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- Author or Editor: Yoshimitsu Ogura x
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Abstract
The equations of motion for an incompressible fluid have been integrated numerically, as an initial value problem, for the axially-symmetric motion produced by release of an isolated lighter mass of the same fluid. The effect of viscosity is included only implicitly in the finite-difference numerical process. The numerical solutions exhibit the similarity (shape-preserving) stage assumed in theoretical treatments and observed in tank experiments. The computations have been repeated for different values of the total weight deficiency (or excess) of the “thermal.” The results agree approximately with the relationships predicted by dimensional analysis. The values of various parameters are compared with those obtained in tank experiments and encouraging agreement between them is found. Truncation errors involved in the numerical integration are briefly discussed.
Abstract
The equations of motion for an incompressible fluid have been integrated numerically, as an initial value problem, for the axially-symmetric motion produced by release of an isolated lighter mass of the same fluid. The effect of viscosity is included only implicitly in the finite-difference numerical process. The numerical solutions exhibit the similarity (shape-preserving) stage assumed in theoretical treatments and observed in tank experiments. The computations have been repeated for different values of the total weight deficiency (or excess) of the “thermal.” The results agree approximately with the relationships predicted by dimensional analysis. The values of various parameters are compared with those obtained in tank experiments and encouraging agreement between them is found. Truncation errors involved in the numerical integration are briefly discussed.
Abstract
Numerical integrations are performed for the equations governing two-dimensional convection flows in a fluid layer confined between two horizontal parallel plates and heated uniformly from below with free surface boundary conditions at the bottom and top of the fluid. In comparison with several previous works using a similar approach, a special feature in this work is that a large horizontal domain (10 times the critical wavelength or 28.28 times the height) is covered by the grid net so that the preferred mode of finite-amplitude convection flows is investigated.
The Rayleigh number covered here is less than four times the critical Rayleigh number. Either random or sinusoidal perturbations with various wavelengths and with various amplitudes are introduced to initiate the motion. In all cases considered, the system achieves an approximate steady state. It is found that: 1) steady-state solutions are not determined uniquely by only the Rayleigh and Prandtl numbers, but also by the initial conditions; 2) a second stability curve or a nonlinear stability curve exists as the dividing line between those cells which exhibit size-adjustment toward a more preferred mode and those which do not; 3) the preferred modes in steady-state solutions depend not only on the wavelength of the initial sinusoidal perturbations but also on their amplitudes; and 4) the extremum principle, such as the maximum heat transport, may be inapplicable in determining the preferred mode.
Abstract
Numerical integrations are performed for the equations governing two-dimensional convection flows in a fluid layer confined between two horizontal parallel plates and heated uniformly from below with free surface boundary conditions at the bottom and top of the fluid. In comparison with several previous works using a similar approach, a special feature in this work is that a large horizontal domain (10 times the critical wavelength or 28.28 times the height) is covered by the grid net so that the preferred mode of finite-amplitude convection flows is investigated.
The Rayleigh number covered here is less than four times the critical Rayleigh number. Either random or sinusoidal perturbations with various wavelengths and with various amplitudes are introduced to initiate the motion. In all cases considered, the system achieves an approximate steady state. It is found that: 1) steady-state solutions are not determined uniquely by only the Rayleigh and Prandtl numbers, but also by the initial conditions; 2) a second stability curve or a nonlinear stability curve exists as the dividing line between those cells which exhibit size-adjustment toward a more preferred mode and those which do not; 3) the preferred modes in steady-state solutions depend not only on the wavelength of the initial sinusoidal perturbations but also on their amplitudes; and 4) the extremum principle, such as the maximum heat transport, may be inapplicable in determining the preferred mode.
Abstract
Based upon an argument by Charney and Eliassen, a tropical cyclone is envisaged as a combined system of a quasi-gradient circular vortex and a slow meridional circulation. The driving mechanism of this circulation is the release of latent heat, which is in turn controlled by the mass convergence in the surface boundary layer. A consistent set of dynamic equations is derived from scale and energy considerations, followed by the presentation of a two-level approximation in which potential temperature is specified only at the mid-tropospheric level. A perturbation analysis based on the linearized system shows that the exponential growth rates are of the correct order of magnitude.
A numerical integration of this set of equations is performed, starting from hypothetical initial distributions of tangential velocities. Unlike the too rapid and too intense development of meridional circulations observed in the numerical integrations of some previous hurricane models, the result obtained here shows a slowly developing circulation; the maximum tangential velocity is increased from 5 m sec−1 (initial value) to 40 m sec−1 in 60 hours and this velocity is twice as large as the maximum inflow. However, the circulation does not seem to approach a steady state. Other shortcomings of the model as revealed by the numerical integration are discussed.
Abstract
Based upon an argument by Charney and Eliassen, a tropical cyclone is envisaged as a combined system of a quasi-gradient circular vortex and a slow meridional circulation. The driving mechanism of this circulation is the release of latent heat, which is in turn controlled by the mass convergence in the surface boundary layer. A consistent set of dynamic equations is derived from scale and energy considerations, followed by the presentation of a two-level approximation in which potential temperature is specified only at the mid-tropospheric level. A perturbation analysis based on the linearized system shows that the exponential growth rates are of the correct order of magnitude.
A numerical integration of this set of equations is performed, starting from hypothetical initial distributions of tangential velocities. Unlike the too rapid and too intense development of meridional circulations observed in the numerical integrations of some previous hurricane models, the result obtained here shows a slowly developing circulation; the maximum tangential velocity is increased from 5 m sec−1 (initial value) to 40 m sec−1 in 60 hours and this velocity is twice as large as the maximum inflow. However, the circulation does not seem to approach a steady state. Other shortcomings of the model as revealed by the numerical integration are discussed.
Abstract
As a preliminary attempt to investigate the applicability of the turbulence theory to the large-scale atmospheric phenomena, the experimental test is made of the isotropy for the large-scale motion of the atmosphere at the 300-mb level. Uses are made of one-dimensional power- and cross-spectra of wind velocities, presented recently by Benton and Kahn (1957). The requirement of isotropy seems to be satisfied at lat 20N and 70N, for the harmonics whose wave lengths lie between 60 deg and 20 deg of longitude. The latter is the shortest wave length analyzed. In the region between lat 30N and 60N, the amount of kinetic energy in the north-south component of eddy velocities, in comparison with that in east-west component, is found to be more than that expected from the isotropic relations for the same domain of wave number.
Abstract
As a preliminary attempt to investigate the applicability of the turbulence theory to the large-scale atmospheric phenomena, the experimental test is made of the isotropy for the large-scale motion of the atmosphere at the 300-mb level. Uses are made of one-dimensional power- and cross-spectra of wind velocities, presented recently by Benton and Kahn (1957). The requirement of isotropy seems to be satisfied at lat 20N and 70N, for the harmonics whose wave lengths lie between 60 deg and 20 deg of longitude. The latter is the shortest wave length analyzed. In the region between lat 30N and 60N, the amount of kinetic energy in the north-south component of eddy velocities, in comparison with that in east-west component, is found to be more than that expected from the isotropic relations for the same domain of wave number.
Abstract
An attempt is made to see what the results of the application of the methods of Heisenberg are to isotropic temperature fluctuations in a stationary isotropic turbulence, under the restriction that temperature differences are too small to have any effect on the velocity field. The power spectrum for temperature fluctuations, thus deduced, degenerates to those obtained previously by Corrsin at two extremes-i.e., in intermediate and highest wave number ranges. The shape of the correlation function is also derived and compared with the experimental results of Shiotani. Finally, the thermal microscale and the size of the smallest eddies are expressed in terms of the turbulent Reynolds number and Péclet number or the fluid Prandtl number.
Abstract
An attempt is made to see what the results of the application of the methods of Heisenberg are to isotropic temperature fluctuations in a stationary isotropic turbulence, under the restriction that temperature differences are too small to have any effect on the velocity field. The power spectrum for temperature fluctuations, thus deduced, degenerates to those obtained previously by Corrsin at two extremes-i.e., in intermediate and highest wave number ranges. The shape of the correlation function is also derived and compared with the experimental results of Shiotani. Finally, the thermal microscale and the size of the smallest eddies are expressed in terms of the turbulent Reynolds number and Péclet number or the fluid Prandtl number.
Abstract
The modification of the power spectrum for the Laplacian of a variable, associated with the use of finite differences instead of derivatives, is discussed for an isotropic scalar field. The results permit one to specify a finite difference scheme which reduces considerably the systematic truncation error in the Laplacian operator.
Abstract
The modification of the power spectrum for the Laplacian of a variable, associated with the use of finite differences instead of derivatives, is discussed for an isotropic scalar field. The results permit one to specify a finite difference scheme which reduces considerably the systematic truncation error in the Laplacian operator.
Abstract
Numerical integrations are performed for the equations governing two-dimensional convection flows in a fluid confined between two horizontal plates. A situation considered here is that local heating at a time-independent rate is provided at the middle level of the fluid so that the upper half of the fluid is destabilized and the lower half stabilized. It is shown that steady-state solutions are obtained when the Rayleigh number (R) is 1.1 times Rc (critical Rayleigh number at which convection sets in according to the linearized theory). For three cases where R=1.5 Rc, 2 Rc and 3 Rc, time-dependent solutions are obtained which describe extremely regular and repeatable convection flows. The flow pattern is such that plume-like cells generated by heating move horizontally, merge with neighboring plumes, and new plumes are generated. This process is repeated. Time-dependent but irregular solutions are obtained for R=5 Rc and beyond.
Abstract
Numerical integrations are performed for the equations governing two-dimensional convection flows in a fluid confined between two horizontal plates. A situation considered here is that local heating at a time-independent rate is provided at the middle level of the fluid so that the upper half of the fluid is destabilized and the lower half stabilized. It is shown that steady-state solutions are obtained when the Rayleigh number (R) is 1.1 times Rc (critical Rayleigh number at which convection sets in according to the linearized theory). For three cases where R=1.5 Rc, 2 Rc and 3 Rc, time-dependent solutions are obtained which describe extremely regular and repeatable convection flows. The flow pattern is such that plume-like cells generated by heating move horizontally, merge with neighboring plumes, and new plumes are generated. This process is repeated. Time-dependent but irregular solutions are obtained for R=5 Rc and beyond.
Abstract
The adaptation of the deep convection equations of Ogura and Phillips to moist convection results in an implicit relationship between temperature, potential temperature, pressure, and saturation vapor pressure. Typically, the pressure is treated as a known function of height to eliminate this condition. The effect of this approximation is investigated by numerically integrating the primitive equations in two-dimensional Cartesian coordinates. The model includes precipitation, and the equations are integrated for the life cycle of a strong cumulus cell. The result indicates that the non-dimensional pressure perturbation is notably an order smaller than scale analysis indicates it might be and that the deviation from the environmental pressure can be ignored in determining the saturation vapor pressure. This is partly because the pressure diagnostic equation acts to smooth out the pressure distribution.
Abstract
The adaptation of the deep convection equations of Ogura and Phillips to moist convection results in an implicit relationship between temperature, potential temperature, pressure, and saturation vapor pressure. Typically, the pressure is treated as a known function of height to eliminate this condition. The effect of this approximation is investigated by numerically integrating the primitive equations in two-dimensional Cartesian coordinates. The model includes precipitation, and the equations are integrated for the life cycle of a strong cumulus cell. The result indicates that the non-dimensional pressure perturbation is notably an order smaller than scale analysis indicates it might be and that the deviation from the environmental pressure can be ignored in determining the saturation vapor pressure. This is partly because the pressure diagnostic equation acts to smooth out the pressure distribution.
Abstract
A cumulus cloud population is determined over the trade-wind region under an undisturbed weather condition from the large-scale heat and moisture budgets. The BOMEX data during the period 22–23 June 1969 are used. Six classes of clouds (A–F) are considered. Each class of clouds changes the large-scale mean temperature and humidity through condensation, evaporation and convective transport processes. The change due to each class of clouds is determined using the time-dependent, two-dimensional, axisymmetric cloud model developed by Soong and Ogura (1973).
It is found that the cloud population, consisting of 66.4 A clouds, 8.9 D clouds and 1.6 E clouds km−2 DAY−1, satisfies approximately the large-scale heat and moisture budget requirements. The cloud top heights of the three classes of clouds are 0.8, 1.6 and 2.0 km, respectively, and the cloud radii at the cloud base level during the mature stage are 62.5, 150 and 225 m, respectively. Consequently, the fractional area coverage of the predicted cloud population is 4.5%. Among the three classes of clouds, only E clouds penetrate into the trade-wind inversion layer. Approximately 18% of the total convective mass flux at the cloud base level is associated with the E clouds. The estimated Bowen ratio from the cloud population is less than 0.1. The estimated evaporation rate is 7.4 mm day−1 and the precipitation rate 0.29 mm day−1. These values are in good agreement with those observed during the period considered.
Abstract
A cumulus cloud population is determined over the trade-wind region under an undisturbed weather condition from the large-scale heat and moisture budgets. The BOMEX data during the period 22–23 June 1969 are used. Six classes of clouds (A–F) are considered. Each class of clouds changes the large-scale mean temperature and humidity through condensation, evaporation and convective transport processes. The change due to each class of clouds is determined using the time-dependent, two-dimensional, axisymmetric cloud model developed by Soong and Ogura (1973).
It is found that the cloud population, consisting of 66.4 A clouds, 8.9 D clouds and 1.6 E clouds km−2 DAY−1, satisfies approximately the large-scale heat and moisture budget requirements. The cloud top heights of the three classes of clouds are 0.8, 1.6 and 2.0 km, respectively, and the cloud radii at the cloud base level during the mature stage are 62.5, 150 and 225 m, respectively. Consequently, the fractional area coverage of the predicted cloud population is 4.5%. Among the three classes of clouds, only E clouds penetrate into the trade-wind inversion layer. Approximately 18% of the total convective mass flux at the cloud base level is associated with the E clouds. The estimated Bowen ratio from the cloud population is less than 0.1. The estimated evaporation rate is 7.4 mm day−1 and the precipitation rate 0.29 mm day−1. These values are in good agreement with those observed during the period considered.
