scholarly journals Rossby wave energy: a local Eulerian isotropic invariant

2021 ◽  
Vol 913 ◽  
Author(s):  
R.C. Kloosterziel ◽  
L.R.M. Maas
Keyword(s):  
Rossby Wave ◽  
Wave Energy

Abstract

scholarly journals Tropical Cyclogenesis in the Western North Pacific as Revealed by the 2008–09 YOTC Data*

2013 ◽  
Vol 28 (4) ◽  
pp. 1038-1056 ◽  
Author(s):  
Yamei Xu ◽  
Tim Li ◽  
Melinda Peng
Keyword(s):  
Rossby Wave ◽  
Wave Energy ◽  
North Pacific ◽  
Western North Pacific ◽  
Large Scale ◽  
Lower Troposphere ◽  
Energy Dispersion ◽  
Reanalysis Dataset ◽  
Initial Development ◽  
Wave Trains

Abstract The Year of Tropical Convection (YOTC) high-resolution global reanalysis dataset was analyzed to reveal precursor synoptic-scale disturbances related to tropical cyclone (TC) genesis in the western North Pacific (WNP) during the 2008–09 typhoon seasons. A time filtering is applied to the data to isolate synoptic (3–10 day), quasi-biweekly (10–20 day), and intraseasonal (20–90 day) time-scale components. The results show that four types of precursor synoptic disturbances associated with TC genesis can be identified in the YOTC data. They are 1) Rossby wave trains associated with preexisting TC energy dispersion (TCED) (24%), 2) synoptic wave trains (SWTs) unrelated to TCED (32%), 3) easterly waves (EWs) (16%), and 4) a combination of either TCED-EW or SWT-EW (24%). The percentage of identifiable genesis events is higher than has been found in previous analyses. Most of the genesis events occurred when atmospheric quasi-biweekly and intraseasonal oscillations are in an active phase, suggesting a large-scale control of low-frequency oscillations on TC formation in the WNP. For genesis events associated with SWT and EW, maximum vorticity was confined in the lower troposphere. During the formation of Jangmi (2008), maximum Rossby wave energy dispersion appeared in the middle troposphere. This differs from other TCED cases in which energy dispersion is strongest at low level. As a result, the midlevel vortex from Rossby wave energy dispersion grew faster during the initial development stage of Jangmi.

scholarly journals Another Note on Rossby Wave Energy Flux

2020 ◽  
Vol 50 (2) ◽  
pp. 531-534
Author(s):  
Theodore S. Durland ◽  
J. Thomas Farrar
Keyword(s):  
Group Velocity ◽  
Energy Flux ◽  
Rossby Wave ◽  
Wave Energy ◽  
Energy Equation ◽  
Divergent Part ◽  
Pressure Work ◽  
Wave Energy Flux ◽  
The Difference ◽  
Definition Of

AbstractLonguet-Higgins in 1964 first pointed out that the Rossby wave energy flux as defined by the pressure work is not the same as that defined by the group velocity. The two definitions provide answers that differ by a nondivergent vector. Longuet-Higgins suggested that the problem arose from ambiguity in the definition of energy flux, which only impacts the energy equation through its divergence. Numerous authors have addressed this issue from various perspectives, and we offer one more approach that we feel is more succinct than previous ones, both mathematically and conceptually. We follow the work described by Cai and Huang in 2013 in concluding that there is no need to invoke the ambiguity offered by Longuet-Higgins. By working directly from the shallow-water equations (as opposed to the more involved quasigeostrophic treatment of Cai and Huang), we provide a concise derivation of the nondivergent pressure work and demonstrate that the two energy flux definitions are equivalent when only the divergent part of the pressure work is considered. The difference vector comes from the nondivergent part of the geostrophic pressure work, and the familiar westward component of the Rossby wave group velocity comes from the divergent part of the geostrophic pressure work. In a broadband wave field, the expression for energy flux in terms of a single group velocity is no longer meaningful, but the expression for energy flux in terms of the divergent pressure work is still valid.

scholarly journals Tropical Cyclogenesis Associated with Rossby Wave Energy Dispersion of a Preexisting Typhoon. Part I: Satellite Data Analyses*

2006 ◽  
Vol 63 (5) ◽  
pp. 1377-1389 ◽  
Author(s):  
Tim Li ◽  
Bing Fu
Keyword(s):  
Rossby Wave ◽  
Satellite Data ◽  
Wave Energy ◽  
Large Scale ◽  
Wave Train ◽  
Vertical Shear ◽  
Energy Dispersion ◽  
Data Analyses ◽  
Wave Trains ◽  
Rossby Wave Train

Abstract The structure and evolution characteristics of Rossby wave trains induced by tropical cyclone (TC) energy dispersion are revealed based on the Quick Scatterometer (QuikSCAT) and Tropical Rainfall Measuring Mission (TRMM) Microwave Imager (TMI) data. Among 34 cyclogenesis cases analyzed in the western North Pacific during 2000–01 typhoon seasons, six cases are associated with the Rossby wave energy dispersion of a preexisting TC. The wave trains are oriented in a northwest–southeast direction, with alternating cyclonic and anticyclonic vorticity circulation. A typical wavelength of the wave train is about 2500 km. The TC genesis is observed in the cyclonic circulation region of the wave train, possibly through a scale contraction process. The satellite data analyses reveal that not all TCs have a Rossby wave train in their wakes. The occurrence of the Rossby wave train depends to a certain extent on the TC intensity and the background flow. Whether or not a Rossby wave train can finally lead to cyclogenesis depends on large-scale dynamic and thermodynamic conditions related to both the change of the seasonal mean state and the phase of the tropical intraseasonal oscillation. Stronger low-level convergence and cyclonic vorticity, weaker vertical shear, and greater midtropospheric moisture are among the favorable large-scale conditions. The rebuilding process of a conditional unstable stratification is important in regulating the frequency of TC genesis.

A closure for eddy-mean flow effects based on the Rossby wave energy equation

2017 ◽  
Vol 114 ◽  
pp. 59-71 ◽  
Author(s):  
Carsten Eden ◽  
Dirk Olbers
Keyword(s):  
Rossby Wave ◽  
Wave Energy ◽  
Energy Equation ◽  
Mean Flow ◽  
Flow Effects

Cyclogenesis Simulation of Typhoon Prapiroon (2000) Associated with Rossby Wave Energy Dispersion*

2010 ◽  
Vol 138 (1) ◽  
pp. 42-54 ◽  
Author(s):  
Xuyang Ge ◽  
Tim Li ◽  
Melinda S. Peng
Keyword(s):  
Rossby Wave ◽  
Wave Energy ◽  
Large Scale ◽  
Wave Train ◽  
Energy Dispersion ◽  
Sensitivity Experiment ◽  
Low Level ◽  
Filtering Technique ◽  
Upper Level

Abstract The genesis of Typhoon Prapiroon (2000), in the western North Pacific, is simulated to understand the role of Rossby wave energy dispersion of a preexisting tropical cyclone (TC) in the subsequent genesis event. Two experiments are conducted. In the control experiment (CTL), the authors retain both the previous typhoon, Typhoon Bilis, and its wave train in the initial condition. In the sensitivity experiment (EXP), the circulation of Typhoon Bilis was removed based on a spatial filtering technique of Kurihara et al., while the wave train in the wake is kept. The comparison between these two numerical simulations demonstrates that the preexisting TC impacts the subsequent TC genesis through both a direct and an indirect process. The direct process is through the conventional barotropic Rossby wave energy dispersion, which enhances the low-level wave train, the boundary layer convergence, and the convection–circulation feedback. The indirect process is through the upper-level outflow jet. The asymmetric outflow jet induces a secondary circulation with a strong divergence tendency to the left-exit side of the outflow jet. The upper-level divergence boosts large-scale ascending motion and promotes favorable environmental conditions for a TC-scale vortex development. In addition, the outflow jet induces a well-organized cyclonic eddy angular momentum flux, which acts as a momentum forcing that enhances the upper-level outflow and low-level inflow and favors the growth of the new TC.

scholarly journals Mixed Rossby–Gravity Wave–Wave Interactions

2019 ◽  
Vol 49 (1) ◽  
pp. 291-308 ◽  
Author(s):  
Carsten Eden ◽  
Manita Chouksey ◽  
Dirk Olbers
Keyword(s):  
Kinetic Equation ◽  
Wave Field ◽  
Gravity Wave ◽  
Rossby Wave ◽  
Wave Energy ◽  
Wave Mode ◽  
Linear Wave ◽  
Wave Interactions ◽  
First Case ◽  
Linear Gravity

AbstractMixed triad wave–wave interactions between Rossby and gravity waves are analytically derived using the kinetic equation for models of different complexity. Two examples are considered: initially vanishing linear gravity wave energy in the presence of a fully developed Rossby wave field and the reversed case of initially vanishing linear Rossby wave energy in the presence of a realistic gravity wave field. The kinetic equation in both cases is numerically evaluated, for which energy is conserved within numerical precision. The results are validated by a corresponding ensemble of numerical model simulations supporting the validity of the weak-interaction assumption necessary to derive the kinetic equation. Since they are generated by nonresonant interactions only, the energy transfers toward the respective linear wave mode with vanishing energy are small in both cases. The total generation of energy of the linear gravity wave mode in the first case scales to leading order as the square of the Rossby number in agreement with independent estimates from laboratory experiments, although a part of the linear gravity wave mode is slaved to the Rossby wave mode without wavelike temporal behavior.

Wave Energy Associated with the Variability of the Stratospheric Polar Vortex

2007 ◽  
Vol 64 (7) ◽  
pp. 2683-2694 ◽  
Author(s):  
M. L. R. Liberato ◽  
J. M. Castanheira ◽  
L. de la Torre ◽  
C. C. DaCamara ◽  
L. Gimeno
Keyword(s):  
Rossby Wave ◽  
Wave Energy ◽  
General Circulation ◽  
Polar Vortex ◽  
Stratospheric Polar Vortex ◽  
Vortex Strength ◽  
Wave Forcing ◽  
Zonal Wavenumber ◽  
Baroclinic Modes ◽  
The Waves

Abstract A study is performed on the energetics of planetary wave forcing associated with the variability of the northern winter polar vortex. The analysis relies on a three-dimensional normal mode expansion of the atmospheric general circulation that allows partitioning the total (i.e., kinetic + available potential) atmospheric energy into the energy associated with Rossby and inertio-gravity modes with barotropic and baroclinic vertical structures. The analysis mainly departs from traditional ones in respect to the wave forcing, which is here assessed in terms of total energy amounts associated with the waves instead of heat and momentum fluxes. Such an approach provides a sounder framework than traditional ones based on Eliassen–Palm (EP) flux diagnostics of wave propagation and related concepts of refractive indices and critical lines, which are strictly valid only in the cases of small-amplitude waves and in the context of the Wentzel–Kramers–Brillouin–Jeffries (WKBJ) approximation. Positive (negative) anomalies of the energy associated with the first two baroclinic modes of the planetary Rossby wave with zonal wavenumber 1 are followed by a downward progression of negative (positive) anomalies of the vortex strength. A signature of the vortex vacillation is also well apparent in the lagged correlation curves between the wave energy and the vortex strength. The analysis of the correlations between individual Rossby modes and the vortex strength further confirmed the result from linear theory that the waves that force the vortex are those associated with the largest zonal and meridional scales. The two composite analyses of displacement- and split-type stratospheric sudden warming (SSW) events have revealed different dynamics. Displacement-type SSWs are forced by positive anomalies of the energy associated with the first two baroclinic modes of planetary Rossby waves with zonal wavenumber 1; split-type SSWs are in turn forced by positive anomalies of the energy associated with the planetary Rossby wave with zonal wavenumber 2, and the barotropic mode appears as the most important component. In respect to stratospheric final warming (SFW) events, obtained results suggest that the wave dynamics is similar to the one in displacement-type SSW events.

Rossby wave energy dispersion from tropical cyclone in zonal basic flows

2016 ◽  
Vol 121 (7) ◽  
pp. 3120-3138 ◽  
Author(s):  
Wenli Shi ◽  
Jianfang Fei ◽  
Xiaogang Huang ◽  
Yudi Liu ◽  
Zhanhong Ma ◽  
...  
Keyword(s):  
Tropical Cyclone ◽  
Rossby Wave ◽  
Wave Energy ◽  
Energy Dispersion

Tropical Cyclone Energy Dispersion in a Three-Dimensional Primitive Equation Model: Upper-Tropospheric Influence*

2008 ◽  
Vol 65 (7) ◽  
pp. 2272-2289 ◽  
Author(s):  
Xuyang Ge ◽  
Tim Li ◽  
Yuqing Wang ◽  
Melinda S. Peng
Keyword(s):  
Tropical Cyclone ◽  
Rossby Wave ◽  
Wave Energy ◽  
Wave Train ◽  
Three Dimensional ◽  
Equation Model ◽  
Energy Dispersion ◽  
Primitive Equation ◽  
Primitive Equation Model ◽  
Rossby Wave Train

Abstract The three-dimensional (3D) Rossby wave energy dispersion of a tropical cyclone (TC) is studied using a baroclinic primitive equation model. The model is initialized with a symmetric vortex on a beta plane in an environment at rest. The vortex intensifies while becoming asymmetric and moving northwestward because of the beta effect. A synoptic-scale wave train forms in its wake a few days later. The energy-dispersion-induced Rossby wave train has a noticeable baroclinic structure with alternating cyclonic–anticyclonic–cyclonic (anticyclonic–cyclonic–anticyclonic) circulations in the lower (upper) troposphere. A key feature associated with the 3D wave train development is a downward propagation of the relative vorticity and kinetic energy. Because of the vertical differential inertial stability, the upper-level wave train develops faster than the lower-level counterpart. The upper anticyclonic circulation rapidly induces an intense asymmetric outflow jet in the southeast quadrant, and then further influences the lower-level Rossby wave train. On one hand, the outflow jet exerts an indirect effect on the lower-level wave train strength through changing TC intensity and structure. On the other hand, it triggers downward energy propagation that further enhances the lower-level Rossby wave train. A sudden removal of the diabatic heating may initially accelerate the energy dispersion through the increase of the radius of maximum wind and the reduction of the lower-level inflow. The latter may modulate the group velocity of the Rossby wave train through the Doppler shift effect. The 3D numerical results illustrate more complicated Rossby wave energy dispersion characteristics than 2D barotropic dynamics.

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