Relation between the interannual variability in the stratospheric Rossby wave forcing and zonal mean fields suggesting an interhemispheric link in the stratosphere

Focusing on the interannual variabilities in the zonal mean fields and Rossby wave forcing in austral winter, an interhemispheric coupling in the stratosphere is examined using reanalysis data: the Modern-Era Retrospective Analysis for Research and Applications, version 2 (MERRA-2). In the present study, the Eliassen–Palm (EP) flux divergence averaged over the latitude and height regions of 50–30∘ S and 0.3–1 hPa, respectively, are used as a proxy of the Rossby wave forcing, where the absolute value of the EP flux divergence is maximized in the winter in the Southern Hemisphere (SH). The interannual variabilities in the zonal mean temperature and zonal wind are significantly correlated with the SH Rossby wave forcing in the stratosphere in both the SH and Northern Hemisphere (NH). The interannual variability in the strength of the poleward residual mean flow in the SH stratosphere is also correlated with the strength of the wave forcing. This correlation is significant even around the Equator at an altitude of 40 km and at NH low latitudes of 20–40 km. The temperature anomaly is consistent with this residual mean flow anomaly. The relation between the cross-equatorial flow and the zonal mean absolute angular momentum gradient (M‾y) is examined in the meridional cross section. The M‾y around the Equator at the altitude of 40 km is small when the wave forcing is strong, which provides a pathway for the cross-equatorial residual mean flow. These results indicate that an interhemispheric coupling is present in the stratosphere through the meridional circulation modulated by the Rossby wave forcing.

Relation Between the Interannual Variability in the Stratospheric Rossby Wave Forcing and Zonal Mean Fields Suggesting an Interhemispheric Link in the Stratosphere

Focusing on the interannual variabilities in the zonal mean fields and Rossby wave forcing in austral winter, an interhemispheric coupling in the stratosphere is examined using reanalysis data: the Modern-Era Retrospective Analysis for Research and Applications, version 2 (MERRA-2). In the present study, the Eliassen-Palm (EP) flux divergence averaged over the latitude and height regions of 50°–30° S and 0.3–1 hPa, respectively, are used as a proxy of the Rossby wave forcing, where the absolute value of the EP flux divergence is maximized in the winter in the Southern Hemisphere (SH). The interannual variabilities in the zonal mean temperature and zonal wind are significantly correlated with the SH Rossby wave forcing in the stratosphere in both the SH and Northern Hemisphere (NH). The interannual variability in the strength of the poleward residual mean flow in the SH stratosphere is also correlated with the strength of the wave forcing. This correlation is significant even around the equator at an altitude of 40 km and at NH low latitudes of 20–40 km. The temperature anomaly is consistent with this residual mean flow anomaly. The relationship between the cross-equatorial flow and the zonal mean absolute angular momentum gradient (My) is examined in the meridional cross section. The My around the equator at the altitude of 40 km is small when the wave forcing is strong, which provides a pathway for the cross-equatorial residual mean flow. These results indicate that an interhemispheric coupling is present in the stratosphere through the meridional circulation modulated by the Rossby wave forcing.

Quasi-12 h inertia–gravity waves in the lower mesosphere observed by the PANSY radar at Syowa Station (39.6° E, 69.0° S)

The first observations made by a complete PANSY radar system (Program of the Antarctic Syowa MST/IS Radar) installed at Syowa Station (39.6° E, 69.0° S) were successfully performed from 16 to 24 March 2015. Over this period, quasi-half-day period (12 h) disturbances in the lower mesosphere at heights of 70 to 80 km were observed. Estimated vertical wavelengths, wave periods and vertical phase velocities of the disturbances were approximately 13.7 km, 12.3 h and −0.3 m s−1, respectively. Under the working hypothesis that such disturbances are attributable to inertia–gravity waves, wave parameters are estimated using a hodograph analysis. The estimated horizontal wavelengths are longer than 1100 km, and the wavenumber vectors tend to point northeastward or southwestward. Using the nonhydrostatic numerical model with a model top of 87 km, quasi-12 h disturbances in the mesosphere were successfully simulated. We show that quasi-12 h disturbances are due to wave-like disturbances with horizontal wavelengths longer than 1400 km and are not due to semidiurnal migrating tides. Wave parameters, such as horizontal wavelengths, vertical wavelengths and wave periods, simulated by the model agree well with those estimated by the PANSY radar observations under the abovementioned assumption. The parameters of the simulated waves are consistent with the dispersion relationship of the inertia–gravity wave. These results indicate that the quasi-12 h disturbances observed by the PANSY radar are attributable to large-scale inertia–gravity waves. By examining a residual of the nonlinear balance equation, it is inferred that the inertia–gravity waves are likely generated by the spontaneous radiation mechanism of two different jet streams. One is the midlatitude tropospheric jet around the tropopause while the other is the polar night jet. Large vertical fluxes of zonal and meridional momentum associated with large-scale inertia–gravity waves are distributed across a slanted region from the midlatitude lower stratosphere to the polar mesosphere in the meridional cross section. Moreover, the vertical flux of the zonal momentum has a strong negative peak in the mesosphere, suggesting that some large-scale inertia–gravity waves originate in the upper stratosphere.

Quasi 12 h inertia-gravity waves in the lower mesosphere observed by the PANSY radar at Syowa Station (39.6 °E, 69.0 °S)

The first observations made by a complete PANSY radar system (Program of the Antarctic Syowa MST/IS Radar) installed at Syowa Station (39.6 °E, 69.0 °S) were successfully performed from March 16–24, 2015. Over this period, quasi-half-day period (12 h) disturbances in the lower mesosphere at heights of 70 km to 80 km were observed. Estimated vertical wavelengths, wave periods and vertical phase velocities of the disturbances were approximately 13.7 km, 12.3 h and −0.3 m s−1, respectively. Under the working hypothesis that such disturbances are attributable to inertia-gravity waves, wave parameters are estimated using a hodograph analysis. The estimated horizontal wavelengths are longer than 1100 km, and the wavenumber vectors tend to point northeastward or southwestward. Using the non-hydrostatic numerical model with a model top of 87 km, quasi 12 h disturbances in the mesosphere were successfully simulated. We show that quasi 12 h disturbances are due to wave-like disturbances with horizontal wavelengths longer than 1400 km and are not due to semi-diurnal migrating tides. Wave parameters, such as horizontal wavelengths, vertical wavelengths and wave periods, simulated by the model agree well with those estimated by the PANSY radar observations under the above-mentioned assumption. The parameters of the simulated waves are consistent with the dispersion relationship of the inertia-gravity wave. These results indicate that the quasi 12 h disturbances observed by the PANSY radar are attributable to large-scale inertia-gravity waves. By examining a residual of the nonlinear balance equation, it is inferred that the inertia-gravity waves are likely generated by the spontaneous radiation mechanism of two different jet streams. One is the mid-latitude tropospheric jet around the tropopause while the other is the polar night jet. Large vertical fluxes of zonal and meridional momentum associated with large-scale inertia-gravity waves are distributed across a slanted region from the mid-latitude lower stratosphere to the polar mesosphere in the meridional cross-section. Moreover, the vertical flux of the zonal momentum has a strong negative peak in the mesosphere, suggesting that some large-scale inertia-gravity waves originate in the upper stratosphere.

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

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.

Velocity Characteristics of the Wheel in Grinding Axisymmetric Aspheric with AEGM

It is an important method to machine revolution aspheric with Arc Envelope Grinding Method（AEGM）. CNC system controls the feed rate of the arc center of the end of the wheel in grinding, Disk-shaped grinding wheel processing curve (ie, cross-section curve of rotary aspheric) and motion curve of the arc center of the wheel are equidistant curves each other . Based on the analysis of the angular velocity (ω) of the grinding point, the relationship between the feed rate of the arc of the wheel (υ0) and the feed rate of the grinding point (υ) is analyzed, the feed rate and the angular velocity of the grind point is discussed when the eccentricity of the meridional cross-section curve take different values. The results show: 1) the feed rate of the grinding pointυ=υ0±ωr; 2)ω is changing in grinding, When the caliber of axisymmetric aspheric (ie, z value) is small, ω will change slowly, otherwise, ω will change rapidly when the caliber of axisymmetric aspheric is large; 3) the ratio of υ/υ0 will change with the z-axis coordinate changes. υ/υ0is larger when the caliber of axisymmetric aspheric is smaller. By analyzing ,υ/υ0 and other parameters, the motion law of the wheel is obtained, which will provide confirm base for optimizing feed rate in grinding and improve the precision of grinding.

Inertial waves in a rotating spherical shell

The structure and spectrum of inertial waves of an incompressible viscous fluid inside a spherical shell are investigated numerically. These modes appear to be strongly featured by a web of rays which reflect on the boundaries. Kinetic energy and dissipation are indeed concentrated on thin conical sheets, the meridional cross-section of which forms the web of rays. The thickness of the rays is in general independent of the Ekman number E but a few cases show a scaling with E1/4 and statistical properties of eigenvalues indicate that high-wavenumber modes have rays of width O(E1/3). Such scalings are typical of Stewartson shear layers. It is also shown that the web of rays depends on the Ekman number and shows bifurcations as this number is decreased.This behaviour also implies that eigenvalues do not evolve smoothly with viscosity. We infer that only the statistical distribution of eigenvalues may follow some simple rules in the asymptotic limit of zero viscosity.