scholarly journals Moisture Modes and the Eastward Propagation of the MJO

2013 ◽  
Vol 70 (1) ◽  
pp. 187-192 ◽  
Author(s):  
Adam Sobel ◽  
Eric Maloney

Abstract The authors discuss modifications to a simple linear model of intraseasonal moisture modes. Wind–evaporation feedbacks were shown in an earlier study to induce westward propagation in an eastward mean low-level flow in this model. Here additional processes, which provide effective sources of moist static energy to the disturbances and which also depend on the low-level wind, are considered. Several processes can act as positive sources in perturbation easterlies: zonal advection (if the mean zonal moisture gradient is eastward), modulation of synoptic eddy drying by the MJO-scale wind perturbations, and frictional convergence. If the sum of these is stronger than the wind–evaporation feedback—as observations suggest may be the case, though with considerable uncertainty—the model produces unstable modes that propagate weakly eastward relative to the mean flow. With a small amount of horizontal diffusion or other scale-selective damping, the growth rate is greatest at the largest horizontal scales and decreases monotonically with wavenumber.

1967 ◽  
Vol 27 (4) ◽  
pp. 657-689 ◽  
Author(s):  
R. E. Kelly

In experiments concerning the instability of free shear layers, oscillations have been observed in the downstream flow which have a frequency exactly half that of the dominant oscillation closer to the origin of the layer. The present analysis indicates that the phenomenon is due to a secondary instability associated with the nearly periodic flow which arises from the finite-amplitude growth of the fundamental disturbance.At first, however, the stability of inviscid shear flows, consisting of a non-zero mean component, together with a component periodic in the direction of flow and with time, is investigated fairly generally. It is found that the periodic component can serve as a means by which waves with twice the wavelength of the periodic component can be reinforced. The dependence of the growth rate of the subharmonic wave upon the amplitude of the periodic component is found for the case when the mean flow profile is of the hyperbolic-tangent type. In order that the subharmonic growth rate may exceed that of the most unstable disturbance associated with the mean flow, the amplitude of the streamwise component of the periodic flow is required to be about 12 % of the mean velocity difference across the shear layer. This represents order-of-magnitude agreement with experiment.Other possibilities of interaction between disturbances and the periodic flow are discussed, and the concluding section contains a discussion of the interactions on the basis of the energy equation.


2014 ◽  
Vol 142 (1) ◽  
pp. 320-342 ◽  
Author(s):  
James D. Doyle ◽  
Clark Amerault ◽  
Carolyn A. Reynolds ◽  
P. Alex Reinecke

Abstract The sensitivity and predictability of a rapidly developing extratropical cyclone, Xynthia, that had a severe impact on Europe is explored using a high-resolution moist adjoint modeling system. The adjoint diagnostics indicate that the intensity of severe winds associated with the front just prior to landfall was particularly sensitive to perturbations in the moisture and temperature fields and to a lesser degree the wind fields. The sensitivity maxima are found in the low- and midlevels, oriented in a sloped region along the warm front, and maximized within the warm conveyor belt. The moisture sensitivity indicates that only a relatively small filament of moisture within an atmospheric river present at the initial time was critically important for the development of Xynthia. Adjoint-based optimal perturbations introduced into the tangent linear and nonlinear models exhibit rapid growth over 36 h, while initial perturbations of the opposite sign show substantial weakening of the low-level jet and a marked reduction in the spatial extent of the strong low-level winds. The sensitivity fields exhibit an upshear tilt along the sloping warm conveyor belt and front, and the perturbations extract energy from the mean flow as they are untilted by the shear, consistent with the PV unshielding mechanism. The results of this study underscore the need for accurate moisture observations and data assimilation systems that can adequately assimilate these observations in order to reduce the forecast uncertainties for these severe extratropical cyclones. However, given the nature of the sensitivities and the potential for rapid perturbation and error growth, the intrinsic predictability of severe cyclones such as Xynthia is likely limited.


2019 ◽  
Vol 865 ◽  
pp. 212-246 ◽  
Author(s):  
J. D. Pickles ◽  
B. R. Mettu ◽  
P. K. Subbareddy ◽  
V. Narayanaswamy

Interactions between an oblique shock wave generated by a sharp fin placed on a cylindrical surface and the incoming boundary layer are investigated to unravel the mean features of the resulting shock/boundary layer interaction (SBLI) unit. This fin-on-cylinder SBLI unit has several unique features caused by the three-dimensional (3-D) relief offered by the cylindrical surface that noticeably alter the shock structure. Complementary experimental and computational studies are made to delineate both the surface and off-body flow features of the fin-on-cylinder SBLI unit and to obtain a detailed understanding of the mechanisms that dictate the mean flow and wall pressure features of the SBLI unit. Results show that the fin-on-cylinder SBLI exhibits substantial deviation from quasi-conical symmetry that is observed in planar fin SBLI. Furthermore, the separated flow growth rate appears to decrease with downstream distance and the separation size is consistently smaller than the planar fin SBLI with the same inflow and fin configurations. The causes for the observed diminution of the separated flow and its downstream growth rate were investigated in the light of changes caused by the cylinder curvature on the inviscid as well as separation shock. It was found that the inviscid shock gets progressively weakened in the region close to the triple point with downstream distance due to the 3-D relief effect from cylinder curvature. This weakening of the inviscid shock feeds into the separation shock, which is also independently impacted by the 3-D relief, to result in the observed modifications in the fin-on-cylinder SBLI unit.


2018 ◽  
Vol 48 (11) ◽  
pp. 2779-2797 ◽  
Author(s):  
Megan A. Stamper ◽  
John R. Taylor ◽  
Baylor Fox-Kemper

AbstractMotivated by recent observations of submesoscales in the Southern Ocean, we use nonlinear numerical simulations and a linear stability analysis to examine the influence of a barotropic jet on submesoscale instabilities at an isolated front. Simulations of the nonhydrostatic Boussinesq equations with a strong barotropic jet (approximately matching the observed conditions) show that submesoscale disturbances and strong vertical velocities are confined to a small region near the initial frontal location. In contrast, without a barotropic jet, submesoscale eddies propagate to the edges of the computational domain and smear the mean frontal structure. Several intermediate jet strengths are also considered. A linear stability analysis reveals that the barotropic jet has a modest influence on the growth rate of linear disturbances to the initial conditions, with at most a ~20% reduction in the growth rate of the most unstable mode. On the other hand, a basic state formed by averaging the flow at the end of the simulation with a strong barotropic jet is linearly stable, suggesting that nonlinear processes modify the mean flow and stabilize the front.


2020 ◽  
Vol 50 (1) ◽  
pp. 3-33
Author(s):  
Shih-Nan Chen ◽  
Chiou-Jiu Chen ◽  
James A. Lerczak

AbstractThis study examines the utility of Eady-type theories as applied to understanding baroclinic instability in coastal flows where depth variations and bottom drag are important. The focus is on the effects of nongeostrophy, boundary dissipation, and bottom slope. The approach compares theoretically derived instability properties against numerical model calculations, for experiments designed to isolate the individual effects and justified to have Eady-like basic states. For the nongeostrophic effect, the theory of Stone (1966) is shown to give reasonable predictions for the most unstable growth rate and wavelength. It is also shown that the growing instability in a fully nonlinear model can be interpreted as boundary-trapped Rossby wave interactions—that is, wave phase locking and westward phase tilt allow waves to be mutually amplified. The analyses demonstrate that both the boundary dissipative and bottom slope effects can be represented by vertical velocities at the lower boundary of the unstable interior, via inducing Ekman pumping and slope-parallel flow, respectively, as proposed by the theories of Williams and Robinson (1974; referred to as the Eady–Ekman problem) and Blumsack and Gierasch (1972). The vertical velocities, characterized by a friction parameter and a slope ratio, modify the bottom wave and thus the scale selection. However, the theories have inherent quantitative limitations. Eady–Ekman neglects boundary layer responses that limit the increase of bottom stress, thereby overestimating the Ekman pumping and growth rate reduction at large drag. Blumsack and Gierasch’s (1972) model ignores slope-induced horizontal shear in the mean flow that tilts the eddies to favor converting energy back to the mean, thus having limited utility over steep slopes.


2006 ◽  
Vol 63 (12) ◽  
pp. 3421-3436 ◽  
Author(s):  
Marat Khairoutdinov ◽  
David Randall

Results are presented from a high-resolution three-dimensional simulation of shallow-to-deep convection transition based on idealization of observations made during the Large-Scale Biosphere–Atmosphere (LBA) experiment in Amazonia, Brazil, during the Tropical Rainfall Measuring Mission (TRMM)-LBA mission on 23 February. The doubly periodic grid has 1536 × 1536 × 256 grid cells with horizontal grid spacing of 100 m, thus covering an area of 154 × 154 km2. The vertical resolution varies from 50 m in the boundary layer to 100 m in the free troposphere and gradually coarsens to 250 m near the domain top at 25.4 km. The length of the simulation is 6 h, starting from an early morning sounding corresponding to 0730 local time. Convection is forced by prescribed surface latent and sensible heat fluxes and prescribed horizontally uniform radiative heating Despite a considerable amount of convective available potential energy (CAPE) in the range of 1600–2400 J kg−1, and despite virtually no convective inhibition (CIN) in the mean sounding throughout the simulation, the cumulus convection starts as shallow, gradually developing into congestus, and becomes deep only toward the end of simulation. Analysis shows that the reason is that the shallow clouds generated by the boundary layer turbulence are too small to penetrate deep into the troposphere, as they are quickly diluted by mixing with the environment. Precipitation and the associated cold pools are needed to generate thermals big enough to support the growth of deep clouds. This positive feedback involving precipitation is supported by a sensitivity experiment in which the cold pools are effectively eliminated by artificially switching off the evaporation of precipitation; in the experiment, the convection remains shallow throughout the entire simulation, with a few congestus but no deep clouds. The probability distribution function (PDF) of cloud size during the shallow, congestus, and deep phases is analyzed using a new method. During each of the three phases, the shallow clouds dominate the mode of the PDFs at about 1-km diameter. During the deep phase, the PDFs show cloud bases as wide as 4 km. Analysis of the joint PDFs of cloud size and in-cloud variables demonstrates that, as expected, the bigger clouds are far less diluted above their bases than their smaller counterparts. Also, thermodynamic properties at cloud bases are found to be nearly identical for all cloud sizes, with the moist static energy exceeding the mean value by as much as 4 kJ kg−1. The width of the moist static energy distribution in the boundary layer is mostly due to variability of water vapor; therefore, clouds appear to grow from the air with the highest water vapor content available. No undiluted cloudy parcels are found near the level of neutral buoyancy. It appears that a simple entraining-plume model explains the entrainment rates rather well. The least diluted plumes in the simulation correspond to an entrainment parameter of about 0.1 km−1.


1983 ◽  
Vol 137 ◽  
pp. 331-345 ◽  
Author(s):  
Y. Nakamura ◽  
Y. Ohya

There are two main effects of turbulence on the mean flow past rods of square cross-section aligned with the approaching flow. Small-scale turbulence increases the growth rate of the shear layer, while large-scale turbulence enhances the roll-up of the shear layer. The consequences of these depend on the length of a square rod. The mean base pressure of a square rod varies considerably with turbulence intensity and scale as well as with its length.


2011 ◽  
Vol 68 (8) ◽  
pp. 1806-1820 ◽  
Author(s):  
Kristofer Döös ◽  
Johan Nilsson

Abstract The atmospheric meridional overturning circulation is computed using the interim European Centre for Medium-Range Weather Forecasts Re-Analysis (ERA-Interim) data. Meridional mass transport streamfunctions are calculated not only using pressure as a vertical coordinate but also using temperature, specific humidity, and geopotential height as generalized vertical coordinates. Moreover, mass transport streamfunctions are calculated using the latent, the dry static, or the moist static energy as generalized vertical coordinates. The total meridional energy transport can be obtained by integrating these streamfunctions “vertically” over their entire energy range. The time-averaged mass transport streamfunctions are also decomposed into mean-flow and eddy-induced components. The meridional mass transport streamfunctions with temperature and specific humidity as independent variables yield a two-cell structure with a tropical Hadley-like cell and a pronounced extratropical Ferrel-like cell, which carries warm and moist air poleward. These Ferrel-like cells are much stronger than the Eulerian zonal-mean Ferrel cell, a feature that can be understood by considering the residual circulation related to specific humidity or temperature. Regardless of the generalized vertical coordinate, the present meridional mass transport streamfunctions yield essentially a two-layer structure with one poleward and one equatorward branch. The strongest meridional overturning in the midlatitudes is obtained when the specific humidity or the moist static energy is used as the vertical coordinate, indicating that the specific humidity is the variable that best distinguishes between poleward- and equatorward-moving air in the lower troposphere.


2014 ◽  
Vol 755 ◽  
pp. 603-627 ◽  
Author(s):  
Yuji Hattori ◽  
Mohd Syafiq bin Marzuki

AbstractThe time evolution of localized disturbances in an elliptical flow confined in an elliptical cylinder is studied by direct numerical simulation (DNS). The base flow is subject to the elliptic instability. The unstable growth of localized disturbances predicted by the short-wavelength stability analysis is captured. The time evolution can be divided into four stages: linear, weakly nonlinear, nonlinear and turbulent. In the linear stage a single wavepacket grows exponentially without changing its shape. The exponential growth is accompanied by large oscillations which have time period half that of the fluid particles in the elliptical flow. An averaged wavepacket, which is a train of bending waves that has a finite spatial extent, also grows exponentially, while the oscillations of the growth rate are small. The averaged growth rate increases as the kinematic viscosity decreases; the inviscid limit is close to the value predicted by the short-wavelength stability analysis. In the weakly nonlinear stage the energy stops growing. The vortical structure of the initial disturbances is deformed into wavy patterns. The energy spectrum loses the peak at the initial wavenumber, developing a broad spectrum, and the flow goes into the next stage. In the nonlinear stage weak vorticity is scattered in the whole domain although strong vorticity is still localized. The probability density functions (p.d.f.) of a velocity component and its longitudinal derivative are similar to those of isotropic turbulence; however, the energy spectrum does not have an inertial range showing the Kolmogorov spectrum. Finally in the turbulent stage fine-scale structures appear in the vorticity field. The p.d.f. of the longitudinal derivative of velocity shows the strong intermittency known for isotropic turbulence. The energy spectrum attains an inertial range showing the Kolmogorov spectrum. The turbulence is not symmetric because of rotation and strain; the component of vorticity in the compressing direction is smaller than the other two components. The energy of the mean flow as well as the total energy decreases. The ratio of the lost energy to the initial energy of the mean flow is large in the core region.


2017 ◽  
Vol 826 ◽  
pp. 503-521 ◽  
Author(s):  
P. Meliga

The flow over an open cavity is an example of supercritical Hopf bifurcation leading to periodic limit-cycle oscillations. One of its distinctive features is the existence of strong higher harmonics, which results in the time-averaged mean flow being strongly linearly unstable. For this class of flows, a simplified formalism capable of unravelling how exactly the instability grows and saturates is lacking. This study builds on previous work by Mantič-Lugo et al. (Phys. Rev. Lett., vol. 113, 2014, 084501) to fill in the gap using a parametrized approximation of an instantaneous, phase-averaged mean flow, coupled in a quasi-static manner to multiple linear harmonic disturbances interacting nonlinearly with one another and feeding back on the mean flow via their Reynolds stresses. This provides a self-consistent modelling of the mean flow–fluctuation interaction, in the sense that all perturbation structures are those whose Reynolds stresses force the mean flow in such a way that the mean flow generates exactly the aforementioned perturbations. The first harmonic is sought as the superposition of two components, a linear component generated by the instability and aligned along the leading eigenmode of the mean flow, and a nonlinear orthogonal component generated by the higher harmonics, which progressively distorts the linear growth rate and eigenfrequency of the eigenmode. Saturation occurs when the growth rate of the first harmonic is zero, at which point the stabilizing effect of the second harmonic balances exactly the linear instability of the eigenmode. The model does not require any input from numerical or experimental data, and accurately predicts the transient development and the saturation of the instability, as established from comparison to time and phase averages of direct numerical simulation data.


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