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S. K. Mishra

Abstract

The nonlinear evolution of perturbation superimposed on the barotropic, unstable observed mean easterly jet at 100 hPa is studied over the sphere. The nondivergent barotropic nonlinear global spectral model with rhomboidal truncation at zonal wavenumber 21 is integrated for 120 days for initial random and linear unstable perturbations. The model includes a Rayleigh friction and restoring mechanism for zonal wind to its initial distribution. Time variations of eddy and zonal kinetic energy, zonal-wave and wave-wave interactions, and eddy and zonal kinetic energy dissipations are examined. The growth of perturbation begins with exponential increase in its kinetic energy for a short period, followed by a linear increase. The perturbations undergo oscillations before approaching a steady state. During the initial exponential phase, the nonlinear interactions further destabilize the jet, and this effect is more pronounced for the random initial perturbation. It is found that oscillations in kinetic energy are due to the time lag between energy source (zonal-wave interaction) and sink (frictional dissipation).

It is noticed that the random initial perturbation is more efficient than the linear unstable modes in reaching the steady state. Nonlinear interactions shift the preferred wave towards the lower wavenumber 6. Wave 6 accounts for more than 98% of eddy kinetic energy of steady state. The role of wave-wave interaction is secondary to zonal-wave interaction.

Steady-state wave 6 has an inviscid growth rate of 0.104 × 10−5 s−1, a phase speed of −20.9° day−1, and a meridional scale comparable to the half-width of the easterly jet. The zonal scale of the wave is close to the Rossby radius of deformation. The maximum meridional velocity associated with the wave is 3.8 m s−1. Nonlinear interactions modify the jet to a more asymmetric distribution, which induces a southward shift in the wave- amplitude maximum location. Strong correlation between latitude of maxima for wave amplitude and meridional gradient of basic-state potential vorticity is noticed. A close agreement is seen between observation and nonlinear preferred wave 6.

The kinetic energy cycle for steady-state wave 6 on the sphere and in the latitude belt 10°S–40°N is computed and discussed. The kinetic energy of wave 6 in the latitude belt agrees well with the observed value.

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S. K. Mishra

Abstract

A barotropic global spectral model is used to determine the linear divergent barotropic instability characteristics of the tropical easterly jet by applying an initial value technique. These characteristics are compared with those on a beta plane, in order to identify the important effects of the spherical geometry an unstable modes. The increase in the growth rate of unstable modes on the sphere is due to the absence of lateral walls. The primary and secondary maxima of the wave amplitude are located at 3.5° and 18.5°N, respectively. It is found that the spherical geometry plays an important role in locating the wave amplitude maximum and the angular momentum transports by the wave. There exists a strong correlation between the two wave amplitude maxima and the extrema of q̄μ/a q̄.

It is seen that the midlatitude westerly jets stabilize the easterly jet. The influence of westerly jets is investigated in terms of the overreflection of the meridional propagation of waves from critical latitudes.

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S. K. Mishra and P. S. Salvekar

Abstract

A linear baroclinic stability analysis of the zonal wind representing the mean monsoon situation over India is performed by the use of a multi-level quasi-geostrophic numerical model. An initial value approach is chosen to determine the instability characteristics of the wind. The dependency of the growth rate spectrum on the number of levels in the vertical and on the presence of vertical walls is studied. It is shown that 20 levels in the vertical are sufficient to realize the baroclinic instability of the monsoon mean wind.

A shorter unstable wave of wavelength 1500 km and a longer unstable wave of wavelength 4750 km are found to be the most preferred growing waves from the growth rate spectrum. The shorter unstable wave is essentially confined below 500 mb, whereas the longer unstable wave is above 500 mb. It is also shown that the removal of wind shear below (above) the level of the westerly (easterly) jet from the wind profile, shifts the shorter (longer) unstable wave toward higher wavelengths by ∼ 1000 km, with a significant decrease in the growth rates.

The horizontal scale (1500 km), level of nondivergence (900 mb), and level of maximum intensity (825 mb) associated with the shorter unstable wave are in close agreement with the observed values, obtained from a composite monsoon depression. The computed phase velocity of the unstable wave is opposite to the observed westward motion. The computed levels of cold core, warm core and top of the wave are at 900, 800 and 500 mb, respectively, which are ∼100 mb lower than the observed levels. The computed phase velocity of the longer unstable wave (−23 m s−1) is found to be very close to the observed value for disturbances along the easterly jet level. The longer unstable wave has a level of nondivergence at 200 mb which is supported from the results of barotropic studies obtained by others.

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G. C. Asnani and S. K. Mishra

Abstract

In Part I of this paper, influence functions are derived for the response of a quasi-geostrophic atmosphere to transient heat sources and sinks, assuming that the effects of horizontal advection can be neglected and assuming a fairly reasonable vertical distribution of static stability. The influence is studied for diabatic heating of different horizontal wavelengths and for two different types of the vertical distribution. In Type I, heating is largest at the ground, decreasing to zero at p = 0. In Type II, heating is maximum in the middle atmosphere and decreases parabolically to zero at p = 0 and at the ground. It is shown that, in both types, the horizontal wavelength L of the heating function is very important in determining not only the intensity of pressure fall in the lower levels and of pressure rise aloft in the region of heating, but also the level of maximum pressure effect. It is seen that wavelengths of the order of 15,000 km produce maximum geopotential variations around the 150-mb level.

Introduction of Ekman layer friction decreases the intensity of pressure fall in the lower layers, increases the intensity of pressure rise aloft, lowers the level of phase reversal, and introduces a phase lag between the high pressure wave aloft and the low pressure wave below.

Part II deals with the application of theoretical results obtained in Part I to the problem of the Indian monsoon. It is visualized that the 12-monthly monsoon oscillation in southeast Asia is a linear perturbation on the annual mean flow pattern, the perturbation being essentially forced by differential diabatic heating in the horizontal plane; the perturbation is materially affected by low-level friction, while advection is assumed to be only of secondary importance.

In the first instance a 2-dimensional model of the monsoon in the y, p plane is constructed along the meridian 77.5°E, where observed annual mean conditions are taken as a basic state. On this is superimposed a linear perturbation forced by diabatic heating, sinusoidal in y and t and incorporating a combination of heating of Types I and II. The resulting total patterns of zonal wind in different months are presented. It is very encouraging to find that such a simple model, with only one wavelength in the y direction, is able to reproduce quite a few observed features of the zonal wind pattern in all months, including the westerly jet stream in winter and the easterly, jet stream in summer.

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S. K. Mishra and M. Y. Tandon

Abstract

A combined barotropic-baroclinic stability analysis is performed for an upper tropospheric tropical easterly jet representing the observed mean monsoon zonal flow during summer. Numerical solutions are obtained by time integration of a 20-layer linear spectral quasi-geostrophic model, which is based on truncated Fourier series representations in y. It is seen from the growth rate and phase speed spectra that the asymmetric barotropic-baroclinic preferred wave has a wavelength of 6500 km, an e-folding time of 3.3 days, a westward phase speed of 20.5 m s and a period of 3.8 days.

The geopotential, vertical velocity and temperature fields associated with the most unstable barotropic-baroclinic wave are computed. The most unstable wave has a vertical scale of 125 mb, a meridional scale of 1650 km and a zonal scale of 2135 km. The relationship between the vertical and meridional scales of the wave with the corresponding basic zonal flow scales is discussed.

The large southward easterly momentum transports associated with the unstable wave are essentially due to the antisymmetric components of the jet. The computed sensible heat transports are found to be down the basic state meridional temperature gradient. The energetics of the unstable wave is computed and it is inferred that the energy sources for the wave growth lie in a narrow vertical layer around the jet level. It is also found that the contribution of baroclinic process is larger than the contribution of barotropic in the wave growth.

The contribution of different processes in the movement of the unstable wave are also investigated. The beta effect is identified as the most important physical factor responsible for the westward propagation of the wave.

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S. K. Mishra, D. Subrahmanyam, and M. K. Tandon

Abstract

The divergent barotropic instability of a zonally averaged, observed, tropical, upper tropospheric, monsoon easterly jet is investigated by numerical integration of a linear spectral model. The Rossby radius of deformation for the upper troposphere is computed from a three-layer model of the atmosphere. It is shown that the antisymmetric zonal flow components in the jet contribute in stabilizing the short waves and destabilizing the long waves. Furthermore, the maximum amplitude of the asymmetric preferred wave is shifted southward (to 6°N) to a region where a largest positive maximum of −ūvv is located for the asymmetric profile. A large decrease in the meridional scale of the wave and a threefold increase in the ratio of the computed maximum southward-to-northward easterly momentum transports is also found for the asymmetric jet compared to the symmetric jet. The divergence is found to increase the growth rates of all the waves and, also to increase the preferred wavelength.

The most unstable divergent asymmetric wave is shown to have a wavelength of 6500 km, an e-folding time of 6.5 days and a westward phase speed of 23.5 m s−1. The zonal scale of the preferred wave is nearly equal to the Rossby radius of deformation.

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S. K. Mishra, V. Brahmananda Rao, and Sergio H. Franchito

Abstract

The primitive equation barotropic unstable linear normal modes are computed using an eigenvalue approach for daily latitudinal profiles of zonal flow in the upper-tropospheric layer of 100–350 hPa before and after formation of cyclonic vortices during January 1993 and November 2001 off the coast of northeast Brazil. The wave kinetic energy equation for u- and υ-motion is presented. Equations are derived to isolate the contribution of divergence and other dynamical processes in the movement and growth of unstable modes. Numerical accuracy and physical nature of unstable modes are tested.

In a short span of 2–3 days, prior to formation of vortices, a progressive and a sharp intensification of the basic flow shear zone and its barotropic instability are seen with time. The horizontal structure, momentum transport, and zonal and meridional scales of the most unstable normalized wave are obtained and compared with the vortex extracted from the 200-hPa observed winds using a bandpass smoother. A close agreement is found between them. It is shown that the zonal and meridional scales of the preferred wave are related to the length scale of the shear zone. The wave is confined to the shear zone and its maximum amplitude is located at the latitude of maximum βuyy. The role of divergence in the movement and growth of the wave is investigated. The energetics of the unstable wave u- and υ-motion is computed, and it is inferred that the energy source for the growth of wave u- (υ-) motion is the energy conversion (work done by pressure force), which lies in the shear zone.

It is emphasized that a deeper insight regarding the genesis of the cyclonic vortex can be gained on the basis of stability analysis of daily observed zonal flow profiles, which may not be possible using idealized or mean profiles. An explanation for nonmanifestation of the instability in the monthly mean flow is provided.

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S. K. Mishra, V. B. Rao, and M. A. Gan

Abstract

Horizontal structure and evolution of large-scale flow and an embedded synoptic-scale cyclonic vortex over northeast Brazil as separate systems and dynamical interaction between them are studied at 200 hPa. A quasi-stationary cyclonic vortex with its average position at 10°S and 35°W that formed and remained active during 5–10 January 1993 is selected for the investigation. The evolution of large-scale flow in the prevortex period 1–4 January is also explored. An efficient and effective scale separation technique is developed and used to separate the large-scale flow and embedded synoptic-scale vortex.

It is shown that a strong positive shear zone developed in the latitude domain 17.5°–7.5°S, within the South Atlantic trough region before the vortex formation. The shear zone has a characteristic meridional (zonal) scale of 1000 km (3000 km) and satisfies strongly the necessary condition for barotropic instability. It is identified that the development of a strong shear zone is associated with the intensification of a Bolivian anticyclone and associated ridge and their eastward shift, and intensification of the South Atlantic trough, east–west orientation of the Atlantic trough, and the presence of a transient trough over the equatorial Atlantic Ocean.

The average structure of vortex including zonal and meridional characteristic scales is computed from the synoptic bandpass flow. The vortex is identified as a nonlinear wave packet with an average zonal wavelength of 2750 km and it is confined to a latitude belt of about 17.5°. The vortex shows a strong westward tilt with latitude; the convergence zone is located to its southwest and it is a weak cold cored system. Maximum cyclonic vorticity of the vortex is −3.24 × 10−5 s−1, which is comparable to the value for embedding flow.

The momentum transports due to the vortex, large-scale eddy, and the vortex–large-scale eddy interaction are computed. It is found that the vortex and vortex–large-scale eddy westerly momentum transports are southward, down the gradient of embedding zonal flow, and their divergence (convergence) is located over the latitudes of large scale westerlies (easterlies). The sensible heat transports are weak. It is noted that the vortex–large-scale flow interaction leads to the weakening of the shear zone and restoration of the large circulation features to their January 1993 mean configuration, which have undergone significant deviation during the prevortex period. The signature of vortex–large-scale interaction is also seen in the evolution of dynamical parameters q y and n 2 (square of refractive index parameter).

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Saroj K. Mishra, J. Srinivasan, and Ravi S. Nanjundiah

Abstract

Several numerical experiments have been conducted using the NCAR Community Atmosphere Model, version 3 (CAM3) to examine the impact of the time step on rainfall in the intertropical convergence zone (ITCZ) in an aquaplanet. When the model time step was increased from 5 to 60 min the rainfall in the ITCZ decreased substantially. The impact of the time step on the ITCZ rainfall was assessed for a fixed spatial resolution (T63 with L26) for the semi-Lagrangian dynamical core (SLD). The increase in ITCZ rainfall at higher temporal resolution was primarily a result of the increase in large-scale precipitation. This increase in rainfall was caused by the positive feedback between surface evaporation, latent heating, and surface wind speed. Similar results were obtained when the semi-Lagrangian dynamical core was replaced by the Eulerian dynamical core. When the surface evaporation was specified, changes in rainfall were largely insensitive to temporal resolution. The impact of temporal resolution on rainfall was more sensitive to the latitudinal gradient of SST than to the magnitude of SST.

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K. J. Evans, P. H. Lauritzen, S. K. Mishra, R. B. Neale, M. A. Taylor, and J. J. Tribbia

Abstract

The authors evaluate the climate produced by the Community Climate System Model, version 4, running with the new spectral element atmospheric dynamical core option. The spectral element method is configured to use a cubed-sphere grid, providing quasi-uniform resolution over the sphere and increased parallel scalability and removing the need for polar filters. It uses a fourth-order accurate spatial discretization that locally conserves mass and total energy. Using the Atmosphere Model Intercomparison Project protocol, the results from the spectral element dynamical core are compared with those produced by the default finite-volume dynamical core and with observations. Even though the two dynamical cores are quite different, their simulated climates are remarkably similar. When compared with observations, both models have strengths and weaknesses but have nearly identical root-mean-square errors and the largest biases show little sensitivity to the dynamical core. The spectral element core does an excellent job reproducing the atmospheric kinetic energy spectra, including fully capturing the observed Nastrom–Gage transition when running at 0.125° resolution.

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