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課程名稱 |
大氣海洋流體力學特論
Topics in Atmosphere-Ocean Fluid Dynamics |
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開課學期 |
107-1 |
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授課對象 |
理學院 大氣科學系 |
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授課教師 |
郭鴻基 |
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課號 |
AtmSci5090 |
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課程識別碼 |
229 U5850 |
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班次 |
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學分 |
1.0 |
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全/半年 |
半年 |
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必/選修 |
選修 |
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上課時間 |
第14,15,16 週
星期三10,A,B,C(17:30~21:05)星期六2,3,4,6,7,8(9:10~16:20) |
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上課地點 |
大氣A104大氣A104 |
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備註 |
密集課程。上課時間12/15,19,22,26(週三晚上6至8點;週六上午9至12點,下午1點半至4點半)
總人數上限：20人 |
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課程簡介影片 |
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核心能力關聯 |
本課程尚未建立核心能力關連 |
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課程大綱
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為確保您我的權利,請尊重智慧財產權及不得非法影印
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課程概述 |
1. Conservation laws and basic equations:
Rotation and stratification; potential temperature/density; the primitive equations;
The vertical transform and shallow-water equations
2. Circulation, vorticity, absolute vorticity and potential vorticity:
Helmholtz theorem, Gauss’ theorem, Stoke’s theorem, and Kelvin circulation theorem;
Bjerknes solenoidal term, Rossby and Ertel’s potential vorticity (PV) equation;
Impermeability theorem of PV substance.
3. Potential vorticity conservation and isentropic fluid dynamics:
Thermodynamic reversibility and entropy,
Diabaticity and mixing,
The equations of motion in isentropic coordinates,
Ertel’s PV and entropy conservation
Quasi-geostrophy in isentropic coordinates
4. Slow manifold quasi-balanced dynamics and 2D turbulence
Bachelor’s hypothesis, selective decay of enstrophy;
Geostrophic Adjustment, secondary circulation equation;
Examples in vortex dynamics and filamentations.
5. Hamiltonian formulation [*optional]
Re-derivation of isentropic equations
Particle-re-labelling symmetry and PV conservation (Chapter 7.2 of Salmon)
Non-canonical Hamiltonian dynamics and PV as a Casmir (Chapter 7.10 of Salmon)
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課程目標 |
Earth’s atmosphere and ocean exhibit complex patterns of fluid motion over a wide range of space and time scales. The slow-manifold dynamics, as well as the scale interactions, are of vital importance. This is a special short course focusing on the large-scale atmosphere-ocean fluid dynamics (AOFD), the geostrophic turbulence (i.e., 2D turbulence) dynamics and some related topics. The theory of geostrophic turbulence relies on two important components: a conservation principle that energy and potential vorticity are nearly conserved and an irreversibility principle that breaks the time-reversal symmetry of the exact inviscid dynamics. The AOFD can be understood quite simply in the form of isentropic fluid dynamics. The course may be useful for people who are interested in the understanding of the climate, weather, physics, chemistry, and/or biology of Earth’s fluid environment. |
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課程要求 |
待補 |
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預期每週課後學習時數 |
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Office Hours |
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指定閱讀 |
待補 |
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參考書目 |
待補 |
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評量方式
(僅供參考) |
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