transport in tropical convective lines suggest that horizontal momentum can be generated by the pressure low located near the center of the convective part of the line. A simple convective parameterization is used to evaluate this effect. The parameterization is a version of the Fritsch and Chappell scheme, modified in order to evaluate the influence of the horizontal pressure gradients on momentum transport. The results suggest that in modeling of convective (particularly slow-moving) lines with 20 km resolution, subgrid horizontal pressure gradients should be taken into account. Sensitivity studies show that the magnitude of the calculated momentum flux strongly depends on the average vertical velocity and the vertical velocity in clouds.

A linear model of wave-CISK consisting of the primitive equations formulated on an equatorial beta-plane with a resting basic state, is used to compare the relatively simple cumulus parameterization scheme developed by Stevens and Lindzen with the relatively complex one developed by Arakawa and Schubert. The comparison is based mainly on the instability characteristics and vertical structure of the wave. Discrete forms of the equations are developed and the inhomogeneous vertical structure equation is solved as a generalized matrix eigenvalue problem. The eigenvalues correspond to complex equivalent depths which determine the growth rates through the use of the dispersion relation for an equatorial beta-plane. The eigenvectors, which are the vertical velocities at discrete levels in the model, determine the vertical structure. Results indicate that the growth rates obtained with Arakawa and Schubert's parameterization are smaller than those obtained with Stevens and Lindzen's parameterization. Co...

Large-amplitude planetary waves in the southern winter stratosphere are observed to occur episodically, the result of episodic tropospheric forcing. This work is an observational study of the dynamics of the planetary waves, focusing on the evolution through a typical life cycle. Time lag correlations of wave amplitude with the Eliassen-Palm flux vector reveal the characteristic heat and momentum flux patterns associated with wave evolution. Energetic studies clearly show that the stratospheric waves can be understood in terms of a life cycle of vertical propagation from the troposphere, followed by decay from barotropic interactions with the zonal mean flow. Although usually of secondary importance baroclinic decay of stratospheric wave energy is also observed, resulting from equatorward heat flux in the lower stratosphere. Good agreement in the energy balances discounts in situ instability in the stratosphere as a source of wave activity. An average or composite over several clearly propagating...