| Budget Amount *help |
¥9,300,000 (Direct Cost: ¥9,300,000)
Fiscal Year 2000: ¥2,000,000 (Direct Cost: ¥2,000,000)
Fiscal Year 1999: ¥5,000,000 (Direct Cost: ¥5,000,000)
Fiscal Year 1998: ¥2,300,000 (Direct Cost: ¥2,300,000)
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| Research Abstract |
The combined effects of buoyancy and Coriolis forces were investigated using direct numerical simulation (DNS) of homogeneous turbulence. First, we investigated how the mixed effects of rotation and stable stratification affect the generation and development mechanism of the vertical vortices and their asymmetry. We studied two kinds of flow fields, i.e., stably stratified rotating turbulence and thermal wind. The conclusions are as follows :
Stably stratified rotating turbulence.
(1) The effects of the anisotropy of Reynolds stresses and Prandtl number on the asymmetry of the vertical vortices were examined. The asymmetry of the vertical vortices is associated with vortex stretching. Vertical vortices associated with ∂u_3/∂x_3>0$ are enhanced in comparison with the other vortices with ∂u_3/∂x_3<0. In two-component and low Prandtl number cases. the anticyclones are well correlated with the stretching term ∂u_3/∂x_3>0. On the other hand, in one-component and high Prandtl number cases, the
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cyclones are correlated with it. When the vertical vortices are correlated with the positive strain rate ∂u_3/∂x_3>0, their horizontal scale becomes smaller than the internal Rossby radius of deformation.
(2) At low Prandtl numbers, turbulence is two-dimensionalized and the merging of the cyclonie vortices results in the elongated Taylor columns observed in the numerical simulation with the quasi-geostrophic approximation.
Thermal wind.
(1) The intensity of the stable stratification affects turbulence statistics and vortical structures. When the stable stratification is weak, the vertical velocity increases and the flow field is one-componentalized. However, the flow field tends to become isotropic with an increase in the Reynolds number. On the other hand, the vertical velocity component is suppressed and the flow field tends to be two-componentalized when the stable stratification is intense. Then, the structures of the pancake-shaped vortex patches are generated.
(2) When the stable stratification is weak and the flow field becomes unstable, the nonlinear vortex stretching term surpasses the incrcase in the Reynolds number. Then, the dominance of the cyclones disappears and both the cyclones and anticyclones are enhanced. When the stable stratification is intense. however, the dominance of the cyclones is still observed at relatively high Reynolds numbers.
(3) The vertical vortices are generated by vortex tilting due to the mean shear in the first period, and then they are developed by the linear vortex stretching due to the Coriolis force. In addition, when the effect of the nonlinear vortex stretching is added, the cyclones become dominant.
Next, the combined effects of rotation, unstable stratification and nonlinear term were studied in detail using both DNS and rapid distortion theory (RDT). The conclusions are as follows :
(1) In the unstably stratified flow with rotation, the elongated vortex columns are generated in the direction parallel to the axis of rotation. These vortex columns are generated by the effect of linear vortex stretching associated with the externally imposed rotation Ω and strain rate ∂u_3/∂x_3. The linear vortex stretching is closely associated with the process of energy conversion from baroclinic vorticity to barotropic vorticity. RDT cannot generate the vortex columns, because the nonlinear term is required to suppress the oscillation and enhance the magnitude of the strain rate ∂u_3/∂x_3.
(2) The time evolution of vortex columns is determined by the parameter representing the ratio of the Brunt-Vaisala frequency to the angular frequency of rotation. The vortex columns begin to emerge when both velocity and temperature fluctuations become two-dimensional, and their cross-correlation coeflicient becomes almost unity. The horizontal length scale of the vertical vortex becomes larger than the internal Rossby radius of deformation. Thus, the Coriolis force directly affects the horizontal structures of the vortex, although the buoyancy force should determine their vertical structure. Less
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