颱風邊界層似震結構對於颱風眼牆演變的影響探討

Abstract

颱風觀測中可以發現，邊界層的風場具有高梯度的似震結構特徵。Williams et al. (2013) 工作中以軸對稱單層邊界層模式中，具有 u ∂u/∂r 項而能夠掌握似震結構。 為了能夠更精確的模擬似震結構，我們研究WENO5 (Weighted Essentially Non-Oscillatory)、CRWENO5 (Compact Reconstruction WENO5) 以及CRWENO5-LD (CRWENO5-Low Dissipation)。並且與四階中差分法以及傅立葉波譜法做比較。我們也研究這些方法的收斂特性，以及二維理想流場中的物理量保守特性。 Williams et al. (2013) 在其邊界層模式中假設為軸對稱。然而，在觀測中可以發現，颱風邊界層內的似震結構也具有高度的不對稱性。為了探討颱風邊界層內的不對稱似震結構，我們將Williams et al. (2013) 的邊界層模式改寫成卡式座標，並且耦合淺水模式。我們發現，單眼牆颱風較大的上升速度，發生在慣性穩定度較大的區域，這可能表示，單眼牆颱風邊界層內的似震結構，對於颱風的增強有重要的影響。 在雙眼牆實驗中，我們發現moat較小的雙眼牆結構，內眼牆上升速度較小，且moat的下降速度較強。由於此為乾模式，實驗結果顯示，邊界層內的似震結構也傾向於增強外眼牆，並減弱內眼牆。另外，在其他的實驗中，我們也發現雙眼牆颱風的核心渦旋的渦度結構，對於內、外眼牆上升速度的分布有重要的影響。 本研究結果顯示，除了邊界層內的熱力過程，動力過程所導致的似震結構，對颱風的強度與結構也有重要的影響。

Observations of tropical cyclones reveal high-gradient shock-like structures in its boundary layer. Williams et al. (2013) proposed an axisymmetric slab boundary layer model with a u ∂u/∂r term which is capable of simulating such shock-like structures. In order to simulate the shock structures most accurately, study the numerical shock capturing methods WENO5 (Weighted Essentially Non-Oscillatory fifth-order), CRWENO5 (Compact Reconstruction WENO5) and CRWENO5-LD (CRWENO5-Low Dissipation). We compare these methods with a fourth-order finite difference scheme and with the Fourier spectral method. We also study their convergence behavior and conservations of physical quantities in the two dimensional ideal flow field. The boundary layer model of Williams et al. (2013) is formulated assuming axisymmetry. However, observational evidence suggests that the shock-like structures found in the boundary layers of real tropical cyclones can far from axisymmetric. Here, we transform the axisymmetric slab boundary layer model of Williams et al. (2013) to Cartesian coordinates and couple it with shallow water model in order to study asymmetric shock-like structures in the boundary layer of a tropical cyclone. We find that large updrafts occur in the region of large inertial instability of tropical cyclones with single eyewall. This may indicate that updrafts associated with shock-like structures play an important role in the intensification of tropical cyclones with a single eyewall. In our experiments with concentric eyewall, we found weaker updrafts at the inner eyewall and stronger downward motion in the moat region for a smaller moat size. Since this study employs a dry model, the results indicate that shock-like structures in the boundary layer also tend to intensify the outer eyewall and weaken the inner eyewall. In the other experiment, we found that the vorticity structure inside the core vortex of a concentric eyewall structure significantly affects the vertical velocity distribution at the inner and outer eyewalls. The results in this study indicate that not only thermodynamic processes but also shock-like structures associated with dynamical processes would significantly affect structures and intensity of tropical cyclones.