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Abstract
Lilly's model of a horizontally homogeneous cloud-topped mixed layer is studied. The model is closed by taking a weighted (weighting factor or entrainment parameter k) average of Lilly's maximum and minimum entrainment cases. The dependence of steady-state solutions on large-scale divergence, sea surface temperature and entrainment parameter k is investigated. By numerical integration the response of the mixed layer to a diurnally varying radiative flux is investigated. Significant variations in the state of the mixed layer and in the convective fluxes are found.
Abstract
Lilly's model of a horizontally homogeneous cloud-topped mixed layer is studied. The model is closed by taking a weighted (weighting factor or entrainment parameter k) average of Lilly's maximum and minimum entrainment cases. The dependence of steady-state solutions on large-scale divergence, sea surface temperature and entrainment parameter k is investigated. By numerical integration the response of the mixed layer to a diurnally varying radiative flux is investigated. Significant variations in the state of the mixed layer and in the convective fluxes are found.
Abstract
The geopotential tendency form of semigeostrophic theory is derived and compared with the potential vorticity form. The tendency form is compact and particularly convenient for non-Boussinesq, nonuniform potential vorticity flows.
Abstract
The geopotential tendency form of semigeostrophic theory is derived and compared with the potential vorticity form. The tendency form is compact and particularly convenient for non-Boussinesq, nonuniform potential vorticity flows.
Some statistical measures of growth of American Meteorological Society technical journals have been compiled. A general upward trend in total number of articles, pages, and an increase (nearly doubling during the past 20 years) in the average length of articles is found. Approximately half of this growth appears to be attributable to the increasing figure content of papers and half to the expansion of text apart from figures. Growth causes and impacts are discussed.
Some statistical measures of growth of American Meteorological Society technical journals have been compiled. A general upward trend in total number of articles, pages, and an increase (nearly doubling during the past 20 years) in the average length of articles is found. Approximately half of this growth appears to be attributable to the increasing figure content of papers and half to the expansion of text apart from figures. Growth causes and impacts are discussed.
Abstract
The spiral bands that occur in tropical cyclones can be conveniently divided into two classes—outer bands and inner bands. Evidence is presented here that the outer bands form as the result of nonlinear effects during the breakdown of the intertropical convergence zone (ITCZ) through barotropic instability. In this process a zonal strip of high potential vorticity (the ITCZ shear zone or monsoon trough) begins to distort in a varicose fashion, with the potential vorticity (PV) becoming pooled in local regions that are connected by filaments of high PV. As the pooled regions become more axisymmetric, the filaments become thinner and begin to wrap around the PV centers.
It is argued that inner bands form in a different manner. As a tropical cyclone intensifies due to latent heat release, the PV field becomes nearly circular with the highest values of PV in the cyclone center. The radial gradient of PV provides a state on which PV waves (the generalization of Rossby waves) can propagate. The nonlinear breaking of PV waves then leads to an irreversible distortion of the PV contours and a downgradient flux of PV. The continuation of this proem tends to erode the high PV core of the tropical cyclone, to produce a surrounding surf zone, and hence to spread the PV horizontally. In a similar fashion, inner bands can also form by the merger of a vortex with a patch of relatively high PV air. As the merger proem occurs the patch of PV is quickly elongated and wrapped around the vortex. The resulting vortex is generally larger in horizontal extent and exhibits a spiral band of PV.
When the formation of outer and inner bands is interpreted in the context of a normal-mode spectral model, they emerge as slow manifold phenomena; that is, they have both rotational and (balanced or slaved) gravitational mode aspects. In this sense, regarding them as simply gravity waves leads to an incomplete dynamical picture.
Abstract
The spiral bands that occur in tropical cyclones can be conveniently divided into two classes—outer bands and inner bands. Evidence is presented here that the outer bands form as the result of nonlinear effects during the breakdown of the intertropical convergence zone (ITCZ) through barotropic instability. In this process a zonal strip of high potential vorticity (the ITCZ shear zone or monsoon trough) begins to distort in a varicose fashion, with the potential vorticity (PV) becoming pooled in local regions that are connected by filaments of high PV. As the pooled regions become more axisymmetric, the filaments become thinner and begin to wrap around the PV centers.
It is argued that inner bands form in a different manner. As a tropical cyclone intensifies due to latent heat release, the PV field becomes nearly circular with the highest values of PV in the cyclone center. The radial gradient of PV provides a state on which PV waves (the generalization of Rossby waves) can propagate. The nonlinear breaking of PV waves then leads to an irreversible distortion of the PV contours and a downgradient flux of PV. The continuation of this proem tends to erode the high PV core of the tropical cyclone, to produce a surrounding surf zone, and hence to spread the PV horizontally. In a similar fashion, inner bands can also form by the merger of a vortex with a patch of relatively high PV air. As the merger proem occurs the patch of PV is quickly elongated and wrapped around the vortex. The resulting vortex is generally larger in horizontal extent and exhibits a spiral band of PV.
When the formation of outer and inner bands is interpreted in the context of a normal-mode spectral model, they emerge as slow manifold phenomena; that is, they have both rotational and (balanced or slaved) gravitational mode aspects. In this sense, regarding them as simply gravity waves leads to an incomplete dynamical picture.
Abstract
A potential pseudodensity principle is derived for the quasi-static primitive equations on the sphere. An important step in the derivation of this principle is the introduction of “vorticity coordinates”—that is, new coordinates whose Jacobian with respect to the original spherical coordinates is the dimensionless absolute isentropic vorticity. The vorticity coordinates are closely related to Clebsch variables and are the primitive equation generalizations of the geostrophic coordinates used in semigeostrophic theory. The vorticity coordinates can be used to transform the primitive equations into a canonical form. This form is mathematically similar to the geostrophic relation. There is flexibility in the choice of the potential function appearing in the canonical momentum equations. This flexibility can be used to force the vorticity coordinates to move with some desired velocity, which results in an associated simplification of the material derivative operator. The end result is analogous to the way ageostrophic motions become implicit when geostrophic coordinates are used in semigeostrophic theory.
Abstract
A potential pseudodensity principle is derived for the quasi-static primitive equations on the sphere. An important step in the derivation of this principle is the introduction of “vorticity coordinates”—that is, new coordinates whose Jacobian with respect to the original spherical coordinates is the dimensionless absolute isentropic vorticity. The vorticity coordinates are closely related to Clebsch variables and are the primitive equation generalizations of the geostrophic coordinates used in semigeostrophic theory. The vorticity coordinates can be used to transform the primitive equations into a canonical form. This form is mathematically similar to the geostrophic relation. There is flexibility in the choice of the potential function appearing in the canonical momentum equations. This flexibility can be used to force the vorticity coordinates to move with some desired velocity, which results in an associated simplification of the material derivative operator. The end result is analogous to the way ageostrophic motions become implicit when geostrophic coordinates are used in semigeostrophic theory.
Abstract
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Abstract
We consider the axisymmetric balanced flow occurring in a thermally forced vortex in which the frictional inflow is confined to a thin boundary layer. Above the boundary layer the absolute angular momentum ½fR 2=rv+½fr 2 is conserved. We refer to R as the potential radius, i.e., the radius to which a particle must be moved (conserving absolute angular momentum) in order to change its tangential component v to zero. Using R as one of the dependent variables we review the equations of the Eliassen balanced vortex model.
We next reverse the roles of the actual radius r and the potential radius R, i.e., we treat R as an independent variable and r as a dependent variable. Introducing transformed components (u *, w *) of the transverse circulation we obtain the transformed Eliassen balanced vortex equations, which differ from the original equations in the following respects: 1) the radial coordinate is R which results in a stretching of positive relative vorticity regions and a shrinking of negative relative vorticity regions; 2) the thermodynamic equation contains only the transverse circulation component w *, the coefficient of which is the potential vorticity q; 3) the equation for r contains only the transverse circulation component u *; 4) the transverse circulation equation contains only two vortex structure functions, the potential vorticity q and the inertial stability s, where pq=(ζ/f)(g/θ0)(∂θ/∂Z) and ρs=f 2 R 4/r 4.
The form of the transverse circulation equation leads naturally to a generalized Rossby radius proportional to (q/s)½. A typical distribution Of (q/s)½ is calculated using the composite tropical cyclone data of Gray. The fundamental dynamical role of (q/s)½ is then illustrated with a simple analytical example.
Abstract
We consider the axisymmetric balanced flow occurring in a thermally forced vortex in which the frictional inflow is confined to a thin boundary layer. Above the boundary layer the absolute angular momentum ½fR 2=rv+½fr 2 is conserved. We refer to R as the potential radius, i.e., the radius to which a particle must be moved (conserving absolute angular momentum) in order to change its tangential component v to zero. Using R as one of the dependent variables we review the equations of the Eliassen balanced vortex model.
We next reverse the roles of the actual radius r and the potential radius R, i.e., we treat R as an independent variable and r as a dependent variable. Introducing transformed components (u *, w *) of the transverse circulation we obtain the transformed Eliassen balanced vortex equations, which differ from the original equations in the following respects: 1) the radial coordinate is R which results in a stretching of positive relative vorticity regions and a shrinking of negative relative vorticity regions; 2) the thermodynamic equation contains only the transverse circulation component w *, the coefficient of which is the potential vorticity q; 3) the equation for r contains only the transverse circulation component u *; 4) the transverse circulation equation contains only two vortex structure functions, the potential vorticity q and the inertial stability s, where pq=(ζ/f)(g/θ0)(∂θ/∂Z) and ρs=f 2 R 4/r 4.
The form of the transverse circulation equation leads naturally to a generalized Rossby radius proportional to (q/s)½. A typical distribution Of (q/s)½ is calculated using the composite tropical cyclone data of Gray. The fundamental dynamical role of (q/s)½ is then illustrated with a simple analytical example.
