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- Author or Editor: STANLEY L. ROSENTHAL x
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Abstract
Numerical experiments with an axisymmetric model of the tropical cyclone are described. The model contains a cumulus parameterization of the type proposed by Ooyama (1971). It is shown that the growth of the hurricane scale is significantly affected when the cloud model and the form of the cloud spectrum are altered. The growth of the hurricane is also strongly affected by the manner in which resolvable supersaturation is treated.
Abstract
Numerical experiments with an axisymmetric model of the tropical cyclone are described. The model contains a cumulus parameterization of the type proposed by Ooyama (1971). It is shown that the growth of the hurricane scale is significantly affected when the cloud model and the form of the cloud spectrum are altered. The growth of the hurricane is also strongly affected by the manner in which resolvable supersaturation is treated.
Abstract
Disturbances with scales of a few thousand kilometers are commonly observed in the troposphere over the subtropical oceans. Synoptic experience seems to indicate that many of these large-scale disturbances are driven by latent heat released in organized convection. To explore this possibility, a series of numerical experiments were conducted with a simple, two-layer, quasi-geostrophic model. The convective heating function was treated in the same manner as that employed by various investigators in recent studies of hurricane dynamics. In this formulation, convection is controlled by frictional convergence in the Ekman layer. These numerical experiments show that this heating mechanism, within the framework of the simple dynamical model employed, can produce significant intensification of large-scale disturbances.
Abstract
Disturbances with scales of a few thousand kilometers are commonly observed in the troposphere over the subtropical oceans. Synoptic experience seems to indicate that many of these large-scale disturbances are driven by latent heat released in organized convection. To explore this possibility, a series of numerical experiments were conducted with a simple, two-layer, quasi-geostrophic model. The convective heating function was treated in the same manner as that employed by various investigators in recent studies of hurricane dynamics. In this formulation, convection is controlled by frictional convergence in the Ekman layer. These numerical experiments show that this heating mechanism, within the framework of the simple dynamical model employed, can produce significant intensification of large-scale disturbances.
Abstract
Wave solutions to the linearized, quasi-hydrostatic equations for adiabatic, nonviscous flow on an equatorially oriented beta plane are obtained. The basic current is assumed to be zonal and invariant in both space and time. Only solutions for which the meridional wind component is symmetric with respect to the equator are considered. Disturbances with wavelengths on the order of 103 km. are found to be very nearly nondivergent. The solutions show the meridional wind component to be very nearly geostrophic even at very low latitudes. The perturbation of the zonal wind, however, is highly ageostrophic at the very low latitudes and significantly ageostrophic even in subtropical latitudes.
Abstract
Wave solutions to the linearized, quasi-hydrostatic equations for adiabatic, nonviscous flow on an equatorially oriented beta plane are obtained. The basic current is assumed to be zonal and invariant in both space and time. Only solutions for which the meridional wind component is symmetric with respect to the equator are considered. Disturbances with wavelengths on the order of 103 km. are found to be very nearly nondivergent. The solutions show the meridional wind component to be very nearly geostrophic even at very low latitudes. The perturbation of the zonal wind, however, is highly ageostrophic at the very low latitudes and significantly ageostrophic even in subtropical latitudes.
Abstract
In the treatment of numerical models of symmetrical vortices, balanced radial and vertical velocity components may be obtained from a diagnostic equation first derived by Eliassen. However, when this equation is applied to vortices which resemble tropical cyclones, one finds hyperbolicity in regions where saturated ascent is accompanied by conditional static instability. Eliassen suggests that the equation can, nevertheless, be solved as a boundary-value problem through an iterative technique and predicts that the iterations will produce a solution in the form of a convergent geometric series. We have applied Eliassen's procedure to two vortices. For the first of these, we obtained the numerical values of the first three terms in the series. The results do not confirm Eliassen's suggestion concerning the behavior of the ratio of successive terms in the series. In the second case, 27 terms of the series were obtained. Here, convergence does appear to take place but not in the manner predicted by Eliassen's geometric formula.
Abstract
In the treatment of numerical models of symmetrical vortices, balanced radial and vertical velocity components may be obtained from a diagnostic equation first derived by Eliassen. However, when this equation is applied to vortices which resemble tropical cyclones, one finds hyperbolicity in regions where saturated ascent is accompanied by conditional static instability. Eliassen suggests that the equation can, nevertheless, be solved as a boundary-value problem through an iterative technique and predicts that the iterations will produce a solution in the form of a convergent geometric series. We have applied Eliassen's procedure to two vortices. For the first of these, we obtained the numerical values of the first three terms in the series. The results do not confirm Eliassen's suggestion concerning the behavior of the ratio of successive terms in the series. In the second case, 27 terms of the series were obtained. Here, convergence does appear to take place but not in the manner predicted by Eliassen's geometric formula.
Abstract
The results of a series of numerical experiments which were intended to simulate the warming and developing stages of hurricane formation are discussed. In the experiments, an initially weak cyclone develops into an intense vortex. However, the deepening proceeds too rapidly and meridional circulations which are too intense develop. The inclusion of ground friction and vertical mixing leads to solutions which are even less acceptable. Lateral mixing slows the development but only provides a temporary delay in the generation of an unacceptably intense meridional circulation.
Abstract
The results of a series of numerical experiments which were intended to simulate the warming and developing stages of hurricane formation are discussed. In the experiments, an initially weak cyclone develops into an intense vortex. However, the deepening proceeds too rapidly and meridional circulations which are too intense develop. The inclusion of ground friction and vertical mixing leads to solutions which are even less acceptable. Lateral mixing slows the development but only provides a temporary delay in the generation of an unacceptably intense meridional circulation.
Abstract
Tropical cyclone model experiments are summarized in which the drag coefficient and the analogous exchange coefficients for sensible and latent heat are varied. During the early portions of the immature stage, the response of the model storm follows linear theory and growth is more rapid with larger drag coefficients. However, the ultimate intensity reached by model storms varies inversely with the drag coefficient. The experiments indicate that air-sea exchanges of latent heat are crucial for the development and maintenance of the model storm. The air-sea exchange of sensible heat appears to be far less important.
Experiments conducted with open lateral boundary conditions revealed that the structure and intensity of the mature stage of the model cyclone is relatively insensitive to the initial perturbation and to the size of the computational domain. The time required to reach the mature stage is, however, quite sensitive to these influences.
Comparisons between experiments with open and mechanically closed lateral boundaries show the lateral boundary conditions to be extremely important. For computational domains of 2000 km or less, model cyclones with closed lateral boundaries are less intense than their counterparts with open lateral boundaries. However, the intensity of the closed systems increases markedly with domain size and the experiments suggest that differences due to boundary conditions might be minimized if the domain size exceeded 2000 km.
Abstract
Tropical cyclone model experiments are summarized in which the drag coefficient and the analogous exchange coefficients for sensible and latent heat are varied. During the early portions of the immature stage, the response of the model storm follows linear theory and growth is more rapid with larger drag coefficients. However, the ultimate intensity reached by model storms varies inversely with the drag coefficient. The experiments indicate that air-sea exchanges of latent heat are crucial for the development and maintenance of the model storm. The air-sea exchange of sensible heat appears to be far less important.
Experiments conducted with open lateral boundary conditions revealed that the structure and intensity of the mature stage of the model cyclone is relatively insensitive to the initial perturbation and to the size of the computational domain. The time required to reach the mature stage is, however, quite sensitive to these influences.
Comparisons between experiments with open and mechanically closed lateral boundaries show the lateral boundary conditions to be extremely important. For computational domains of 2000 km or less, model cyclones with closed lateral boundaries are less intense than their counterparts with open lateral boundaries. However, the intensity of the closed systems increases markedly with domain size and the experiments suggest that differences due to boundary conditions might be minimized if the domain size exceeded 2000 km.
EXPERIMENTS WITH A NUMERICAL MODEL OF TROPICAL CYCLONE DEVELOPMENT
Some Effects of Radial Resolution
Abstract
The model assumes the storm to be circularly symmetric and is expressed in z-coordinates. The information levels correspond to pressures in the mean tropical atmosphere of 1015, 900, 700, 500, 300, 200, and 100 mb. The heating function for the cyclone scale motion is simulated by a convective adjustment of the lapse rate towards a pseudoadiabat representative of ascent from the surface boundary layer. The rate of this adjustment is calibrated so that the vertically integrated heating function is related to the upward flux of water vapor through the surface boundary layer.
Experiments with 10- and 20-km radial resolution are compared. The 10-km calculation yields a storm with more realistic structure. The 20-km case does not contain a well-defined eye, whereas the 10-km experiment does. Rainfall, kinetic energy production, and efficiency are all larger with 20-km resolution. In both experiments, computational damping is an important component of the kinetic energy budget; however, the total dissipation of kinetic energy (computational plus explicit) is fairly reasonable in comparison to that found in empirical studies.
Abstract
The model assumes the storm to be circularly symmetric and is expressed in z-coordinates. The information levels correspond to pressures in the mean tropical atmosphere of 1015, 900, 700, 500, 300, 200, and 100 mb. The heating function for the cyclone scale motion is simulated by a convective adjustment of the lapse rate towards a pseudoadiabat representative of ascent from the surface boundary layer. The rate of this adjustment is calibrated so that the vertically integrated heating function is related to the upward flux of water vapor through the surface boundary layer.
Experiments with 10- and 20-km radial resolution are compared. The 10-km calculation yields a storm with more realistic structure. The 20-km case does not contain a well-defined eye, whereas the 10-km experiment does. Rainfall, kinetic energy production, and efficiency are all larger with 20-km resolution. In both experiments, computational damping is an important component of the kinetic energy budget; however, the total dissipation of kinetic energy (computational plus explicit) is fairly reasonable in comparison to that found in empirical studies.
Abstract
The tropical cyclone model described in previous reports is extended to include an explicit water vapor cycle. Results of experiments that examine effects due to initial humidity conditions, radial resolution, and the finite-difference scheme are discussed. Growth to the mature stage is more rapid in the moist environment, but peak intensity is not strongly affected by the initial moisture content. Rainfall rates are quite reasonable, and nonconvective precipitation is found to be a significant proportion of the total rainfall, in agreement with recent empirical results. Experiments with upstream differencing yield more realistic solutions than do experiments with centered differences. This surprising result is discussed in detail.
Abstract
The tropical cyclone model described in previous reports is extended to include an explicit water vapor cycle. Results of experiments that examine effects due to initial humidity conditions, radial resolution, and the finite-difference scheme are discussed. Growth to the mature stage is more rapid in the moist environment, but peak intensity is not strongly affected by the initial moisture content. Rainfall rates are quite reasonable, and nonconvective precipitation is found to be a significant proportion of the total rainfall, in agreement with recent empirical results. Experiments with upstream differencing yield more realistic solutions than do experiments with centered differences. This surprising result is discussed in detail.
Abstract
The accuracy of a numerical technique devised for the purpose of obtaining approximate solutions to an initial value problem defined by linearized equations for quasi-geostrophic flow is tested in certain simple cases for which it is possible to obtain closed solutions. The numerical technique is found to be extremely accurate.
Abstract
The accuracy of a numerical technique devised for the purpose of obtaining approximate solutions to an initial value problem defined by linearized equations for quasi-geostrophic flow is tested in certain simple cases for which it is possible to obtain closed solutions. The numerical technique is found to be extremely accurate.
Abstract
Simulations of the natural (unmodified) evolution of tropical cyclones with a circularly symmetric model suggest that seeding of hurricanes with silver iodide at radii greater than that of the surface wind maximum might be more effective in decreasing the surface wind maximum than seedings at or within the wind maximum. Seeding simulations with the model strongly suggest that the model storm responds in the sense anticipated. On the other hand, simulated seedings at radii less than that of the surface wind maximum produce temporary increases in the strength of the maximum. However, termination of the seeding is followed by a rapid recovery of the modified storm to a state close to that of the control.
Abstract
Simulations of the natural (unmodified) evolution of tropical cyclones with a circularly symmetric model suggest that seeding of hurricanes with silver iodide at radii greater than that of the surface wind maximum might be more effective in decreasing the surface wind maximum than seedings at or within the wind maximum. Seeding simulations with the model strongly suggest that the model storm responds in the sense anticipated. On the other hand, simulated seedings at radii less than that of the surface wind maximum produce temporary increases in the strength of the maximum. However, termination of the seeding is followed by a rapid recovery of the modified storm to a state close to that of the control.
