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.

scholarly journals A Formulation of Three-Dimensional Residual Mean Flow Applicable Both to Inertia–Gravity Waves and to Rossby Waves

2013 ◽  
Vol 70 (6) ◽  
pp. 1577-1602 ◽  
Author(s):  
Takenari Kinoshita ◽  
Kaoru Sato
Keyword(s):  
Gravity Waves ◽  
General Circulation ◽  
Rossby Waves ◽  
Three Dimensional ◽  
Stokes Drift ◽  
Eastern Region ◽  
Mean Flow ◽  
Southern Andes ◽  
Horizontal Structure ◽  
Inertia Gravity Waves

Abstract The three-dimensional (3D) residual mean flow is expressed as the sum of the Eulerian-mean flow and the Stokes drift. The present study derives formulas that are approximately equal to the 3D Stokes drift for the primitive equation (PRSD) and for the quasigeostrophic equation (QGSD) using small-amplitude theory for a slowly varying time-mean flow. The PRSD has a broad utility that is applicable to both Rossby waves and inertia–gravity waves. The 3D wave activity flux whose divergence corresponds to the wave forcing is also derived using PRSD. The PRSD agrees with QGSD under the small-Rossby-number assumption, and it agrees with the 3D Stokes drift derived by S. Miyahara and by T. Kinoshita et al. for inertia–gravity waves under the constant-Coriolis-parameter assumption. Moreover, a phase-independent 3D Stokes drift is derived under the QG approximation. The 3D residual mean flow in the upper troposphere in April is investigated by applying the new formulas to the European Centre for Medium-Range Weather Forecasts (ECMWF) Interim Re-Analysis (ERA-Interim) data. It is observed that the PRSD is strongly poleward (weakly equatorward) upstream (downstream) of the storm track. A case study was also made for dominant gravity waves around the southern Andes in the simulation by a gravity wave–resolving general circulation model. The 3D residual mean flow associated with the gravity waves is poleward (equatorward) in the western (eastern) region of the southern Andes. This flow is due to the horizontal structure of the variance in the zonal component of the mountain waves, which do not change much while they propagate upward.

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>

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 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 Stratospheric Wave–Mean Flow Feedbacks and Sudden Stratospheric Warmings in a Simple Model Forced by Upward Wave Activity Flux

2014 ◽  
Vol 71 (11) ◽  
pp. 4055-4071 ◽  
Author(s):  
Jeremiah P. Sjoberg ◽  
Thomas Birner
Keyword(s):  
Wave Propagation ◽  
Inversion Layer ◽  
Wave Activity ◽  
Mean Flow ◽  
Stable States ◽  
Mass Model ◽  
Incoming Wave ◽  
Wave Forcing ◽  
The Mean ◽  
Wave Activity Flux

Abstract A classic result of studying stratospheric wave–mean flow interactions presented by Holton and Mass is that, for constant incoming wave forcing (at a notional tropopause), a vacillating stratospheric response may ensue. Simple models, such as the Holton–Mass model, typically prescribe the incoming wave forcing in terms of geopotential perturbation, which is not a proxy for upward wave activity flux. Here, the authors reformulate the Holton–Mass model such that incoming upward wave activity flux is prescribed. The Holton–Mass model contains a positive wave–mean flow feedback whereby wave forcing decelerates the mean flow, allowing enhanced wave propagation, which then further decelerates the mean flow, etc., until the mean flow no longer supports wave propagation. By specifying incoming wave activity flux, this feedback is constrained to the model interior. Bistability—where the zonal wind may exist at one of two distinct steady states for a given incoming wave forcing—is maintained in this reformulated model. The model is perturbed with transient pulses of upward wave activity flux to produce transitions between the two stable states. A minimum of integrated incoming wave activity flux necessary to force these sudden stratospheric warming–like transitions exists for pulses with time scales on the order of 10 days, arising from a wave time scale internal to the model at which forcing produces the strongest mean-flow response. The authors examine how the tropopause affects the internal feedback for this model setup and find that the tropopause inversion layer may potentially provide an important source of wave activity in the lower stratosphere.

Silencer for high-frequency turbocharger compressor noise via an acoustic straightener

2021 ◽  
Vol 263 (5) ◽  
pp. 1744-1755
Author(s):  
Pranav Sriganesh ◽  
Rick Dehner ◽  
Ahmet Selamet
Keyword(s):  
Wave Propagation ◽  
Plane Wave ◽  
High Frequency ◽  
Three Dimensional ◽  
Mean Flow ◽  
Analytical Treatment ◽  
Underlying Assumption ◽  
Wide Range ◽  
Plane Wave Propagation ◽  
Dimensional Wave

Decades of successful research and development on automotive silencers for engine breathing systems have brought about significant reductions in emitted engine noise. A majority of this research has pursued airborne noise at relatively low frequencies, which typically involve plane wave propagation. However, with the increasing demand for downsized turbocharged engines in passenger cars, high-frequency compressor noise has become a challenge in engine induction systems. Elevated frequencies promote multi-dimensional wave propagation rendering at times conventional silencer treatments ineffective due to the underlying assumption of one-dimensional wave propagation in their design. The present work focuses on developing a high-frequency silencer that targets tonal noise at the blade-pass frequency within the compressor inlet duct for a wide range of rotational speeds. The approach features a novel "acoustic straightener" that creates exclusive plane wave propagation near the silencing elements. An analytical treatment is combined with a three-dimensional acoustic finite element method to guide the early design process. The effects of mean flow and nonlinearities on acoustics are then captured by three-dimensional computational fluid dynamics simulations. The configuration developed by the current computational effort will set the stage for further refinement through future experiments.

scholarly journals Quasigeostrophic Transient Wave Activity Flux: Updated Climatology and Its Role in Polar Vortex Anomalies

2010 ◽  
Vol 67 (10) ◽  
pp. 3164-3189 ◽  
Author(s):  
Mototaka Nakamura ◽  
Minoru Kadota ◽  
Shozo Yamane
Keyword(s):  
Lower Troposphere ◽  
Polar Vortex ◽  
Wave Activity ◽  
Vertical Flux ◽  
Storm Tracks ◽  
Mean Flow ◽  
Transient Wave ◽  
Upper Troposphere ◽  
Wave Flux ◽  
Wave Activity Flux

Abstract The climatology of transient wave activity flux defined by Plumb has been calculated for each calendar month, for high-frequency (HF) and low-frequency (LF) waves, using the NCAR–NCEP reanalyses for both hemispheres. Wave activity flux of both HF and LF waves shows upward propagation of waves from the lower troposphere into the upper troposphere, then into the lower stratosphere during the summer and at least up to the midstratosphere during other seasons. While the upward flux emanating from the lower troposphere is particularly large in the two storm tracks in the Northern Hemisphere (NH), it is large in most of the extratropics in the Southern Hemisphere (SH). The HF waves radiate equatorward most noticeably in the upper troposphere, whereas the LF waves do not show visible signs of equatorward radiation. The total horizontal flux is generally dominated by the advective flux that represents the eddy enstrophy advection by the mean flow and appears predominantly pseudoeastward. Divergence of the wave activity flux exhibits discernible large-scale characteristics at the lowest level in both hemispheres and in the upper troposphere in the NH. The divergence field indicates acceleration of the pseudoeastward mean flow near the surface in both hemispheres. In the NH, acceleration and deceleration, respectively, of the pseudoeastward mean flow in the storm tracks and downstream of the storm tracks in the upper troposphere are found. Seasonal variations in the wave flux are substantial in the NH but relatively minor in the SH. In the NH, the wave flux fields exhibit generally larger values during the cold months than during warm months. Also, the latitudes at which large wave flux values are seen are higher during warm months, as the jets and storm tracks shift northward from the winter to the summer. Anomalously large vertical flux of both HF and LF wave activity propagating up from the lower troposphere throughout the troposphere and stratosphere in the northern flank of the North Atlantic storm track is found to precede anomalous deceleration in the NH winter polar vortex, while anomalously small vertical flux in the same area precedes anomalous acceleration of the vortex. The accompanying horizontal flux anomalies tend to counteract the action of the anomalous vertical flux. These cases are found to be dissipation of strong anomalies in the polar vortex. The anomalous flux divergence does not prove the active role of the waves in the anomalous change in the polar vortex, however. No signs of the wave flux originating from specific areas preceding anomalous change in the polar vortex are found for the SH.

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
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