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

Kinoshita, Takenari; Tomikawa, Yoshihiro; Sato, K.

doi:10.2151/jmsj.2010-307

Cited by 27 publications

(44 citation statements)

References 33 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…However, as is clear from (17), this is attributable not to a problem with the behavior of the antisymmetric diffusion tensor L itself but to the condition for solving a set of equations to obtain the components of L, that is, 0 · c = 0 occurs at the singular domain. Therefore, we can avoid the singularity by invoking the L'Hospital's rule mathematically as suggested by Kinoshita et al (2010), or by using values smoothly interpolated from adjacent points in practice, on applying the present TEM to equatorial waves.…”

Section: Discussion and Concluding Remarksmentioning

confidence: 99%

A General Three-Dimensional Transformed Eulerian Mean Formulation

Noda

2010

SOLA

View full text Add to dashboard Cite

The transformed Eulerian mean (TEM) formulation for equations of motion, which was originally defined for waves on a zonally averaged flow, is extended three-dimensionally to a nonhydrostatic Boussinesq fluid in the general coordinate system. The three-dimensional antisymmetric diffusion tensor that plays a central role in defining the residual circulation and the EliassenPalm flux tensor is derived systematically by assuming that eddies consist of neutral waves. A modification of the formulation for application to practical data analyses is made by introducing a symmetric eddy diffusion tensor.

show abstract

Section: Discussion and Concluding Remarksmentioning

confidence: 99%

A General Three-Dimensional Transformed Eulerian Mean Formulation

Noda

2010

SOLA

View full text Add to dashboard Cite

show abstract

“…However, only recently did Miyahara (2006) succeed in generalizing the TEM for a nonhydrostatic Boussinesq fluid. Kinoshita (2010Kinoshita ( , 2013a has extended Miyaharaʼs result to the case where the Coriolis parameter depends on latitude. Noda (2010, hereafter referred to as N2010) further extended Miyaharaʼs result to a more general situation, i.e., a nonhydrostatic Boussinesq fluid with a weak shear flow, and he derived a general three-dimensional TEM (3D-TEM), including the thus far neglected vertical component of the EP tensor.…”

Section: Introductionmentioning

confidence: 90%

“…However, it can be shown after manipulation that ( 38′ ) is equivalent to (38) with f 0 replaced by f under the WKB approximation for the perturbation equations used by Kinoshita et al (2010) and Kinoshita and Sato (2013a). On the other hand, Kinoshita and Sato (2013b) showed the difference between ( 38′ ) and (38) when the β effect of the earthʼs rotation was explicitly considered.…”

Section: Temsmentioning

confidence: 99%

See 1 more Smart Citation

Generalized Transformed Eulerian Mean (GTEM) Description for Boussinesq Fluids

Noda

2014

Journal of the Meteorological Society of Japan

View full text Add to dashboard Cite

The transformed Eulerian mean (TEM) description has been widely used as a standard basic analysis tool for describing wave-mean flow interactions in geophysical fluid dynamics. However, the TEM implicitly assumes that the eddy diffusion tensor is antisymmetric, although the assumption does not hold in general data analyses. To remedy the defect, a generalized transformed Eulerian mean (GTEM) set of equations is derived based on a nonneutral (unstable/dissipative) wave under dissipation and/or diabatic heating conditions in a Boussinesq stratified fluid. All the nine components of the three-dimensional eddy diffusion tensor are derived based on the wave-form. However, the explicit form of the wave frequency and wavenumber of eddies is not referred to so as to apply the GTEM to actual atmospheric and oceanic data analyses. The symmetric part of the eddy diffusion tensor is proportional to the growth rate for the weakly nonneutral wave. It is shown that the Stokes drift velocity defined in the generalized Lagrangian mean (GLM) description agrees to the leading order with the minus sign of the divergence of the transposed eddy diffusion tensor, so that the direction of the transport velocity induced by the symmetric (antisymmetric) part is opposite (identical) to the Stokes drift velocity. An application to the Eady unstable wave is made to illustrate the differences between TEM, GLM, and GTEM.

show abstract

“…In most GWPs, hypothetical wave saturation is considered to limit the wave amplitude (Lindzen 1981). The wave forcings X and Y exerted on largescale (resolved) momentum equations are expressed as the convergence of the pseudomomentum flux (e.g., Kinoshita et al 2010):…”

Section: Calculation Of Wave Amplitudes and Gwfmentioning

confidence: 99%

A New Gravity Wave Parameterization Including Three-Dimensional Propagation

Amemiya

Sato

2016

Journal of the Meteorological Society of Japan

Self Cite

View full text Add to dashboard Cite

Recent studies suggest that the horizontal propagation of gravity waves (GWs) is important in the spatial distribution of gravity wave forcing (GWF), especially during winter in the high latitudes of the Southern Hemisphere (SH). However, most standard gravity wave parameterizations (GWPs) treat GW propagation simply in the vertical. In this study, a new orographic GWP that includes three-dimensional (3D) GW propagation is developed and its impact on large-scale dynamical fields is examined. Our GWP calculates the horizontal locations and changes in the 3D wavenumbers of GWs explicitly through vertical integration of the ray tracing equations. The GWF due to wave refraction, which occurs in inhomogeneous background fields even without wave dissipation, is also calculated. In addition, the computational cost of parallelization is greatly reduced by adopting a Taylor's series approximation for the horizontal gradient of the background fields needed for the ray tracing calculation. Two numerical experiments are performed using the Model for Interdisciplinary Research of Climate (MIROC)-AGCM: one uses the new orographic GWP and the other uses a conventional GWP. In the experiment with the new GWP, the westward GWF is enhanced in the SH winter mesosphere above the core of the polar night jet. This enhancement results from the significant latitudinal propagation of the parameterized GWs toward the jet axis. The zonal wind is slightly stronger in the SH winter polar upper stratosphere, which is consistent with the differences in GWF caused mainly by refraction. However, the strength and seasonal evolution of the polar night jet is less affected by the different GWPs. This result may be because of the compensation by Eliassen-Palm flux divergence due to the resolved waves. These results suggest that 3D propagation in GWPs is potentially important for better representation of the momentum budget of the middle atmosphere in climate models.

show abstract

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

Cited by 27 publications

References 33 publications

A General Three-Dimensional Transformed Eulerian Mean Formulation

A General Three-Dimensional Transformed Eulerian Mean Formulation

Generalized Transformed Eulerian Mean (GTEM) Description for Boussinesq Fluids

A New Gravity Wave Parameterization Including Three-Dimensional Propagation

Contact Info

Product

Resources

About