第一模內波傳播受一垂直於其行進方向之斜壓地轉流影響之數值實驗研究

Numerical Study of Mode-1 Internal Wave Propagation under the Influence of a Transverse Baroclinic Geostrophic Flow

郭天俠(Tien-Hsia Kuo)

指導教授 ： 詹森

國立臺灣大學/理學院/海洋研究所/碩士(2011年)

https://doi.org/10.6342/NTU.2011.01583

摘要

本研究利用三維數值模式，在f-plane的近似下，以理想化的條件探討地形平坦、水深1000 m的海洋中，不同頻率(近慣性頻率f和潮汐分量K1、M2、M4頻率)的第一模內波由東往西傳播，碰到固定流量22 Sv (1 Sv=106 m3/s)、流幅寬約120 km北向斜壓地轉流時所受的影響，並由能量方程式中各項物理量，討論其中的動力機制。數值實驗結果顯示，通過地轉流區的內波能量隨著內波頻率降低而減少，頻率越高的內波越容易維持其行進方向能量通量，並繼續西行穿越密度梯度區；反之，越低頻的內波波傳角度越接近地轉流等密面斜率，此時水平密度梯度似一南北向的屏障阻擋內波通過，一部分內波能量因所受有效浮力減弱而轉向下傳遞，一部份碰到流後被反射往東，並與方向相反、振幅相異的入射波疊加形成部分駐波，另一部份則在地轉流區受斜壓地轉流平流輸送作用而往北。內波頻率越接近慣性頻率f時，能量傳遞方向越偏往地轉流向。
由能量方程式來分析，地轉流兩側的x方向入射與反射能量通量在Case M4、M2、K1、及F僅佔入射値的89%、72%、66%、及30%左右，其餘內波能量大部份在地轉流區由內波-地轉流間能量交換、地轉流平流作用等動力機制導致能量損失。較高頻的Case M4內波動能主要因地轉流區的壓力變化而損失；次高頻的Case M2透過波‐流交互作用項將能量損失給北向斜壓地轉流，減少的能量通量輻散項與浮力變化和波‐流交互作用項平衡，小部份能量受地轉流的平流作用轉往北傳遞；頻率越低、波長越長的內波能量傳播方向受地轉流平流效應導致的北向分量越大，Case K1的全日潮頻率內波在地轉流區除地轉流平流項與波‐流交互作用項平衡外，部份能量被反射而在地轉流東側形成部份駐波，導致輻散項在空間中的起伏振盪；而更低頻的Case F近慣性內波因頻率與慣性頻率接近，能量輻散項主要由地轉流平流項與波‐流交互作用項平衡，大部份的內波能量皆在密度梯度區被地轉流帶往北傳遞。
斜壓地轉流對第一模內波能量傳遞的影響主要由兩種過程進入內波頻散關係，一是水平流速在水平方向的流速梯度，二是等密面抬升及對應的速度垂直剪切。水平流速梯度以流軸為中心，兩側的有效慣性頻率(feff)導致內波頻率於地轉流正(負)相對渦度側增加(減少)，改變波傳特性，並可能因內波存在頻帶最低頻率下限被提高，使得低頻的近慣性頻率內波無法穿越水平地轉流切形成的屏障；地轉流區等密度面的抬升使有效浮力頻率恆為負，造成內波受地轉流影響後，頻率變得較其入射値小，而有較接近低頻內波的波傳行為。

關鍵字

內波 ； 斜壓地轉流 ； 數值模式

並列摘要

The influence of a northward-flowing baroclinic geostrophic current with volume transport 22 Sv (1 Sv=106 m3/s) to westward-propagating mode-1 internal waves is investigated using a three-dimensional numerical model with idealized conditions as well as an internal wave and geostrophic current energy equation. Four different frequencies (M4, M2, K1, and near-inertia) of mode-1 internal waves are applied at the eastern boundary individually as the incident wave conditions. The incident internal wave encounters a 120-km-wide northward baroclinic geostrophic flow in the middle section of a 1000 m deep flat-bottom ocean. Results analyzed from numerical experiments suggest that the transmission of internal wave energy after the internal wave encountered the geostrophic flow decreases with the decrease of internal wave frequency; while the northward advection of the internal wave energy by the geostrophic flow and the wave-mean flow energy exchanges both increase with the decrease of internal wave frequency. Lower frequency internal waves, which characteristics are close to the isopycnal slopes, are partly reflected when confronting the geostrophic flow. The reflected and incident waves on the east side of the geostrophic flow combine to form a partial internal standing wave and thus weakens westward-propagating internal wave energy. The transmitted and reflected energy fluxes on both sides of the geostrophic flow are 89% (Case M4), 72% (M2), 66% (K1), and 30% (F) of the incident energy fluxes; the remainders are converted to the geostrophic flow or are advected by the northward flow.
The kinetic energy of higher frequency internal waves (M4) is balanced by the buoyancy gradiant in the geostrophic flow, leading to a conversion of potential energy. Lower frequency internal waves (Case M2, K1, F), on the other hand, exchange energy with the background geostrophic flow. The wave energy is converted to the momentum redistribution in geostrophic flow through wave-mean flow interactions. The kinetic energy of lower frequency internal waves is more easily advected northward by the geostrophic flow.
The horizontal density gradient of the geostrophic flow, with negative effective buoyancy frequency (Neff), acts as a reduced buoyancy restoring force lowers the intrinsic internal wave frequency and makes that the wave behaves more likely as an inertial wave. The horizontal velocity shear of the geostrophic flow on the positive relative vorticity side increases the effective Coriolis frequency (feff) and thus increases the lower bound of the internal waveband, which impedes the penetration of near-inertial internal waves. On the other hand, the decrease of feff on the negative relative vorticity side reduces the lower bound of the internal waveband. Thus, westward-propagating, lower frequency internal waves are easily trapped or reflected in the right half of the geostrophic flow.

並列關鍵字

internal wave ； baroclinic geostrophic flow ； numerical model

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