scholarly journals On the Effect of Surface Friction and Upward Radiation of Energy on Equatorial Waves

2021 ◽  
Author(s):  
Kerry Emanuel
Keyword(s):  
Growth Rates ◽  
Numerical Solutions ◽  
Surface Friction ◽  
Wave Radiation ◽  
Quasi Equilibrium ◽  
Equatorial Waves ◽  
Kelvin Wave ◽  
Surface Drag ◽  
Model Framework ◽  
Barotropic Mode

Abstract In theoretical models of tropical dynamics, the effects of both surface friction and upward wave radiation through interaction with the stratosphere are oft-ignored, as they greatly complicate mathematical analysis. In this study, we relax the rigid-lid assumption and impose surface drag, which allows the barotropic mode to be excited in equatorial waves. In particular, a previously developed set of linear, strict quasi-equilibrium tropospheric equations is coupled with a dry, passive stratosphere, and surface drag is added to the troposphere momentum equations. Theoretical and numerical model analysis is performed on the model in the limits of an inviscid surface coupled to a stratosphere, as well as a frictional surface under a rigid-lid. This study confirms and extends previous research that shows the presence of a stratosphere strongly shifts the growth rates of fast propagating equatorial waves to larger scales, reddening the equatorial power spectrum. The growth rates of modes that are slowly propagating and highly interactive with cloud-radiation are shown to be negligibly affected by the presence of a stratosphere. Surface friction in this model framework acts as purely a damping mechanism and couples the baroclinic mode to the barotropic mode, increasing the poleward extent of the equatorial waves. Numerical solutions of the coupled troposphere-stratosphere model with surface friction show that the stratosphere stratification controls the extent of tropospheric trapping of the barotropic mode, and thus the poleward extent of the wave. The superposition of phase-shifted barotropic and first baroclinic modes is also shown to lead to an eastward vertical tilt in the dynamical fields of Kelvin-wave like modes.

scholarly journals Convectively Coupled Equatorial Waves. Part I: Horizontal and Vertical Structures

2007 ◽  
Vol 64 (10) ◽  
pp. 3406-3423 ◽  
Author(s):  
Gui-Ying Yang ◽  
Brian Hoskins ◽  
Julia Slingo
Keyword(s):  
Composite Structures ◽  
Wave Structure ◽  
Wave Theory ◽  
Western Hemisphere ◽  
Equatorial Waves ◽  
Kelvin Wave ◽  
Ambient Flow ◽  
Convectively Coupled Equatorial Waves ◽  
Eastern Hemisphere ◽  
Equatorial Wave

Abstract Multilevel 15-yr ECMWF Re-Analysis (ERA-15) and satellite-observed brightness temperature (Tb) data for the period May–October 1992 are used to examine the horizontal and vertical structures of convectively coupled equatorial waves. Dynamical waves are isolated using a methodology developed previously. Composite structures of convectively coupled equatorial waves are obtained using linear regression/correlation between convection (Tb) and dynamical structures. It is found that the relationship depends on the ambient flow and the nature of the convective coupling, and varies between off-equatorial- and equatorial-centered convection, different hemispheres, and seasons. The Kelvin wave structure in the Western Hemisphere is generally consistent with classic equatorial wave theory and has its convection located in the region of low-level convergence. In the Eastern Hemisphere the Kelvin wave tends to have convection in the region of enhanced lower-tropospheric westerlies and a tilted vertical structure. The Kelvin wave also tends to have a third peak in zonal wind amplitude at 500 hPa and exhibits upward propagation into the lower stratosphere. Lower-tropospheric westward-moving mixed Rossby–gravity (WMRG) and n = 1 Rossby (R1) wave structures and their relationship with convection are consistent with classic equatorial wave theory and the implied lower-tropospheric convergences. In the Eastern Hemisphere the WMRG and R1 waves have first baroclinic mode structures in the vertical. However, in the Western Hemisphere, the R1 wave has a barotropic structure. In the Eastern Hemisphere the R1 wave, like the Kelvin wave, tends to have equatorial convection in the region of enhanced lower-level westerlies, suggesting that enhanced surface energy fluxes associated with these waves may play an important organizing role for equatorial convection in this warm-water hemisphere. In the upper troposphere, eastward-moving Rossby–gravity (EMRG) and n = 1 gravity waves are found in the Eastern Hemisphere, and eastward-moving WMRG and R1 waves are found in the Western Hemisphere, suggestive of Doppler shifting of waves by the ambient flow.

scholarly journals Kelvin Wave-CISK Controlled by Surface Friction

1997 ◽  
Vol 75 (2) ◽  
pp. 497-511 ◽  
Author(s):  
Kazuyoshi Ohuchi ◽  
Masanori Yamasaki
Keyword(s):  
Surface Friction ◽  
Kelvin Wave

scholarly journals Response of the West African Monsoon to the Madden–Julian Oscillation

2009 ◽  
Vol 22 (15) ◽  
pp. 4097-4116 ◽  
Author(s):  
Sally L. Lavender ◽  
Adrian J. Matthews
Keyword(s):  
West Africa ◽  
Monsoon Season ◽  
West African Monsoon ◽  
Circulation Model ◽  
Negative Temperature ◽  
Equatorial Waves ◽  
Madden Julian Oscillation ◽  
Global Circulation Model ◽  
Kelvin Wave ◽  
Sst Anomalies

Abstract Observations show that rainfall over West Africa is influenced by the Madden–Julian oscillation (MJO). A number of mechanisms have been suggested: 1) forcing by equatorial waves; 2) enhanced monsoon moisture supply; and 3) increased African easterly wave (AEW) activity. However, previous observational studies are not able to unambiguously distinguish between cause and effect. Carefully designed model experiments are used to assess these mechanisms. Intraseasonal convective anomalies over West Africa during the summer monsoon season are simulated in an atmosphere-only global circulation model as a response to imposed sea surface temperature (SST) anomalies associated with the MJO over the equatorial warm pool region. 1) Negative SST anomalies stabilize the atmosphere leading to locally reduced convection. The reduced convection leads to negative midtropospheric latent heating anomalies that force dry equatorial waves. These waves propagate eastward (Kelvin wave) and westward (Rossby wave), reaching Africa approximately 10 days later. The associated negative temperature anomalies act to destabilize the atmosphere, resulting in enhanced monsoon convection over West and central Africa. The Rossby waves are found to be the most important component, with associated westward-propagating convective anomalies over West Africa. The eastward-propagating equatorial Kelvin wave also efficiently triggers convection over the eastern Pacific and Central America, consistent with observations. 2) An increase in boundary layer moisture is found to occur as a result of the forced convective anomalies over West Africa rather than a cause. 3) Increased shear on the African easterly jet, leading to increased AEW activity, is also found to occur as a result of the forced convective anomalies in the model.

Uncertainties of Estimates of Inertia–Gravity Energy in the Atmosphere. Part II: Large-Scale Equatorial Waves

2009 ◽  
Vol 137 (11) ◽  
pp. 3858-3873 ◽  
Author(s):  
N. Žagar ◽  
J. Tribbia ◽  
J. L. Anderson ◽  
K. Raeder
Keyword(s):  
Large Scale ◽  
Normal Modes ◽  
Lower Troposphere ◽  
Physical Space ◽  
Significant Degree ◽  
Hadley Cell ◽  
Equatorial Waves ◽  
Kelvin Wave ◽  
Energy Propagation ◽  
Zonal Wavenumber

Abstract This paper analyzes the spectra and spatiotemporal features of the large-scale inertia-gravity (IG) circulations in four analysis systems in the tropics. Of special interest is the Kelvin wave (KW), which represents between 7% and 25% of the total IG wave (zonal wavenumber k ≠ 0) energy. The mixed Rossby–gravity (MRG) mode comprises between 4% and 15% of the IG wave energy. At the longest scales, the KW spectra are fitted by a law while the MRG energy spectrum appears flat. At shorter scales both modes follow a −3 law. Energy spectra of the total IG wave motion at long zonal scales (zonal wavenumber smaller than 7) have slopes close to −1. The average circulation associated with KW is characterized by reverse flows in the upper and lower troposphere consistent with the ideas behind simple tropical models. The inverse projection is used to quantify the role of Kelvin and MRG waves in current analysis systems in the upper troposphere over the Indian Ocean. At these levels, easterlies between 10°S and 30°N are represented by the KW to a significant degree while the cross-equatorial flow toward the descending branch of the Hadley cell at 10°S is associated with the MRG waves. The transient structure of equatorial waves is presented in the space of normal modes defined by the zonal wavenumbers, meridional Hough functions, and the vertical eigenfunctions. The difference in the depth of the model domain in DART–CAM and NCEP–NCAR on one hand and ECMWF and NCEP on the other appears to be one reason for different wave propagation properties. In the latter case the vertical energy propagation is diagnosed by filtering the propagating KW modes back to physical space. The results agree with the linear theory of vertically propagating equatorial waves.

scholarly journals Dynamical properties of vortical structures on the beta-plane

1994 ◽  
Vol 268 ◽  
pp. 103-131 ◽  
Author(s):  
G. G. Sutyrin ◽  
J. S. Hesthaven ◽  
J. P. Lynov ◽  
J. Juul Rasmussen
Keyword(s):  
Rossby Wave ◽  
Potential Vorticity ◽  
Fluid Transport ◽  
Numerical Solutions ◽  
Critical Value ◽  
Wave Radiation ◽  
Approximate Theory ◽  
Initial Direction ◽  
Vortical Structures ◽  
Long Time

The long-time evolution of monopolar and dipolar vortices influenced by the largescale gradient of the ambient potential vorticity (the β-effect) is studied by direct numerical solutions of the equivalent barotropic quasi-geostrophic equation. Translation and reorganization of vortical structures are shown to depend strongly on their intensity. Transport of trapped fluid by vortical structures is illustrated by calculating particle trajectories and by considering closed isolines of potential vorticity and the streamfunction in a co-moving reference frame.The initial behaviour of strong monopoles is found to be well described by a recent approximate theory for the evolution of azimuthal mode one, even for times longer than the linear Rossby wave period. In the long-time limit, strong monopoles transport particles mainly westward, although the meridional displacement is several times larger than the initial vortex size. The appearance of an annulus with opposite radial gradient of the potential vorticity around the vortex core is demonstrated. This annulus forms owing to the meridional vortex drift on the β-plane and results in reorganization of a strong monopolar vortex into a rotating tripole. A critical value of the vortex intensity is found, below which the tripolar structure does not appear even in the case of an initially shielded vortex. Weak monopolar vortices are able to trap particles and provide some west-meridional fluid transport, even in the case when they decay like a linear Rossby wave packet.The evolution of initial f-plane dipoles on the β-plane is strongly dependent on the initial direction of propagation. Strong dipoles adjust to steadily propagating modon solutions either accelerating (westward case), decelerating (eastward case) or oscillating with a decaying amplitude (meridional case), thereby carrying trapped particles predominantly eastward. A steady state is not reached if the dipole intensity is below a critical value which depends on the initial direction of propagation. Weak dipoles either decay and shrink owing to Rossby wave radiation (westward case), gradually separate and split (eastward case), or disintegrate (meridional case) without longdistance fluid transport. Thus, on the β-plane monopoles provide mainly westward transport of trapped fluid, whereas dipoles provide mainly eastward transport. Only strong monopoles are found to provide significant meridional fluid transport.

scholarly journals The Spontaneous Imbalance of an Atmospheric Vortex at High Rossby Number

2008 ◽  
Vol 65 (8) ◽  
pp. 2498-2521 ◽  
Author(s):  
David A. Schecter
Keyword(s):  
Rossby Wave ◽  
Potential Vorticity ◽  
Formal Theory ◽  
Resonant Absorption ◽  
Critical Layer ◽  
Wave Radiation ◽  
Rossby Number ◽  
Mean Flow ◽  
Surface Drag ◽  
Isentropic Coordinates

Abstract This paper discusses recent progress toward understanding the instability of a monotonic vortex at high Rossby number, due to the radiation of spiral inertia–gravity (IG) waves. The outward-propagating IG waves are excited by inner undulations of potential vorticity that consist of one or more vortex Rossby waves. An individual vortex Rossby wave and its IG wave emission have angular pseudomomenta of opposite sign, positive and negative, respectively. The Rossby wave therefore grows in response to producing radiation. Such growth is potentially suppressed by the resonant absorption of angular pseudomomentum in a critical layer, where the angular phase velocity of the Rossby wave matches the angular velocity of the mean flow. Suppression requires a sufficiently steep radial gradient of potential vorticity in the critical layer. Both linear and nonlinear steepness requirements are reviewed. The formal theory of radiation-driven instability, or “spontaneous imbalance,” is generalized in isentropic coordinates to baroclinic vortices that possess active critical layers. Furthermore, the rate of angular momentum loss by IG wave radiation is reexamined in the hurricane parameter regime. Numerical results suggest that the negative radiation torque on a hurricane has a smaller impact than surface drag, despite recent estimates of its large magnitude.

scholarly journals Constraining uncertainties in particle-wall deposition correction during SOA formation in chamber experiments

2017 ◽  
Vol 17 (3) ◽  
pp. 2297-2310 ◽  
Author(s):  
Theodora Nah ◽  
Renee C. McVay ◽  
Jeffrey R. Pierce ◽  
John H. Seinfeld ◽  
Nga L. Ng
Keyword(s):  
Surface Area ◽  
Loss Rate ◽  
High Surface ◽  
High Surface Area ◽  
Correction Method ◽  
Quasi Equilibrium ◽  
Model Framework ◽  
Wall Deposition ◽  
Wall Loss ◽  
Seed Aerosol

Abstract. The effect of vapor-wall deposition on secondary organic aerosol (SOA) formation has gained significant attention; however, uncertainties in experimentally derived SOA mass yields due to uncertainties in particle-wall deposition remain. Different approaches have been used to correct for particle-wall deposition in SOA formation studies, each having its own set of assumptions in determining the particle-wall loss rate. In volatile and intermediate-volatility organic compound (VOC and IVOC) systems in which SOA formation is governed by kinetically limited growth, the effect of vapor-wall deposition on SOA mass yields can be constrained by using high surface area concentrations of seed aerosol to promote the condensation of SOA-forming vapors onto seed aerosol instead of the chamber walls. However, under such high seed aerosol levels, the presence of significant coagulation may complicate the particle-wall deposition correction. Here, we present a model framework that accounts for coagulation in chamber studies in which high seed aerosol surface area concentrations are used. For the α-pinene ozonolysis system, we find that after accounting for coagulation, SOA mass yields remain approximately constant when high seed aerosol surface area concentrations ( ≥  8000 µm2 cm−3) are used, consistent with our prior study (Nah et al., 2016) showing that α-pinene ozonolysis SOA formation is governed by quasi-equilibrium growth. In addition, we systematically assess the uncertainties in the calculated SOA mass concentrations and yields between four different particle-wall loss correction methods over the series of α-pinene ozonolysis experiments. At low seed aerosol surface area concentrations (< 3000 µm2 cm−3), the SOA mass yields at peak SOA growth obtained from the particle-wall loss correction methods agree within 14 %. However, at high seed aerosol surface area concentrations ( ≥  8000 µm2 cm−3), the SOA mass yields at peak SOA growth obtained from different particle-wall loss correction methods can differ by as much as 58 %. These differences arise from assumptions made in the particle-wall loss correction regarding the first-order particle-wall loss rate. This study highlights the importance of accounting for particle-wall deposition accurately during SOA formation chamber experiments and assessing the uncertainties associated with the application of the particle-wall deposition correction method when comparing and using SOA mass yields measured in different studies.

scholarly journals Correlation between Animal and Mathematical Models for Prostate Cancer Progression

2009 ◽  
Vol 10 (4) ◽  
pp. 241-252 ◽  
Author(s):  
Z. Jackiewicz ◽  
C. L. Jorcyk ◽  
M. Kolev ◽  
B. Zubik-Kowal
Keyword(s):  
Mathematical Model ◽  
Cancer Progression ◽  
Growth Rates ◽  
Numerical Solutions ◽  
Initial Conditions ◽  
Tumour Progression ◽  
Prostate Cancer Progression ◽  
The Mathematical Model

This work demonstrates that prostate tumour progressionin vivocan be analysed by using solutions of a mathematical model supplemented by initial conditions chosen according to growth rates of cell linesin vitro. The mathematical model is investigated and solved numerically. Its numerical solutions are compared with experimental data from animal models. The numerical results confirm the experimental results with the growth ratesin vivo.

scholarly journals Enhanced Persistence of Equatorial Waves via Convergence Coupling in the Stochastic Multicloud Model

2015 ◽  
Vol 72 (12) ◽  
pp. 4701-4720 ◽  
Author(s):  
Noah D. Brenowitz ◽  
Yevgeniy Frenkel ◽  
Andrew J. Majda
Keyword(s):  
Large Scale ◽  
Heat Fluxes ◽  
Sea Surface ◽  
Theoretical Studies ◽  
Equatorial Waves ◽  
Moist Convection ◽  
Kelvin Wave ◽  
Surface Heat Fluxes ◽  
Walker Cell ◽  
Conditional Instability

Abstract Recent observational and theoretical studies show a systematic relationship between tropical moist convection and measures related to large-scale convergence. It has been suggested that cloud fields in the column stochastic multicloud model compare better with observations when using predictors related to convergence rather than moist energetics (e.g., CAPE) as per Peters et al. Here, this work is extended to a fully prognostic multicloud model. A nonlocal convergence-coupled formulation of the stochastic multicloud model is implemented without wind-dependent surface heat fluxes. In a series of idealized Walker cell simulations, this convergence coupling enhances the persistence of Kelvin wave analogs in dry regions of the domain while leaving the dynamics in moist regions largely unaltered. This effect is robust for changes in the amplitude of the imposed sea surface temperature (SST) gradient. In essence, this method provides a soft convergence coupling that allows for increased interaction between cumulus convection and the large-scale circulation but does not suffer from the deleterious wave–conditional instability of the second kind (CISK) behavior of the Kuo-type moisture-convergence closures.

Convectively Coupled Waves Propagating along an Equatorial ITCZ

2009 ◽  
Vol 66 (8) ◽  
pp. 2237-2255 ◽  
Author(s):  
Juliana Dias ◽  
Olivier Pauluis
Keyword(s):  
Gravity Wave ◽  
Large Scale ◽  
Water System ◽  
Propagation Speed ◽  
Advection Equation ◽  
Quasi Equilibrium ◽  
Kelvin Wave ◽  
Precipitation Band ◽  
Shallow Water System ◽  
Large Scale Atmospheric Circulation

Abstract The dynamics of convectively coupled gravity waves traveling over a precipitating region are analyzed in an idealized model for the large-scale atmospheric circulation. The model is composed of a shallow water system coupled to an advection equation for moisture through the convection term, utilizing a quasi-equilibrium relaxation to moisture closure. Here the authors investigate the model in the strict quasi-equilibrium (SQE) of infinitely short relaxation time. This framework is applied to study the behavior of a disturbance propagating along a narrow precipitation band, similar to the intertropical convergence zone (ITCZ). For an ITCZ width on the order of the equatorial Rossby radius, Kelvin waves propagate at the moist gravity wave speed (about 15 m s−1), whereas for a narrow ITCZ, the propagation speed is comparable to the dry gravity wave (about 50 m s−1). It is also shown that a Kelvin wave propagating along a narrow precipitation region exhibits a meridional circulation that modulates the precipitation rate and affects the propagation speed of the wave.

Sign in / Sign up

Export Citation Format

Share Document