Shin Ichi Takehiro

Penetration of columnar convection into an outer stably stratified layer in rapidly rotating spherical fluid shells

Abstract Penetration of columnar convection in a rapidly rotating spherical shell into a stably stratified fluid layer near the outer boundary is investigated. An analytical expression for the penetration thickness is derived by considering perturbations to a stably stratified rotating Boussinesq fluid in a semi-infinite region with the rotation axis tilted relative to the gravity axis. Solutions for the response to vortical motion applied at the bottom boundary show that the penetration thickness is proportional to the angular velocity of the system and to the horizontal scale of the vortices, and inversely proportional to the Brunt–Vaisala frequency in the stratified layer. Thus the stratification acts as a low-pass filter to forcing from below. The analytic expression for the penetration thickness gives good agreement with numerical results for critical convection in a rotating spherical shell with a stably stratified outer layer. The results suggest that if deep convection is to penetrate the stratified layer observed by the Galileo probe then the horizontal scale needs to be more than several thousand kilometers. Parameter values from recent studies of the thermal history of the Earth’s core also suggest that any convection columns with horizontal scale larger than several hundred kilometers would be expected to penetrate into any stable layer in the outer part of the Earth’s fluid outer core when the Lorentz force plays a subdominant role.

Numerical modeling of Jupiter's moist convection layer

Moist convection of Jupiters atmosphere is examined using a large-domain two-dimensional fluid dynamical model with simplified cloud microphysics of water. The result shows that the water condensation level acts as a dynamical and compositional boundary. The convection below the condensation level is characterized by a steady regular cellular structure and a homogeneous distribution of water mixing ratio. Above the condensation level, cloud elements accompanied by the upward motion develop and disappear irregularly but successively, and water mixing ratio is highly inhomogeneous. The horizontal average of mixing ratio decreases rapidly with height just above the condensation level, resulting in a distinctive stable layer at 5 bar. The stable layer prevents the air masses above and below it from mixing with each other. As a result, the upper dry air does not reach 20 bar level, where the Galileo probe observed low humidity.

A Numerical Study on Appearance of the Runaway Greenhouse State of a Three-Dimensional Gray Atmosphere

Abstract A numerical study on the runaway greenhouse state is performed by using a general circulation model (GCM) with simplified hydrologic and radiative processes. Except for the inclusion of three-dimensional atmospheric motion, the system utilized is basically equivalent to the one-dimensional radiative–convective equilibrium model of Nakajima et al. in which the runaway greenhouse state is defined. The results of integrations with various values of solar constant show that there exists an upper limit of the solar constant with which the atmosphere can reach a statistical equilibrium state. When the value of solar constant exceeds the limit, 1600 W m−2, the atmosphere sets in a “thermally runaway” state. It is characterized by continuous increase of the amount of water vapor, continuous decrease of the outgoing longwave radiation, and continuous warming of the atmosphere and the ground surface. The upper-limit value of the solar constant obtained by the GCM experiments corresponds to the upper limit ...

Linear stability of thermal convection in rotating systems with fixed heat flux boundaries

Linear stability of rotating thermal convection in a horizontal layer of Boussinesq fluid under the fixed heat flux boundary condition is examined by the use of a vertically truncated system up to wavenumber one. When the rotation axis is in the vertical direction, the asymptotic behavior of the critical convection for large rotation rates is almost the same as that under the fixed temperature boundary condition. However, when the rotation axis is horizontal and the lateral boundaries are inclined, the mode with zero horizontal wavenumber remains as the critical mode regardless of the rotation rate. The neutral curve has another local minimum at a nonzero horizontal wavenumber, whose asymptotic behavior coincides with the critical mode under the fixed temperature condition. The difference of the critical horizontal wavenumber between those two geometries is qualitatively understood by the difference of wave characteristics; inertial waves and Rossby waves, respectively.

Surface zonal flows induced by thermal convection trapped below a stably stratified layer in a rapidly rotating spherical shell

[1]xa0Penetration of finite-amplitude columnar convection into an outer stably stratified layer in a rapidly rotating spherical shell is examined numerically. It is shown that penetration of columnar convection is not always required for generation of surface zonal flows. When the strength of the stratification of the outer stable layer is increased, small-scale columnar convection cells are trapped below the layer, but induced mean zonal flows still penetrate to the surface. Our results suggest that the surface zonal flows of the giant planets may be a consequence of penetration of deep zonal flows generated by small-scale columnar convection trapped below a near-surface stably stratified layer.

A numerical study of the Martian atmospheric convection with a two-dimensional anelastic model

Thermal convection of the Martian lower atmosphere is examined by the use of a two-dimensional anelastic model with a resolution fine enough to describe convection eddies.For a homogeneous radiative cooling of 50 K/day given in the layer below 5 km, a layer of time-dependent convection develops up to about 6 km in height. The intensity of realized vertical winds ranges up to 20 m/s. The dust, which is injected into the lowest layer and treated as a passive tracer, is transported immediately in the convection layer and mixed uniformly.The intensity of the horizontal winds near the surface reaches about 10 m/s, which, combined with large-scale motions, is expected to contribute to the dust injection into the atmosphere.

Mean zonal flows excited by critical thermal convection in rotating spherical shells

Abstract Mean zonal flows excited by critical modes of Boussinesq convection in rotating spherical shells are evaluated systematically by the weak nonlinear method. Calculations are executed in the ranges of the Prandtl number 0.01 ≤ P ≤ 102, the Taylor number 100 ≤ T ≤ 107, and the radius ratio 0.2 ≤ η ≤ 0.8. In the case of small rotation rates, two new states of zonal flow at the equatorial outer boundary are obtained; westerly flow emerges even when the Prandtl number is large, and easterly flow emerges even when the Prandtl number is small. The latter case is interesting since the induced equatorial easterly is in the opposite direction to that of the acceleration. In the case of large rotation rates, it is confirmed that the direction of mean zonal flow at the equatorial outer boundary does not depend on the thickness of the shell.