scholarly journals A Formulation of Three Dimensional Wave Activity Flux Describing Wave Propagation on the Mass-Weighted Isentropic Time Mean Equation

SOLA ◽  
2016 ◽  
Vol 12 (0) ◽  
pp. 198-202 ◽  
Author(s):  
Takenari Kinoshita ◽  
Toshiki Iwasaki ◽  
Kaoru Sato
Keyword(s):  
Wave Propagation ◽  
Three Dimensional ◽  
Wave Activity ◽  
Wave Activity Flux ◽  
Dimensional Wave

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.

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

IS WAVE PROPAGATION COMPUTABLE OR CAN WAVE COMPUTERS BEAT THE TURING MACHINE?

2002 ◽  
Vol 85 (2) ◽  
pp. 312-332 ◽  
Author(s):  
KLAUS WEIHRAUCH ◽  
NING ZHONG
Keyword(s):  
Wave Propagation ◽  
Turing Machine ◽  
Sobolev Spaces ◽  
Three Dimensional ◽  
Subject Classification ◽  
Physical Machine ◽  
The Church ◽  
Dimensional Wave

According to the Church-Turing Thesis a number function is computable by the mathematically defined Turing machine if and only if it is computable by a physical machine. In 1983 Pour-El and Richards defined a three-dimensional wave $u(t,x)$ such that the amplitude $u(0,x)$ at time 0 is computable and the amplitude $u(1,x)$ at time 1 is continuous but not computable. Therefore, there might be some kind of wave computer beating the Turing machine. By applying the framework of Type 2 Theory of Effectivity (TTE), in this paper we analyze computability of wave propagation. In particular, we prove that the wave propagator is computable on continuously differentiable waves, where one derivative is lost, and on waves from Sobolev spaces. Finally, we explain why the Pour-El-Richards result probably does not help to design a wave computer which beats the Turing machine.2000 Mathematical Subject Classification: 03D80, 03F60, 35L05, 68Q05.

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.

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