scholarly journals On the Three-Dimensional Residual Mean Circulation and Wave Activity Flux of the Primitive Equations

2010 ◽  
Vol 88 (3) ◽  
pp. 373-394 ◽  
Author(s):  
Takenari KINOSHITA ◽  
Yoshihiro TOMIKAWA ◽  
Kaoru SATO
Keyword(s):  
Three Dimensional ◽  
Wave Activity ◽  
Primitive Equations ◽  
Mean Circulation ◽  
Residual Mean Circulation ◽  
Wave Activity Flux

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 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 A New Method to Estimate Three-Dimensional Residual-Mean Circulation in the Middle Atmosphere and Its Application to Gravity Wave–Resolving General Circulation Model Data

2013 ◽  
Vol 70 (12) ◽  
pp. 3756-3779 ◽  
Author(s):  
Kaoru Sato ◽  
Takenari Kinoshita ◽  
Kota Okamoto
Keyword(s):  
Gravity Wave ◽  
Gravity Waves ◽  
General Circulation ◽  
Three Dimensional ◽  
Circulation Model ◽  
Mean Flow ◽  
Flux Divergence ◽  
Mean Circulation ◽  
Residual Mean Circulation ◽  
Wave Induced

Abstract A new method is proposed to estimate three-dimensional (3D) material circulation driven by waves based on recently derived formulas by Kinoshita and Sato that are applicable to both Rossby waves and gravity waves. The residual-mean flow is divided into three, that is, balanced flow, unbalanced flow, and Stokes drift. The latter two are wave-induced components estimated from momentum flux divergence and heat flux divergence, respectively. The unbalanced mean flow is equivalent to the zonal-mean flow in the two-dimensional (2D) transformed Eulerian mean (TEM) system. Although these formulas were derived using the “time mean,” the underlying assumption is the separation of spatial or temporal scales between the mean and wave fields. Thus, the formulas can be used for both transient and stationary waves. Considering that the average is inherently needed to remove an oscillatory component of unaveraged quadratic functions, the 3D wave activity flux and wave-induced residual-mean flow are estimated by an extended Hilbert transform. In this case, the scale of mean flow corresponds to the whole scale of the wave packet. Using simulation data from a gravity wave–resolving general circulation model, the 3D structure of the residual-mean circulation in the stratosphere and mesosphere is examined for January and July. The zonal-mean field of the estimated 3D circulation is consistent with the 2D circulation in the TEM system. An important result is that the residual-mean circulation is not zonally uniform in both the stratosphere and mesosphere. This is likely caused by longitudinally dependent wave sources and propagation characteristics. The contribution of planetary waves and gravity waves to these residual-mean flows is discussed.

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.

Diagnostics of a WN2‐Type Major Sudden Stratospheric Warming Event in February 2018 Using a New Three‐Dimensional Wave Activity Flux

2019 ◽  
Vol 124 (12) ◽  
pp. 6120-6142
Author(s):  
Yayoi Harada ◽  
Kaoru Sato ◽  
Takenari Kinoshita ◽  
Ryosuke Yasui ◽  
Toshihiko Hirooka ◽  
...  
Keyword(s):  
Three Dimensional ◽  
Wave Activity ◽  
Stratospheric Warming ◽  
Sudden Stratospheric Warming ◽  
Wave Activity Flux ◽  
Dimensional Wave

scholarly journals Wave Activity for Large-Amplitude Disturbances Described by the Primitive Equations on the Sphere

2013 ◽  
Vol 70 (6) ◽  
pp. 1616-1630 ◽  
Author(s):  
John Methven
Keyword(s):  
Large Amplitude ◽  
Potential Temperature ◽  
Lower Boundary ◽  
Propagation Speed ◽  
Analysis Data ◽  
Wave Activity ◽  
Primitive Equations ◽  
Baroclinic Wave ◽  
Boundary Potential ◽  
Background State

Abstract Pseudomomentum and pseudoenergy are both measures of wave activity for disturbances in a fluid, relative to a notional background state. Together they give information on the propagation, growth, and decay of disturbances. Wave activity conservation laws are most readily derived for the primitive equations on the sphere by using isentropic coordinates. However, the intersection of isentropic surfaces with the ground (and associated potential temperature anomalies) is a crucial aspect of baroclinic wave evolution. A new expression is derived for pseudoenergy that is valid for large-amplitude disturbances spanning isentropic layers that may intersect the ground. The pseudoenergy of small-amplitude disturbances is also obtained by linearizing about a zonally symmetric background state. The new expression generalizes previous pseudoenergy results for quasigeostrophic disturbances on the β plane and complements existing large-amplitude results for pseudomomentum. The pseudomomentum and pseudoenergy diagnostics are applied to an extended winter from the European Centre for Medium-Range Weather Forecasts Interim Re-Analysis data. The time series identify distinct phenomena such as a baroclinic wave life cycle where the wave activity in boundary potential temperature saturates nonlinearly almost two days before the peak in wave activity near the tropopause. The coherent zonal propagation speed of disturbances at tropopause level, including distinct eastward, westward, and stationary phases, is shown to be dictated by the ratio of total hemispheric pseudoenergy to pseudomomentum. Variations in the lower-boundary contribution to pseudoenergy dominate changes in propagation speed; phases of westward progression are associated with stronger boundary potential temperature perturbations.

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