## Vorticity

 prefLabel Vorticity definition Measure of the rotational spin about an axis at some point within a fluid (or wind field). inScheme broader Abstract from DBPedia In continuum mechanics, vorticity is a pseudovector field that describes the local spinning motion of a continuum near some point (the tendency of something to rotate), as would be seen by an observer located at that point and traveling along with the flow. Conceptually, vorticity could be determined by marking parts of a continuum in a small neighborhood of the point in question, and watching their relative displacements as they move along the flow. The vorticity vector would be twice the mean angular velocity vector of those particles relative to their center of mass, oriented according to the right-hand rule. This quantity must not be confused with the angular velocity of the particles relative to some other point. More precisely, the vorticity is a pseudovector field ω→, defined as the curl (rotational) of the flow velocity u→ vector. The definition can be expressed by the vector analysis formula: where ∇ is the del operator. The vorticity of a two-dimensional flow is always perpendicular to the plane of the flow, and therefore can be considered a scalar field. As a consequence, the unit of the vorticity is 1/s, i.e. Hz. The vorticity is related to the flow's circulation (line integral of the velocity) along a closed path by the (classical) Stokes' theorem. Namely, for any infinitesimal surface element C with normal direction n→ and area dA, the circulation dΓ along the perimeter of C is the dot product ω→ ∙ (dA n→) where ω→ is the vorticity at the center of C. Many phenomena, such as the blowing out of a candle by a puff of air, are more readily explained in terms of vorticity, rather than the basic concepts of pressure and velocity. This applies, in particular, to the formation and motion of vortex rings. The name vorticity was created by Horace Lamb in 1916.渦度（うずど、かど）は、流れの回転するありさまを表現する量である。渦度はベクトル量（さらに言えば擬ベクトル）であり、流れの速度ベクトルのなすベクトル場の回転である。 渦度ベクトル Ω は流速ベクトル v = (vx, vy, vz) により、以下のように表される。 渦度ベクトルを流線のようにつなげた曲線を渦線という。流れの中のある閉曲線上の各点を通る渦線によってできる曲面を渦管という。断面積を無限小にした渦管を渦糸という。渦糸が閉曲線になっている場合、これを渦輪という。 data publication(s) found by GCMD Science Keywords) ECMWF AMEX Global Tropospheric and Stratospheric Analyses, daily 1987JanECMWF Joint Observing System Simulation Experiment (OSSE) Nature RunJapanese 25-year Reanalysis ProjectJapanese 25-year Reanalysis Project, Monthly MeansERA-20C Project (ECMWF Atmospheric Reanalysis of the 20th Century)ERA-Interim ProjectERA-Interim Project, Monthly MeansJRA-55: Japanese 55-year Reanalysis, Daily 3-Hourly and 6-Hourly DataJRA-55: Japanese 55-year Reanalysis, Monthly Means and VariancesJRA-55C: The Japanese 55-year Reanalysis Using Conventional Data OnlyJRA-55C: Monthly Means and VariancesJRA-55AMIP: The Japanese 55-year Reanalysis AMIP-type SimulationJRA-55AMIP: Monthly Means and Variances Including Diurnal StatisticsWCRP and WWRP THORPEX YOTC (Year of Tropical Convection) ProjectWCRP and WWRP THORPEX YOTC (Year of Tropical Convection) Project, Single Parameter 6-Hourly Pressure Level Analysis Time Series, Transformed to a Regular 1600 by 800 (N400) Gaussian GridWCRP and WWRP THORPEX YOTC (Year of Tropical Convection) Project, Single Parameter 6-Hourly Pressure Level Forecast Time Series, Transformed to a Regular 1600 by 800 (N400) Gaussian GridWCRP and WWRP THORPEX YOTC (Year of Tropical Convection) Project, Single Parameter 6-Hourly Model Level Analysis Time Series, Transformed to a Regular 1600 by 800 (N400) Gaussian GridWCRP and WWRP THORPEX YOTC (Year of Tropical Convection) Project, Single Parameter 3-Hourly Pressure Level Forecast Time Series, Transformed to a Regular 1600 by 800 (N400) Gaussian Grid, Dynamical Parameters OnlyERA5 ReanalysisERA5 Reanalysis Monthly MeansERA5 Reanalysis (0.25 Degree Latitude-Longitude Grid)Global 500mb and 300mb Vorticity Area IndicesNorthern Hemisphere Winter Circulation StatisticsNorthern Hemisphere Summer Circulation StatisticsDaily Northern Hemisphere Forecast Grids, Sporadically Between November 1967 and December 1971NMC B3 Daily Northern Hemisphere Analyses for 1963 August to 1972 DecemberNCEP FNL Operational Model Global Tropospheric Analyses, July 1976 to April 1997NCEP FNL Operational Model Global Tropospheric Analyses, April 1997 through June 2007NCEP FNL Operational Model Global Tropospheric Analyses, continuing from July 1999NCEP GDAS/FNL 0.25 Degree Global Tropospheric Analyses and Forecast GridsNCEP GFS 0.25 Degree Global Forecast Grids Historical ArchiveNCEP Global T80 Sigma Analyses, daily from September 1990 to February 1999 (from Kistler)NCEP GFS 0.25 Degree Global Forecast Auxiliary Grids Historical ArchiveCAC Monthly Global Analyses for October 1978 to September 1994NCEP/NCAR Global Reanalysis Products, 1948-continuingNCEP Climate Forecast System Reanalysis (CFSR) 6-hourly Products, January 1979 to December 2010NCEP Climate Forecast System Reanalysis (CFSR) Selected Hourly Time-Series Products, January 1979 to December 2010NCEP Climate Forecast System Reanalysis (CFSR) Monthly Products, January 1979 to December 2010NCEP Climate Forecast System Version 2 (CFSv2) 6-hourly ProductsNCEP Climate Forecast System Version 2 (CFSv2) Selected Hourly Time-Series ProductsNCEP Climate Forecast System Version 2 (CFSv2) Monthly ProductsECMWF TOGA Global Advanced Operational Spectral Analysis, daily 1985-2010ECMWF TOGA Global Hybrid Tropospheric Analyses, July 1990 to June 1991ECMWF's Operational Model Analysis, starting in 2011ECMWF IFS CY41r2 High-Resolution Operational ForecastsERA-15 Model Resolution Upper Air AnalysisERA-15 2.5 degree Monthly Means of Upper Air DataERA-40 Global Upper Air Pressure Level AnalysisERA-40 Global Upper Air Model Level AnalysisERA-40 Isentropic Level AnalysisERA-40 2.5 Degree Upper Air Pressure Level Analysis DataERA-40 Monthly Means of Upper Air Pressure Level AnalysisERA-40 Monthly Means of Upper Air Model Level AnalysisERA-40 Monthly Means of Isentropic Level Analysis DataERA-40 Monthly Means of 2.5 Degree Upper Air Pressure Level AnalysisERA-40 Pressure Level ForecastsERA-40 Model Level FOrecastsERA-40 Monthly Means of Upper Air Pressure Level ForecastsERA-40 Monthly Means of Model Level ForecastsERA40 T85 Analysis Fields on Pressure Surfaces, created at NCARERA40 T85 Analysis Fields on Model Levels, created at NCARERA40 T85 Monthly Mean Analysis Fields on Pressure Surfaces, created at NCARERA40 T85 Monthly Mean Analysis Fields on Model Levels, created at NCARERA40 T106 Analysis Fields on Pressure Surfaces, created at NCARERA40 T106 Analysis Fields on Model Levels, created at NCARERA40 T106 Monthly Mean Analysis Fields on Pressure Surfaces, created at NCARClimatology of the January and July Tropics and Mid-LatitudesGFDL Atmospheric Circulation Analyses by Bram Oort, monthly May 1958 to April 1973Climate Analysis Center Base Period Climate Diagnostics Data BaseNCAR MMM 10-member, 3 km, experimental real-time ensemble prediction systemGATE Analyses by Ooyama, Chu, and EsbensenGCIP FSL MAPS MORDS and MOLTS data, hourly.GCIP NCEP Eta model outputGCIP Canadian Meteorological Centre (CMC) GEM model output,