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- Author or Editor: YOSHIO KURIHARA x
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Abstract
A new method of moist convective adjustment is presented. A large-scale state of the atmosphere is assumed to be in a thermodynamically critical condition when a hypothetical cloud element can develop. As a result of the convective adjustment, the atmosphere is altered to a new state that is marginal or unfavorable to the occurrence of a free moist convection. The numerical scheme of the adjustment is described in detail.
Abstract
A new method of moist convective adjustment is presented. A large-scale state of the atmosphere is assumed to be in a thermodynamically critical condition when a hypothetical cloud element can develop. As a result of the convective adjustment, the atmosphere is altered to a new state that is marginal or unfavorable to the occurrence of a free moist convection. The numerical scheme of the adjustment is described in detail.
Abstract
A tropical cyclone simulated in an axisymmetric numerical model is analyzed in detail from various aspects in order to deepen the understanding of the basic mechanisms of its evolution. Namely, the budget equations of temperature, moisture, relative angular momentum, vorticity, radial-vertical circulation, and kinetic energy are investigated for the different stages of the development of a tropical cyclone. The spatial distributions of each term in the budget equations are shown and their role in the following processes are discussed.
In the pre-deepening stage of a large weak vortex in a conditionally unstable atmosphere, a solenoidal field is formed as a result of a delicate heat budget which depends on the static stability and the moisture content. The baroclinicity field thus established drives the system into a deepening stage. A positive feedback process builds up a warm moist core, accelerates the radial-vertical circulation, and intensifies the moist convection. A net outflow of mass from the central region and a resultant drop of central surface pressure take place during this period. The relative angular momentum of the inner column as a whole increases through convergence of relative angular momentum. In terms of relative vorticity, intensification and shrinking of the vortex is due to the combined effects of advection, horizontal convergence and twisting. At the end of the deepening stage, conditional instability in the central region is neutralized. The moment due to Coriolis force acting on the intensified azimuthal flow counterbalances the baroclinicity vector, so that the acceleration of radial-vertical flow ceases. Concentration of relative angular momentum and vorticity in the central region also levels off. In the budget of these quantities, the role of both vertical and lateral steam becomes important. In the troposphere, except the upper part and the boundary layer, the gradient wind relationship is established between the pressure field and the azimuthal flow. In the mature stage, the status in the inner region is quasi-stationary while that of the outer area keeps changing slowly. The importance of evaporation at the central area for the maintenance of an intense tropical cyclone is demonstrated in an additional experiment.
Abstract
A tropical cyclone simulated in an axisymmetric numerical model is analyzed in detail from various aspects in order to deepen the understanding of the basic mechanisms of its evolution. Namely, the budget equations of temperature, moisture, relative angular momentum, vorticity, radial-vertical circulation, and kinetic energy are investigated for the different stages of the development of a tropical cyclone. The spatial distributions of each term in the budget equations are shown and their role in the following processes are discussed.
In the pre-deepening stage of a large weak vortex in a conditionally unstable atmosphere, a solenoidal field is formed as a result of a delicate heat budget which depends on the static stability and the moisture content. The baroclinicity field thus established drives the system into a deepening stage. A positive feedback process builds up a warm moist core, accelerates the radial-vertical circulation, and intensifies the moist convection. A net outflow of mass from the central region and a resultant drop of central surface pressure take place during this period. The relative angular momentum of the inner column as a whole increases through convergence of relative angular momentum. In terms of relative vorticity, intensification and shrinking of the vortex is due to the combined effects of advection, horizontal convergence and twisting. At the end of the deepening stage, conditional instability in the central region is neutralized. The moment due to Coriolis force acting on the intensified azimuthal flow counterbalances the baroclinicity vector, so that the acceleration of radial-vertical flow ceases. Concentration of relative angular momentum and vorticity in the central region also levels off. In the budget of these quantities, the role of both vertical and lateral steam becomes important. In the troposphere, except the upper part and the boundary layer, the gradient wind relationship is established between the pressure field and the azimuthal flow. In the mature stage, the status in the inner region is quasi-stationary while that of the outer area keeps changing slowly. The importance of evaporation at the central area for the maintenance of an intense tropical cyclone is demonstrated in an additional experiment.
Abstract
A study of the seasonal change of a climaticc state of the atmosphere is made through the investigation of a response of a statistical-dynamical model to insolation having seasonal variation. Numerical experiments are performed for the two hypothetical cases: the land-covered earth (LCE) and the ocean-covered earth (OCE). The two cases differ in the thermal and aerodynamical conditions at the surface, and a hydrologic cycle is incorporated only in the model for OCE.
Numerical integrations are carried out until the same climatic state as one year before reappears. Then, annual marches of the zonal mean field, the eddy statistics, and the energetics are analyzed.
Baroclinicity at the middle latitudes is noticeable, in summertime, only for the OCE. Strong upper level easterly flow evolved at low latitudes for the LCE. The mean meridional circulation at low latitudes for both LCE and OCE is characterized by one big Hadley cell extending from the summer into the winter hemisphere. In the OCE, the water vapor is exported from the subtropics equatorward by the mean meridional circulation and poleward by large-scale eddies. The effect of ocean is to moderate the seasonal change of eddy activity so that the eddy transport of heat for the OCE is smaller in winter and larger in summer than that for the LCE.
The additional experiments show the dependency of the eddy statistics of the model an the internal viscosity. It is also shown that the after-effect of a sudden shock lasts about five months in the atmosphere for the OCE.
Abstract
A study of the seasonal change of a climaticc state of the atmosphere is made through the investigation of a response of a statistical-dynamical model to insolation having seasonal variation. Numerical experiments are performed for the two hypothetical cases: the land-covered earth (LCE) and the ocean-covered earth (OCE). The two cases differ in the thermal and aerodynamical conditions at the surface, and a hydrologic cycle is incorporated only in the model for OCE.
Numerical integrations are carried out until the same climatic state as one year before reappears. Then, annual marches of the zonal mean field, the eddy statistics, and the energetics are analyzed.
Baroclinicity at the middle latitudes is noticeable, in summertime, only for the OCE. Strong upper level easterly flow evolved at low latitudes for the LCE. The mean meridional circulation at low latitudes for both LCE and OCE is characterized by one big Hadley cell extending from the summer into the winter hemisphere. In the OCE, the water vapor is exported from the subtropics equatorward by the mean meridional circulation and poleward by large-scale eddies. The effect of ocean is to moderate the seasonal change of eddy activity so that the eddy transport of heat for the OCE is smaller in winter and larger in summer than that for the LCE.
The additional experiments show the dependency of the eddy statistics of the model an the internal viscosity. It is also shown that the after-effect of a sudden shock lasts about five months in the atmosphere for the OCE.
Abstract
A statistical-dynamical, two-layer model of the atmosphere is constructed for the simulation of the climatic state of the global circulation.
The meteorological variables, velocity, temperature and pressure, are decomposed into their zonal mean parts and eddy parts or deviations. The state of circulation is expressed by the zonal mean parts as well as eddy statistics which are the zonal averages of the product of the deviations. Eddy statistics such as the amount of eddy kinetic energy, and eddy transfer of heat and angular momentum are longitudinally integrated measures of the intensity and structure of individual synoptic-scale disturbances.
The equations for the zonal means of wind, temperature and pressure and that of eddy kinetic energy are obtained from the equations of motion, the thermodynamical equation, and the continuity equation, and include the terms depending on the eddy statistics. The prediction equation for the horizontal eddy transfer of heat, as well as an estimate of the vertical eddy transfer of heat and angular momentum, are derived under the quasi-geostrophic assumption. The horizontal eddy transfer of momentum is estimated by a diagnostic formula similar to the one used by Smagorinsky. The results of theoretical studies of long waves are utilized to determine the pressure interaction term, the characteristic size of eddies, and the phase speed which are involved in certain of the equations.
The model atmosphere expressed by the closed system of equations thus established is controlled by insulation, parameters for radiative heat transfer, static stability, lower boundary conditions for the exchange of momentum and heat, and parameters for horizontal stress and for the lateral diffusion of heat in the free atmosphere due to small-scale eddies. The present model does not include the effect of lateral transfer of latent energy.
A numerical experiment is performed for a fixed annual mean insulation and a given specification of other control factors. The model consists of two layers, each having 48 zonal rings between the north and south poles. Starting from rest and a constant temperature at the middle level, the integration is done for the first 50 days without eddies. A small amount of eddy kinetic energy is superimposed on the axially symmetric flow at 50 days. Then, the primary features of the actual circulation, such as the jet stream, the Ferrel cell in mean meridional circulation, and the poleward eddy transport of heat, evolve, and a quasi-equilibrium state with a mode of fluctuation is attained.
Abstract
A statistical-dynamical, two-layer model of the atmosphere is constructed for the simulation of the climatic state of the global circulation.
The meteorological variables, velocity, temperature and pressure, are decomposed into their zonal mean parts and eddy parts or deviations. The state of circulation is expressed by the zonal mean parts as well as eddy statistics which are the zonal averages of the product of the deviations. Eddy statistics such as the amount of eddy kinetic energy, and eddy transfer of heat and angular momentum are longitudinally integrated measures of the intensity and structure of individual synoptic-scale disturbances.
The equations for the zonal means of wind, temperature and pressure and that of eddy kinetic energy are obtained from the equations of motion, the thermodynamical equation, and the continuity equation, and include the terms depending on the eddy statistics. The prediction equation for the horizontal eddy transfer of heat, as well as an estimate of the vertical eddy transfer of heat and angular momentum, are derived under the quasi-geostrophic assumption. The horizontal eddy transfer of momentum is estimated by a diagnostic formula similar to the one used by Smagorinsky. The results of theoretical studies of long waves are utilized to determine the pressure interaction term, the characteristic size of eddies, and the phase speed which are involved in certain of the equations.
The model atmosphere expressed by the closed system of equations thus established is controlled by insulation, parameters for radiative heat transfer, static stability, lower boundary conditions for the exchange of momentum and heat, and parameters for horizontal stress and for the lateral diffusion of heat in the free atmosphere due to small-scale eddies. The present model does not include the effect of lateral transfer of latent energy.
A numerical experiment is performed for a fixed annual mean insulation and a given specification of other control factors. The model consists of two layers, each having 48 zonal rings between the north and south poles. Starting from rest and a constant temperature at the middle level, the integration is done for the first 50 days without eddies. A small amount of eddy kinetic energy is superimposed on the axially symmetric flow at 50 days. Then, the primary features of the actual circulation, such as the jet stream, the Ferrel cell in mean meridional circulation, and the poleward eddy transport of heat, evolve, and a quasi-equilibrium state with a mode of fluctuation is attained.
Abstract
Development of the band structure in a tropical cyclone is investigated by solving an eigenvalue problem for perturbations of spiral shape. The perturbations are superposed on a baroclinic circular vortex accompanied with a radial and vertical basic flow.
It is shown that the spiral bands in three different modes may be intensified in an inner area of a tropical cyclone. The baroclinicity of a basic field is not required for the development of bands in any mode. A spiral band which propagates outward can grow in the presence of the horizontal shear of the basic azimuthal flow. Without the basic circular vortex, this band is reduced to a neutral gravity-inertia wave with a particular vertical structure. The unstable spiral in this mode takes a pattern which extends clockwise from the center of a storm in the Northern Hemisphere. An azimuthal wavenumber 2 and a radial scale (twice the band width) of 200 km are preferred by this band. Another band with the characteristics of an inward propagating gravity wave may be excited in an inner area of a storm by its strong response to the effect of diabatic heating. The third kind of band has the features of a geostrophic mode and moves inward. Its development in an inner area is associated with the horizontal shear of the basic circular flow. The bands of the second and the third mode have not been observed in real storms. Dynamical behavior as well as the energetics of a band are discussed for each mode.
There exists practically no instability in the outer region of the storm for any kind of spiral band. It is speculated that a band which grows in an inner area and propagates outward, i.e., the band of the first mode mentioned above, may become a neutral spiral while moving toward the outer region. Some of the outer spiral bands observed in real tropical cyclones may be interpreted as this kind of internal gravity-inertia waves.
Abstract
Development of the band structure in a tropical cyclone is investigated by solving an eigenvalue problem for perturbations of spiral shape. The perturbations are superposed on a baroclinic circular vortex accompanied with a radial and vertical basic flow.
It is shown that the spiral bands in three different modes may be intensified in an inner area of a tropical cyclone. The baroclinicity of a basic field is not required for the development of bands in any mode. A spiral band which propagates outward can grow in the presence of the horizontal shear of the basic azimuthal flow. Without the basic circular vortex, this band is reduced to a neutral gravity-inertia wave with a particular vertical structure. The unstable spiral in this mode takes a pattern which extends clockwise from the center of a storm in the Northern Hemisphere. An azimuthal wavenumber 2 and a radial scale (twice the band width) of 200 km are preferred by this band. Another band with the characteristics of an inward propagating gravity wave may be excited in an inner area of a storm by its strong response to the effect of diabatic heating. The third kind of band has the features of a geostrophic mode and moves inward. Its development in an inner area is associated with the horizontal shear of the basic circular flow. The bands of the second and the third mode have not been observed in real storms. Dynamical behavior as well as the energetics of a band are discussed for each mode.
There exists practically no instability in the outer region of the storm for any kind of spiral band. It is speculated that a band which grows in an inner area and propagates outward, i.e., the band of the first mode mentioned above, may become a neutral spiral while moving toward the outer region. Some of the outer spiral bands observed in real tropical cyclones may be interpreted as this kind of internal gravity-inertia waves.
Abstract
The numerical properties of the trapezoidal implicit, the backward implicit, and partly implicit methods are investigated. The computational stability of these methods, the selective damping of waves, and the accuracy of the predicted wave are discussed primarily for wave equations in the simple form. Then, their applicability to the integration of the primitive equations is considered for a system of linearized equations.
The characteristic features of four iterative methods, each of which consists of a predictor and a corrector to be used only once, are also described.
Abstract
The numerical properties of the trapezoidal implicit, the backward implicit, and partly implicit methods are investigated. The computational stability of these methods, the selective damping of waves, and the accuracy of the predicted wave are discussed primarily for wave equations in the simple form. Then, their applicability to the integration of the primitive equations is considered for a system of linearized equations.
The characteristic features of four iterative methods, each of which consists of a predictor and a corrector to be used only once, are also described.
Abstract
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Abstract
A new spherical grid system whose grid density on the globe is almost homogeneous is proposed. The elementary rules of finite differencing on the grid system are defined so that a desirable condition for numerical area integration is satisfied.
The integrations of primitive equations for a barotropic atmosphere with free surface are made. The patterns of initial fields are the same as Phillips used in 1959 for a test of his map projection system and computation schemes. Ten test runs are performed for a period of 16 days. Three of these are without viscosity and integrated with different time integration schemes. Four runs include the effect of non-linear viscosity with different coefficients, and the remaining three are computed with different amounts of linear viscosity. A noticeable distortion of the flow pattern does not occur in an early period in any run. Analyses of the results suggest that the damping of high frequency oscillation of both long and short wavelengths can be achieved by an iterative time integration scheme, e.g., the modified Euler-backward iteration method, with little effect on the prediction of a trend of the meteorological wave. Either the non-linear or the linear viscosity can be used to suppress a growth of short waves of both low and high frequency modes, if the optimum amount of viscosity for that purpose does not exceed the amount representing the actual diffusion process in the atmosphere. Analyses are also made concerning the effects caused by different specifications of the parameter in the viscosity term in the equations.
Abstract
A new spherical grid system whose grid density on the globe is almost homogeneous is proposed. The elementary rules of finite differencing on the grid system are defined so that a desirable condition for numerical area integration is satisfied.
The integrations of primitive equations for a barotropic atmosphere with free surface are made. The patterns of initial fields are the same as Phillips used in 1959 for a test of his map projection system and computation schemes. Ten test runs are performed for a period of 16 days. Three of these are without viscosity and integrated with different time integration schemes. Four runs include the effect of non-linear viscosity with different coefficients, and the remaining three are computed with different amounts of linear viscosity. A noticeable distortion of the flow pattern does not occur in an early period in any run. Analyses of the results suggest that the damping of high frequency oscillation of both long and short wavelengths can be achieved by an iterative time integration scheme, e.g., the modified Euler-backward iteration method, with little effect on the prediction of a trend of the meteorological wave. Either the non-linear or the linear viscosity can be used to suppress a growth of short waves of both low and high frequency modes, if the optimum amount of viscosity for that purpose does not exceed the amount representing the actual diffusion process in the atmosphere. Analyses are also made concerning the effects caused by different specifications of the parameter in the viscosity term in the equations.
Abstract
Through the time integration of a simple numerical model, the transfomation of a tropical easterly wave into a tropical depression was investigated. The initial condition selected for the model is a slowly decaying adiabatic linear normal mode resembling an easterly wave. It was found that the addition of a CISK (conditional instability of the second kind) type heating effect to the model results in the growth of the wave. Addition of the nonlinearity effect alone, which includes the nonlinear zonal advection and vertical stretching of relative vorticity, has little impact on the wave evolution. However, if the above nonlinearity effect is combined with the heating effect, it can cause the contraction of the disturbance and enhance the development The initial free wave undergoes significant structural changes during its transformation into a developing system.
Experiments were also performed for three different waves under various basic flow conditions. The obtained results agree with a conclusion of the three-dimensional simulation experiments by Tuleya and Kurihara; the coupling between the upper-level wind and the propagating disturbance at low levels may be an important mechanism in the formation of a tropical depression in the trough region of an easterly wave.
Abstract
Through the time integration of a simple numerical model, the transfomation of a tropical easterly wave into a tropical depression was investigated. The initial condition selected for the model is a slowly decaying adiabatic linear normal mode resembling an easterly wave. It was found that the addition of a CISK (conditional instability of the second kind) type heating effect to the model results in the growth of the wave. Addition of the nonlinearity effect alone, which includes the nonlinear zonal advection and vertical stretching of relative vorticity, has little impact on the wave evolution. However, if the above nonlinearity effect is combined with the heating effect, it can cause the contraction of the disturbance and enhance the development The initial free wave undergoes significant structural changes during its transformation into a developing system.
Experiments were also performed for three different waves under various basic flow conditions. The obtained results agree with a conclusion of the three-dimensional simulation experiments by Tuleya and Kurihara; the coupling between the upper-level wind and the propagating disturbance at low levels may be an important mechanism in the formation of a tropical depression in the trough region of an easterly wave.
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