scholarly journals Formulation of Three-Dimensional Quasi-Residual Mean Flow Balanced with Diabatic Heating Rate and Potential Vorticity Flux

2019 ◽  
Vol 76 (3) ◽  
pp. 851-863
Author(s):  
Takenari Kinoshita ◽  
Kaoru Sato ◽  
Kentaro Ishijima ◽  
Masayuki Takigawa ◽  
Yousuke Yamashita
Keyword(s):  
Potential Vorticity ◽  
Diabatic Heating ◽  
Three Dimensional ◽  
Wave Activity ◽  
Stationary Waves ◽  
Vertical Flow ◽  
Mean Flow ◽  
Material Transport ◽  
Mean State ◽  
Wave Activity Flux

Abstract Three-dimensional (3D) quasi-residual mean flow is derived to diagnose 3D dynamical material transport associated with stationary planetary waves. The 3D quasi-residual mean vertical flow does not include the vertical flow due to tilting of the potential temperature caused by stationary waves, which is apparent but not seen in the mass-weighted isentropic mean state. Thus, the quasi-residual mean vertical flow is balanced with the term of diabatic heating rate. The 3D quasi-residual mean horizontal flow is balanced with the sum of the forcing due to transient wave activity flux divergence and the forcing associated with fluctuation of the potential vorticity due to stationary waves (defined as the effective Coriolis forcing). The zonal mean of the effective Coriolis forcing corresponds to the divergence of stationary wave activity flux. Thus, the zonal mean of derived 3D quasi-residual mean flow is exactly equal to the traditional residual mean flow. To demonstrate the usefulness of this quasi-residual mean flow, we analyze material transport of atmospheric sulfur hexafluoride (SF6) by using an atmospheric chemistry transport model. Comparison between the derived 3D quasi-residual mean flow and traditional residual mean flow shows that the zonal mean of advection of SF6 associated with the 3D quasi-residual mean flow derived is almost equal to that of the traditional residual mean flow. Next, it is confirmed that the horizontal structure of advection of SF6 associated with the 3D quasi-residual mean flow is balanced with the transport because of the nonlinear, nonconservative effects of disturbances. This relation is similar to the results for traditional residual mean flow in the zonal-mean state.

scholarly journals A Formulation of Unified Three-Dimensional Wave Activity Flux of Inertia–Gravity Waves and Rossby Waves

2013 ◽  
Vol 70 (6) ◽  
pp. 1603-1615 ◽  
Author(s):  
Takenari Kinoshita ◽  
Kaoru Sato
Keyword(s):  
Wave Propagation ◽  
Gravity Waves ◽  
Rossby Waves ◽  
Three Dimensional ◽  
Wave Activity ◽  
Storm Tracks ◽  
Mean Flow ◽  
Wave Activity Flux ◽  
Inertia Gravity Waves ◽  
Dimensional Wave

Abstract A companion paper formulates the three-dimensional wave activity flux (3D-flux-M) whose divergence corresponds to the wave forcing on the primitive equations. However, unlike the two-dimensional wave activity flux, 3D-flux-M does not accurately describe the magnitude and direction of wave propagation. In this study, the authors formulate a modification of 3D-flux-M (3D-flux-W) to describe this propagation using small-amplitude theory for a slowly varying time-mean flow. A unified dispersion relation for inertia–gravity waves and Rossby waves is also derived and used to relate 3D-flux-W to the group velocity. It is shown that 3D-flux-W and the modified wave activity density agree with those for inertia–gravity waves under the constant Coriolis parameter assumption and those for Rossby waves under the small Rossby number assumption. To compare 3D-flux-M with 3D-flux-W, an analysis of the European Centre for Medium-Range Weather Forecasts (ECMWF) Interim Re-Analysis (ERA-Interim) data is performed focusing on wave disturbances in the storm tracks during April. While the divergence of 3D-flux-M is in good agreement with the meridional component of the 3D residual mean flow associated with disturbances, the 3D-flux-W divergence shows slight differences in the upstream and downstream regions of the storm tracks. Further, the 3D-flux-W magnitude and direction are in good agreement with those derived by R. A. Plumb, who describes Rossby wave propagation. However, 3D-flux-M is different from Plumb’s flux in the vicinity of the storm tracks. These results suggest that different fluxes (both 3D-flux-W and 3D-flux-M) are needed to describe wave propagation and wave–mean flow interaction in the 3D formulation.

A Formulation of Three-Dimensional Residual Mean Flow and Wave Activity Flux Applicable to Equatorial Waves

2014 ◽  
Vol 71 (9) ◽  
pp. 3427-3438 ◽  
Author(s):  
Takenari Kinoshita ◽  
Kaoru Sato
Keyword(s):  
Large Scale ◽  
3D Structure ◽  
Three Dimensional ◽  
Wave Activity ◽  
Stokes Drift ◽  
Equatorial Waves ◽  
Mean Flow ◽  
Wave Forcing ◽  
Meridional Cross Section ◽  
Wave Activity Flux

Abstract The large-scale waves that are known to be trapped around the equator are called equatorial waves. The equatorial waves cause mean zonal wind acceleration related to quasi-biennial and semiannual oscillations. The interaction between equatorial waves and the mean wind has been studied by using the transformed Eulerian mean (TEM) equations in the meridional cross section. However, to examine the three-dimensional (3D) structure of the interaction, the 3D residual mean flow and wave activity flux for the equatorial waves are needed. The 3D residual mean flow is expressed as the sum of the Eulerian mean flow and Stokes drift. The present study derives a formula that is approximately equal to the 3D Stokes drift for equatorial waves on the equatorial beta plane (EQSD). The 3D wave activity flux for equatorial waves whose divergence corresponds to the wave forcing is also derived using the EQSD. It is shown that the meridionally integrated 3D wave activity flux for equatorial waves is proportional to the group velocity of equatorial waves.

scholarly journals The Emergence of Shallow Easterly Jets within QBO Westerlies

2018 ◽  
Vol 75 (1) ◽  
pp. 21-40 ◽  
Author(s):  
Peter Hitchcock ◽  
Peter H. Haynes ◽  
William J. Randel ◽  
Thomas Birner
Keyword(s):  
Potential Vorticity ◽  
General Circulation ◽  
Circulation Model ◽  
Shear Zones ◽  
Wave Activity ◽  
Mean Flow ◽  
Quasi Biennial Oscillation ◽  
Westerly Jet ◽  
Eddy Fluxes ◽  
Biennial Oscillation

A configuration of an idealized general circulation model has been obtained in which a deep, stratospheric, equatorial, westerly jet is established that is spontaneously and quasi-periodically disrupted by shallow easterly jets. Similar to the disruption of the quasi-biennial oscillation (QBO) observed in early 2016, meridional fluxes of wave activity are found to play a central role. The possible relevance of two feedback mechanisms to these disruptions is considered. The first involves the secondary circulation produced in the shear zones on the upper and lower flanks of the easterly jet. This is found to play a role in maintaining the aspect ratio of the emerging easterly jet. The second involves the organization of the eddy fluxes by the mean flow: the presence of a weak easterly anomaly within a tall, tropical, westerly jet is demonstrated to produce enhanced and highly focused wave activity fluxes that reinforce and strengthen the easterly anomalies. The eddies appear to be organized by the formation of strong potential vorticity gradients on the subtropical flanks of the easterly anomaly. Similar wave activity and potential vorticity structures are found in the ERA-Interim for the observed QBO disruption, indicating this second feedback was active then.

scholarly journals Why Are Stratospheric Sudden Warmings Sudden (and Intermittent)?

2020 ◽  
Vol 77 (3) ◽  
pp. 943-964 ◽  
Author(s):  
Noboru Nakamura ◽  
Jonathan Falk ◽  
Sandro W. Lubis
Keyword(s):  
Zonal Wind ◽  
Vortex Breakdown ◽  
Finite Amplitude ◽  
Wave Activity ◽  
Threshold Behavior ◽  
Mean Flow ◽  
Transient Wave ◽  
Wave Forcing ◽  
Stratospheric Sudden Warmings ◽  
Wave Activity Flux

Abstract This paper examines the role of wave–mean flow interaction in the onset and suddenness of stratospheric sudden warmings (SSWs). Evidence is presented that SSWs are, on average, a threshold behavior of finite-amplitude Rossby waves arising from the competition between an increasing wave activity A and a decreasing zonal-mean zonal wind u¯. The competition puts a limit to the wave activity flux that a stationary Rossby wave can transmit upward. A rapid, spontaneous vortex breakdown occurs once the upwelling wave activity flux reaches the limit, or equivalently, once u¯ drops below a certain fraction of uREF, a wave-free, reference-state wind inverted from the zonalized quasigeostrophic potential vorticity. This fraction is 0.5 in theory and about 0.3 in reanalyses. We propose r≡u¯/uREF as a local, instantaneous measure of the proximity to vortex breakdown (i.e., preconditioning). The ratio r generally stays above the threshold during strong-vortex winters until a pronounced final warming, whereas during weak-vortex winters it approaches the threshold early in the season, culminating in a precipitous drop in midwinter as SSWs form. The essence of the threshold behavior is captured by a semiempirical 1D model of SSWs, similar to the “traffic jam” model of Nakamura and Huang for atmospheric blocking. This model predicts salient features of SSWs including rapid vortex breakdown and downward migration of the wave activity/zonal wind anomalies, with analytical expressions for the respective time scales. The model’s response to a variety of transient wave forcing and damping is discussed.

Stratospheric sudden warming as a threshold behavior of Rossby waves

2020 ◽  
Author(s):  
Noboru Nakamura
Keyword(s):  
Zonal Wind ◽  
Rossby Waves ◽  
Vortex Breakdown ◽  
Finite Amplitude ◽  
Wave Activity ◽  
Reference State ◽  
Threshold Behavior ◽  
Mean Flow ◽  
Transient Wave ◽  
Wave Activity Flux

<p>We present evidence that stratospheric sudden warmings (SSWs) are, on average, a threshold behavior of finite-amplitude Rossby waves arising from wave-mean flow interaction. Competition between an increasing wave activity and a decreasing zonal-mean zonal wind sets a limit to the upward wave activity flux of a stationary Rossby wave.  A rapid, spontaneous vortex breakdown occurs once the upwelling wave activity flux reaches the limit, or equivalently, once the zonal-mean zonal wind drops below a certain fraction of the wave-free, reference-state wind obtained from the zonalized quasigeostrophic potential vorticity.  This threshold faction is 0.5 in theory and about 0.3 in reanalyses.  We use the ratio of the zonal-mean zonal wind to the reference-state wind as a local, instantaneous measure of the proximity to vortex breakdown, i.e. preconditioning.  The ratio generally stays above the threshold during strong-vortex winters until a pronounced final warming, whereas during weak-vortex winters it approaches the threshold early in the season, culminating in a precipitous drop in midwinter as SSWs form. The essence of the threshold behavior is captured by a semiempirical 1D model of SSWs, analogous to the “traffic jam” model of Nakamura and Huang for atmospheric blocking. This model predicts salient features of SSWs including rapid vortex breakdown and downward migration of the wave activity/zonal wind anomalies, with analytical expressions for the respective timescales. Model’s response to a variety of transient wave forcing and damping is discussed.</p><p> </p><p> </p><div> </div><p> </p>

Downward Wave Propagation on the Polar Vortex

2005 ◽  
Vol 62 (9) ◽  
pp. 3382-3395 ◽  
Author(s):  
R. K. Scott ◽  
D. G. Dritschel
Keyword(s):  
Wave Propagation ◽  
Differential Rotation ◽  
Potential Vorticity ◽  
Three Dimensional ◽  
Polar Vortex ◽  
Wave Activity ◽  
Stratospheric Polar Vortex ◽  
Downward Influence ◽  
Downward Propagation ◽  
Propagation Of Waves

Abstract This paper considers the propagation of waves on the edge of a stratospheric polar vortex, represented by a three-dimensional patch of uniform potential vorticity in a compressible quasigeostrophic system. Waves are initialized by perturbing the vortex from axisymmetry in the center of the vortex, and their subsequent upward and downward propagation is measured in terms of a nonlinear, pseudomomentum-based wave activity. Under conditions typical of the winter stratosphere, the dominant direction of wave propagation is downward, and wave activity accumulates in the lower vortex levels. The reason for the preferred downward propagation arises from a recent result of Scott and Dritschel, which showed that the three-dimensional Green’s function in the compressible system contains an anisotropy that causes a general differential rotation in a finite volume vortex. The sense of the differential rotation is to stabilize the upper vortex and destabilize the lower vortex. This mechanism is particularly interesting in view of recent interest in the downward influence of the stratosphere on the troposphere and also provides a possible conservative, balanced explanation of the formation of the robust dome plus annulus potential vorticity structure observed in the upper stratosphere.

scholarly journals Finite-Amplitude Wave Activity and Mean Flow Adjustments in the Atmospheric General Circulation. Part I: Quasigeostrophic Theory and Analysis

2010 ◽  
Vol 67 (12) ◽  
pp. 3967-3983 ◽  
Author(s):  
Noboru Nakamura ◽  
Abraham Solomon
Keyword(s):  
Zonal Wind ◽  
Finite Amplitude ◽  
Wave Activity ◽  
Reference State ◽  
The Arctic ◽  
Surface Boundary ◽  
Mean Flow ◽  
Amplitude Wave ◽  
Finite Amplitude Wave Activity ◽  
Mean State

Abstract A diagnostic relationship between finite-amplitude wave activity and the associated adiabatic adjustments to the zonal-mean zonal wind and temperature is developed in the quasigeostrophic (QG) framework and is applied to a 23-yr segment (1979–2001) of the 40-yr ECMWF Re-Analysis (ERA-40) data. Wave activity is defined in terms of an instantaneous areal displacement of QG potential vorticity (PV) from zonal symmetry. Unlike previous forms, the tendency of wave activity equals exactly the negative of the eddy PV flux (Eliassen–Palm flux divergence) in the conservative limit, even at finite amplitude. This allows one to integrate the transformed Eulerian mean (TEM) theory in time and quantify the departure (adiabatic adjustment) of the zonal-mean state from an eddy-free reference state in terms of the observed wave activity. The structure of wave activity identifies synoptic eddies in the extratropics and planetary waves in the high latitudes of winter-to-spring stratosphere. In addition, a thin layer of high wave activity is found at the top of the lowermost stratosphere (∼17 km) in the summer extratropics. The reference state is constructed by “zonalizing” the PV contours conservatively (preserving area) on the isobaric surface and by inverting the resultant PV gradient for the mean flow. The adjustment associated with wave activity depends on the assumed surface boundary condition for the reference state. With a no-slip condition, the observed zonal-mean temperature is on average ∼33 (90) K higher than the reference state in the troposphere (stratosphere) of the Arctic winter, while the zonal-mean zonal wind is ∼30 m s−1 slower in the upper stratosphere. Since the reference state filters out the advective eddy–mean flow interaction, it fluctuates less than the zonal-mean state, potentially improving the signal-to-noise ratio for climate diagnosis.

scholarly journals Flow Kinematics in Variable-Height Rotating Cylinder Arrays

2016 ◽  
Vol 138 (11) ◽  
Author(s):  
Anna E. Craig ◽  
John O. Dabiri ◽  
Jeffrey R. Koseff
Keyword(s):  
Power Output ◽  
Rotation Rate ◽  
Three Dimensional ◽  
Vertical Axis ◽  
Streamwise Velocity ◽  
Vertical Flow ◽  
Mean Flow ◽  
Freestream Velocity ◽  
Cylinder Arrays ◽  
The Mean

Experimental data are presented for large arrays of rotating, variable-height cylinders in order to study the dependence of the three-dimensional mean flows on the height heterogeneity of the array. Elements in the examined arrays were spatially arranged in the same staggered paired configuration, and the heights of each element pair varied up to ±37.5% from the mean height (kept constant across all arrays), such that the arrays were vertically structured. Four vertical structuring configurations were examined at a nominal Reynolds number (based on freestream velocity and cylinder diameter) of 600 and nominal tip-speed ratios of 0, 2, and 4. It was found that the vertical structuring of the array could significantly alter the mean flow patterns. Most notably, a net vertical flow into the array from above was observed, which was augmented by the arrays' vertical structuring, showing a 75% increase from the lowest to highest vertical flows (as evaluated at the maximum element height, at a single rotation rate). This vertical flow into the arrays is of particular interest as it represents an additional mechanism by which high streamwise momentum can be transported from above the array down into the array. An evaluation of the streamwise momentum resource within the array indicates up to a 56% increase in the incoming streamwise velocity to the elements (from the lowest to highest ranking arrays, at a single rotation rate). These arrays of rotating cylinders may provide insight into the flow kinematics of arrays of vertical axis wind turbines (VAWTs). In a physical VAWT array, an increase in incoming streamwise flow velocity to a turbine corresponds to a (cubic) increase in the power output of the turbine. Thus, these results suggest a promising approach to increasing the power output of a VAWT array.

scholarly journals A Three-Dimensional Wave-Activity Relation for Pseudomomentum

2007 ◽  
Vol 64 (6) ◽  
pp. 2126-2134 ◽  
Author(s):  
Lingkun Ran ◽  
Shouting Gao
Keyword(s):  
Potential Temperature ◽  
Three Dimensional ◽  
Wave Activity ◽  
Primitive Equations ◽  
Casimir Function ◽  
Activity Density ◽  
Atmospheric Data ◽  
Local Wave ◽  
Basic States ◽  
Wave Activity Flux

A three-dimensional, nonhydrostatic local wave-activity relation for pseudomomentum is derived from the nonhydrostatic primitive equations in Cartesian coordinates by using an extension of the momentum–Casimir method. The stationary and zonally symmetric basic states are chosen and a Casimir function, which is the single-valued function of potential vorticity and potential temperature, is introduced in the derivation. The wave-activity density and wave-activity flux of the local wave-activity relation for pseudomomentum are expressed entirely in terms of Eulerian quantities so that they are easily calculated with atmospheric data and do not require the knowledge of particle placements. Constructed in the ageostrophic and nonhydrostatic dynamical framework, the local wave-activity relation for pseudomomentum is applicable to diagnosing the evolution and propagation of mesoscale weather systems.

scholarly journals Atmospheric Blocking: The Impact of Topography in an Idealized General Circulation Model

2020 ◽  
Author(s):  
Veeshan Narinesingh ◽  
James F. Booth ◽  
Spencer K. Clark ◽  
Yi Ming
Keyword(s):  
High Pressure ◽  
General Circulation ◽  
Storm Track ◽  
Circulation Model ◽  
Wave Activity ◽  
Stationary Waves ◽  
Atmospheric Blocking ◽  
The Pacific ◽  
The Impact ◽  
Wave Activity Flux

Abstract. Atmospheric blocking can have important impacts on weather hazards, but the fundamental dynamics of blocking are not yet fully understood. As such, this work investigates the influence of topography on atmospheric blocking in terms of dynamics, spatial frequency, duration and displacement. Using an idealized GCM, an aquaplanet integration, and integrations with topography are analyzed. Block-centered composites show midlatitude aquaplanet blocks exhibit similar wave activity flux behavior to those observed in reality, whereas high-latitude blocks do not. The addition of topography significantly increases blocking and determines distinct regions where blocks are most likely to occur. These regions are found near high-pressure anomalies in the stationary waves and near storm track exit regions. Focusing on block duration, blocks originating near topography are found to last longer than those that are formed without or far from topography but have qualitatively similar evolutions in terms of nearby geopotential height anomalies and wave activity fluxes in composites. Integrations with two mountains have greater amounts of blocking compared to the single mountain case, however, the longitudinal spacing between the mountains is important for how much blocking occurs. Comparison between integrations with longitudinally long and short ocean basins show that more blocking occurs when storm track exits spatially overlap with high-pressure maxima in stationary waves. These results have real-world implications, as they help explain the differences in blocking between the Northern and Southern Hemisphere, and the differences between the Pacific and Atlantic regions in the Northern Hemisphere.

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