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1. Introduction Over the last four decades, the budget of atmospheric angular momentum (AAM) has been the subject of many studies. For geodesists, this interest follows that, for nearly all periodicities, changes in AAM correspond to changes in the parameters of the earth’s rotation ( Barnes et al. 1983 ). For climatologists, this interest follows that the AAM varies with planetary-scale tropical oscillations affecting the climate at intraseasonal ( Madden 1987 ; Hendon 1995 ) and interannual
1. Introduction Over the last four decades, the budget of atmospheric angular momentum (AAM) has been the subject of many studies. For geodesists, this interest follows that, for nearly all periodicities, changes in AAM correspond to changes in the parameters of the earth’s rotation ( Barnes et al. 1983 ). For climatologists, this interest follows that the AAM varies with planetary-scale tropical oscillations affecting the climate at intraseasonal ( Madden 1987 ; Hendon 1995 ) and interannual
tornado in which angular momentum generally increases with increasing radius and a certain degree of axisymmetry is maintained. The angular momentum budget of this TC is analyzed, and its evolution is interpreted in the context of near-ground virtual potential temperature changes, reflectivity changes, and the evolution of the swirl at somewhat larger scales than the tornado cyclone. The angular momentum budget analysis is described in section 2 , and evolution is summarized for each phase of tornado
tornado in which angular momentum generally increases with increasing radius and a certain degree of axisymmetry is maintained. The angular momentum budget of this TC is analyzed, and its evolution is interpreted in the context of near-ground virtual potential temperature changes, reflectivity changes, and the evolution of the swirl at somewhat larger scales than the tornado cyclone. The angular momentum budget analysis is described in section 2 , and evolution is summarized for each phase of tornado
1. Introduction Axial angular momentum (AAM) is a key variable in large-scale dynamics so that AAM budgets are indispensable for understanding the global circulation. Correspondingly, various AAM budgets have been evaluated from data. Of course, the results depend on the coordinate system chosen for the analysis. The investigations of Starr and White (1951) , Hantel and Hacker (1978) , and Oort and Peixoto (1983 ; see also Peixoto and Oort 1992) were performed in pressure p coordinates
1. Introduction Axial angular momentum (AAM) is a key variable in large-scale dynamics so that AAM budgets are indispensable for understanding the global circulation. Correspondingly, various AAM budgets have been evaluated from data. Of course, the results depend on the coordinate system chosen for the analysis. The investigations of Starr and White (1951) , Hantel and Hacker (1978) , and Oort and Peixoto (1983 ; see also Peixoto and Oort 1992) were performed in pressure p coordinates
about the response of the mean zonal current to wave action.” Moreover, Pfeffer (1992) compared observed changes of the zonal mean wind with the vertical component of the Eliassen–Palm flux but did not find a correlation. Holton (1992) remarks in his text book that if we are “primarily concerned with the angular momentum balance for a zonal ring of air extending from the surface to the top of the atmosphere . . . it proves simpler to use the conventional Eulerian mean formalism.” It is the
about the response of the mean zonal current to wave action.” Moreover, Pfeffer (1992) compared observed changes of the zonal mean wind with the vertical component of the Eliassen–Palm flux but did not find a correlation. Holton (1992) remarks in his text book that if we are “primarily concerned with the angular momentum balance for a zonal ring of air extending from the surface to the top of the atmosphere . . . it proves simpler to use the conventional Eulerian mean formalism.” It is the
angular momentum from the mesocyclone. Chow et al. (2002 , hereafter CCL02) argued that large-scale moving outer spiral bands, often seen in full-physics numerical simulations, can be modeled by waves emanating from a rotating elliptical vortex, similar to the Lighthill radiation mechanism ( Lighthill 1952 ; Ford 1994 ). Chow and Chan (2003 , hereafter CC03) derived an analytical expression based on the shallow-water equations of CCL02 to show that gravity waves can transport a significant
angular momentum from the mesocyclone. Chow et al. (2002 , hereafter CCL02) argued that large-scale moving outer spiral bands, often seen in full-physics numerical simulations, can be modeled by waves emanating from a rotating elliptical vortex, similar to the Lighthill radiation mechanism ( Lighthill 1952 ; Ford 1994 ). Chow and Chan (2003 , hereafter CC03) derived an analytical expression based on the shallow-water equations of CCL02 to show that gravity waves can transport a significant
Robinson 1998 ; Scott and Polvani 2007 ) as emphasized in the discussion to follow. A local application of the β -plane model to the sphere was advocated recently by Theiss (2004) and Smith (2004) . As is clear from the title of our paper, another important aspect in the barotropic and shallow-water systems is the conservation of absolute angular momentum. Despite occasional recognition of the importance of this global invariant ( Williams 1978 ; Yoden and Yamada 1993 ; Dritschel and McIntyre
Robinson 1998 ; Scott and Polvani 2007 ) as emphasized in the discussion to follow. A local application of the β -plane model to the sphere was advocated recently by Theiss (2004) and Smith (2004) . As is clear from the title of our paper, another important aspect in the barotropic and shallow-water systems is the conservation of absolute angular momentum. Despite occasional recognition of the importance of this global invariant ( Williams 1978 ; Yoden and Yamada 1993 ; Dritschel and McIntyre
sufficiently far from the equator prove to be a special case in both types of models, because such forcings produce cross-equatorial flow that approximately conserves absolute angular momentum in the free troposphere. In axisymmetric models, the circulation shifts between this nonlinear, angular momentum–conserving (AMC) regime and a nearly linear regime in which angular momentum advection is balanced by viscous damping ( Plumb and Hou 1992 ). In eddy-resolving models, the circulation transitions between
sufficiently far from the equator prove to be a special case in both types of models, because such forcings produce cross-equatorial flow that approximately conserves absolute angular momentum in the free troposphere. In axisymmetric models, the circulation shifts between this nonlinear, angular momentum–conserving (AMC) regime and a nearly linear regime in which angular momentum advection is balanced by viscous damping ( Plumb and Hou 1992 ). In eddy-resolving models, the circulation transitions between
) , McIntyre (2008) , Esler (2008a , b) , and Bühler (2009) . A key point is that PV mixing generically requires angular-momentum changes. In the real world those changes are usually mediated by, or catalyzed by, the radiation stresses or Eliassen–Palm fluxes due to Rossby waves and other wave types, including the form stresses exerted across undulating stratification surfaces. Usually, therefore, there is no such thing as turbulence without waves. PV mixing by baroclinic and barotropic shear
) , McIntyre (2008) , Esler (2008a , b) , and Bühler (2009) . A key point is that PV mixing generically requires angular-momentum changes. In the real world those changes are usually mediated by, or catalyzed by, the radiation stresses or Eliassen–Palm fluxes due to Rossby waves and other wave types, including the form stresses exerted across undulating stratification surfaces. Usually, therefore, there is no such thing as turbulence without waves. PV mixing by baroclinic and barotropic shear
estimating how three-dimensional refraction of internal gravity waves affects the global vertical transport of angular momentum. To this end, we built an offline ray-tracing model in spherical geometry and applied it to output from the Third Generation Atmospheric General Circulation Model (AGCM3) of the Canadian Centre for Climate Modeling and Analysis. The AGCM3 includes a columnar gravity wave parameterization scheme for topographic waves and multiple runs of the ray tracer were computed using the
estimating how three-dimensional refraction of internal gravity waves affects the global vertical transport of angular momentum. To this end, we built an offline ray-tracing model in spherical geometry and applied it to output from the Third Generation Atmospheric General Circulation Model (AGCM3) of the Canadian Centre for Climate Modeling and Analysis. The AGCM3 includes a columnar gravity wave parameterization scheme for topographic waves and multiple runs of the ray tracer were computed using the
consideration, they showed a single thermally direct circulation cell in each hemisphere that links the heat source in the tropics to the heat sink in high latitudes. They have further linked the angular momentum (AM) circulation that is driven by both diabatic heating and force to the mass circulation between the equator and the poles. Since then, the mass circulation in isentropic coordinates has been analyzed in many studies (e.g., Juckes et al. 1994 ; Held and Schneider 1999 ; Schneider 2004
consideration, they showed a single thermally direct circulation cell in each hemisphere that links the heat source in the tropics to the heat sink in high latitudes. They have further linked the angular momentum (AM) circulation that is driven by both diabatic heating and force to the mass circulation between the equator and the poles. Since then, the mass circulation in isentropic coordinates has been analyzed in many studies (e.g., Juckes et al. 1994 ; Held and Schneider 1999 ; Schneider 2004
