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The effect of the equatorially symmetric zonal winds of Saturn on its gravitational field

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Research in Astronomy and Astrophysics 2018年第4期18卷 15-22页

作者： Dali Kong Keke Zhang gerald schubert John D.Anderson Key Laboratory of Planetary Sciences Shanghai Astronomical Observatory Chinese Academy of SciencesShanghai 200030 China College of Engineering Mathematics and Physical Sciences University of Exeter Exeter EX4 4QF UK Lunar and Planetary Science Laboratory Macao University of Science and Technology Macao China Department of Earth Planetary and Space Sciences University of California Los Angeles CA 90095-1567 USA Jet Propulsion Laboratory 4800 Oak Grove Drive Pasadena CA 91109 USA

The penetration depth of Saturn’s cloud-level winds into its interior is unknown.A possible way of estimating the depth is through measurement of the effect of the winds on the planet’s gravitational *** use a self-consistent perturbation approach to study how the equatorially symmetric zonal winds of Saturn contribute to its gravitational *** important advantage of this approach is that the variation of its gravitational field solely caused by the winds can be isolated and identified because the leading-order problem accounts exactly for rotational distortion,thereby determining the irregular shape and internal structure of the hydrostatic *** assume that（i）the zonal winds are maintained by thermal convection in the form of non-axisymmetric columnar rolls and（ii）the internal structure of the winds,because of the Taylor-Proundman theorem,can be uniquely determined by the observed cloud-level *** calculate both the variation △J_n,n=2,4,6...of the axisymmetric gravitational coefficients J_n caused by the zonal winds and the non-axisymmetric gravitational coefficients △J_（nm） produced by the columnar rolls,where m is the azimuthal wavenumber of the *** consider three different cases characterized by the penetration depth 0.36 R_S,0.2 R_S and 0.1 R_S,where R_S is the equatorial radius of Saturn at the 1-bar pressure *** find that the high-degree gravitational coefficient （ J_（12）＋△J_（12）） is dominated,in all the three cases,by the effect of the zonal flow with ｜△J_（12）/J_（12）｜〉100%and that the size of the non-axisymmetric coefficientsdirectly reflects the depth and scale of the flow taking place in the Saturnian interior.

关键词： gravitation — planets and satellites individual(Saturn) — planets and satellites interiors

A model of Saturn inferred from its measured gravitational field

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Research in Astronomy and Astrophysics 2018年第4期18卷 7-14页

作者： Dali Kong Keke Zhang gerald schubert John D.Anderson Key Laboratory of Planetary Sciences Shanghai Astronomical Observatory Chinese Academy of Sciences Shanghai 200030 China College of Engineering Mathematics and Physical Sciences University of Exeter Exeter EX4 4QF UK Lunar and Planetary Science Laboratory Macao University of Science and Technology Macao China Department of Earth Planetary and Space Sciences University of California Los Angeles CA 90095-1567 USA Jet Propulsion Laboratory 4800 Oak Grove Drive Pasadena CA 91109 USA

We present an interior model of Saturn with an ice-rock core,a metallic region,an outer molecular envelope and a thin transition layer between the metallic and molecular *** shape of Saturn’s 1 bar surface is irregular and determined fully self-consistently by the required equilibrium *** the ice-rock core is assumed to have a uniform density,three different equations of state are adopted for the metallic,molecular and transition *** Saturnian model is constrained by its known mass,its known equatorial and polar radii,and its known zonal gravitational coefficients,J_（2n）,n=1,2,*** model produces an ice-rock core with equatorial radius 0.203 R_S,where R_S is the equatorial radius of Saturn at the 1-bar pressure surface;the core densityρ_c=10388.1 kgm^（3）corresponding to 13.06 Earth masses;and an analytical expression describing the Saturnian irregular shape of the 1-bar pressure *** model also predicts the values of the higher-order gravitational coefficients,J_8,J_10 and J_12,for the hydrostatic Saturn and suggests that Saturn’s convective dynamo operates in the metallic region approximately defined by 0.2 R_S

关键词： gravitation — planets and satellites individual(Saturn) — planets and satellites interiors

Saturn＇s gravitational field induced by its equatorially antisymmetric zonal winds

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Research in Astronomy and Astrophysics 2018年第5期18卷 29-36页

作者： Dali Kong Keke Zhang gerald schubert John D.Anderson Key Laboratory of Planetary Sciences Shanghai Astronomical Observatory Chinese Academy of Sciences Shanghai 200030 China College of Engineering Mathematics and Physical Sciences University of Exeter Exeter EX4 4QF UK Lunar and Planetary Science Laboratory Macao University of Science and Technology Macao China Department of Earth Planetary and Space Sciences University of California Los Angeles CA 90095-1567 USA Jet Propulsion Laboratory 4800 Oak Grove Drive Pasadena CA 91109 USA

The cloud-level zonal winds of Saturn are marked by a substantial equatorially antisymmetric component with a speed of about 50 m s^-1 which, if they are sufficiently deep, can produce measurable odd zonal gravitational coefficients △J2 k＋1, k = 1, 2, 3, 4. This study, based on solutions of the thermal-gravitational wind equation, provides a theoretical basis for interpreting the odd gravitational coefficients of Saturn in terms of its equatorially antisymmetric zonal flow. We adopt a Saturnian model comprising an ice-rock core, a metallic dynamo region and an outer molecular envelope. We use an equatorially antisymmetric zonal flow that is parameterized, confined in the molecular envelope and satisfies the solvability condition required for the thermal-gravitational wind equation. The structure and amplitude of the zonal flow at the cloud level are chosen to be consistent with observations of *** calculate the odd zonal gravitational coefficients △J2k＋1, k = 1, 2, 3, 4 by regarding the depth of the equatorially antisymmetric winds as a parameter. It is found that △J3 is-4.197 × 10^-8 if the zonal winds extend about 13 000 km downward from the cloud tops while it is-0.765 × 10^-8 if the depth is about 4000 km. The depth/profile of the equatorially antisymmetric zonal winds can eventually be estimated when the high-precision measurements of the Cassini Grand Finale become available.

关键词： gravitation - planets and satellites individual (Saturn) - planets and satellites interiors

Ripple Tectonics—When Subduction Is Interrupted

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Positioning 2020年第3期11卷 33-44页

作者： Zvi Ben-Avraham gerald schubert Emanuele Lodolo Uri Schattner Department of Geophysics Porter School of the Environment and Earth Sciences Tel Aviv University Tel Aviv Israel Leon H. Charney School of Marine Sciences University of Haifa Haifa Israel Department of Earth Planetary and Space Sciences University of California Los Angeles USA National Institute of Oceanography and Experimental Geophysics Sgonico Italy Dr. Moses Strauss Department of Marine Geosciences Leon H. Charney School of Marine Sciences University of Haifa Haifa Israel

Subduction plays a fundamental role in plate tectonics and is a significant factor in modifying the structure and topography of the Earth. It is driven by convection forces that change over a >100 Myr time scale. However, when an oceanic plateau approaches, it plugs the subduction, and causes slab necking and tearing. This abrupt change may trigger a series of geodynamic (tectonic, volcanic) and sedimentary responses recorded across the convergence boundary and its surrounding regions by synchronous structural modifications. We suggest that a large enough triggering event may lead to a ripple tectonic effect that propagates outwards while speeding up the yielding of localized stress states that otherwise would not reach their threshold. The ripple effect facilitates tectonic, volcanic, and structural events worldwide that are seemingly unrelated. When the world’s largest oceanic plateau, Ontong Java Plateau (OJP), choked the Pacific-Australian convergence zone at ~6 Myr ago, it induced kinematic modifications throughout the Pacific region and along its plate margins. Other, seemingly unrelated, short-lived modifications were recorded worldwide during that time window. These modifications changed the rotation of the entire Pacific plate, which occupies ~20% of the Earth’s surface. In addition, the Scotia Sea spreading stopped, global volcanism increased, the Strait of Gibraltar closed, and the Mediterranean Sea dried up and induced the Messinian salinity crisis. In this paper, we attribute these and many other synchronous events to a new “ripple tectonics” mechanism. We suggest that the OJPincipient collision triggered the Miocene-Pliocene transition. Similarly, we suggest that innovative GPS-based studies conducted today may seek the connectivity between tectonic, seismic, and volcanic events worldwide.

关键词： Plate Tectonics Subduction-Collision Transition Miocene-Pliocene Transition

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染发产品的生产线新革命

中国化妆品 2014年第5期 40-40页

作者： gerald schubert Gerhald schubert有限责任公司

就在Henkel的工厂Viesen-Dulken重新修整两年之后,品牌的重心都放在染发产品的生产上.工厂现在配备了世界上最先进的产品生产设备.

关键词：染发产品生产线生产设备工厂

Scaling the Microphysics Equations and Analyzing the Variability of Hydrometeor Production Rates in a Controlled Parameter Space

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Advances in Atmospheric Sciences 2002年第4期19卷 619-650页

作者： Chungu Lu Paul Schultz and gerald L Browning NOAA Forecast Systems Laboratory Boulder USA Cooperative Institute for Research in the Atmosphere Colorado State University Fort Collins USA

A set of microphysics equations is scaled based on the convective length and velocity scales. Comparisons are made among the dynamical transport and various microphysical processes. From the scaling analysis, it becomes apparent which parameterized microphysical processes present off-scaled influences in the integration of the set of microphysics equations. The variabilities of the parameterized microphysical processes are also studied using the approach of a controlled parameter space. Given macroscopic dynamic and thermodynamic conditions in different regions of convective storms, it is possible to analyze and compare vertical profiles of these processes. Bulk diabatic heating profiles for a cumulus convective updraft and downdraft are also derived from this analysis. From the two different angles, the scale analysis and the controlled-parameter space approach can both provide an insight into and an understanding of microphysics parameterizations.

关键词： cloud microphysical parameterization scale analysis controlled parameter space numerical weather prediction