張萍, 謝梅芳, 楊昊, 蔡華陽, 歐素英, 楊清書

海洋水文學(xué)

潮優(yōu)型河口動(dòng)力對(duì)水深變化的響應(yīng)機(jī)制研究——以葡萄牙Guadiana河口為例*

張萍1,2,3,4, 謝梅芳1,2,3,4, 楊昊1,2,3,4, 蔡華陽1,2,3,4, 歐素英1,2,3,4, 楊清書1,2,3,4

1. 中山大學(xué)海洋工程與技術(shù)學(xué)院河口海岸研究所, 廣東 廣州 510275; 2. 河口水利技術(shù)國家地方聯(lián)合工程實(shí)驗(yàn)室, 廣東 廣州 510275;3. 廣東省海岸與島礁工程技術(shù)研究中心, 廣東 廣州 510275;4. 南方海洋科學(xué)與工程廣東省實(shí)驗(yàn)室, 廣東 珠海 519082

潮汐動(dòng)力、航道疏浚、河道淤積、解析模型、Guadiana河口

潮汐動(dòng)力是潮優(yōu)型河口物質(zhì)沿河流方向上溯的主要?jiǎng)恿? 其時(shí)空變化直接影響河口區(qū)域泥沙、營養(yǎng)鹽、污染物、鹽度等要素的輸運(yùn)及擴(kuò)散過程(Falc?o et al, 2009;Bonaldo et al, 2014; 丁芮等, 2016)。因此, 研究潮汐傳播的變化過程及機(jī)制對(duì)河口的防洪、灌溉、航運(yùn)和生態(tài)系統(tǒng)的保護(hù)等具有重要的指導(dǎo)意義。一維潮波傳播解析模型作為一種重要的數(shù)學(xué)工具, 已被廣泛應(yīng)用于探究河口潮汐動(dòng)力的基本過程及機(jī)制。研究表明, 潮波在沿河道向上傳播的過程中, 將受到底床摩擦、河道地形及徑流等的非線性作用, 主要潮波傳播變量(如潮波振幅、流速振幅、傳播速度、流速和水位之間的相位差等0)具有明顯的多時(shí)空尺度變化(Cai et al, 2018b)。大多數(shù)解析模型基于線性化的圣維南方程組, 僅考慮單一主要分潮(如M2分潮)的傳播過程, 然而, 其他天文分潮(如N2、S2、K1、O1)與主要分潮之間的非線性相互作用及其產(chǎn)生的潮流不對(duì)稱作用是尚待深入的基礎(chǔ)前沿問題。

影響潮汐動(dòng)力的因素眾多, 其中航道疏浚及全球海平面上升引起的沿程水深變化對(duì)潮汐動(dòng)力(如分潮振幅、相位、河口環(huán)流等)(劉俊勇等, 2006; Chernetsky et al, 2010; Ensing et al, 2015; Zhu et al, 2015)、泥沙輸運(yùn)(如懸沙濃度、最大渾濁帶形成變化等)(劉偉東等, 2007; 鄭志華等, 2008)及河口水環(huán)境(如鹽淡水混合、分層、鹽水入侵等)(龐啟秀等, 2005; Zhu et al, 2015)的影響備受關(guān)注。針對(duì)潮汐動(dòng)力變化, 大量研究表明水深增大將導(dǎo)致河口有效摩擦減小, 進(jìn)而引起潮汐動(dòng)力增強(qiáng), 包括潮差及潮波傳播速度的沿程增大, 如英國的Thames河口(Amin, 1983), 荷蘭的Rhine-Meuse河口(Vellinga et al, 2014), 德國的Elbe河口和Ems河口, 法國的Loire河口(Winterwerp et al, 2013), 美國的Delaware河口、Columbia河口(Jay et al, 2011)、Cape Fear河口(Familkhalili et al, 2016)、Newark灣, (Chant et al, 2018)、Hudson河口(Ralston et al, 2019)以及中國的珠江河口(Cai et al, 2018a)和錢塘灣河口(李薇等, 2018)。受潮汐動(dòng)力增強(qiáng)的影響, 部分河口的懸沙濃度明顯增大, 且最大渾濁帶顯著往河口上游方向移動(dòng)(Talke et al, 2009; de Jonge et al, 2014; Jalón-Rojas et al, 2016), 甚至導(dǎo)致河口性質(zhì)發(fā)生異變(Winterwerp, 2011)。雖然針對(duì)水深變化引起的潮汐動(dòng)力時(shí)空變化問題已經(jīng)取得相當(dāng)豐碩的研究成果, 但不同天文分潮對(duì)水深變化的響應(yīng)機(jī)制仍然是有待進(jìn)一步深入研究的科學(xué)問題。

本文基于Cai等(2018b)對(duì)葡萄牙Guadiana河口不同分潮之間非線性相互作用的研究, 進(jìn)一步采用一維水動(dòng)力解析模型探討半封閉潮優(yōu)型河口主要天文分潮的潮波傳播過程及其對(duì)水深變化(模擬人為航道疏浚與河道淤積)的響應(yīng)機(jī)制。研究成果可為河口區(qū)綜合整治及水資源高效開發(fā)利用等提供理論科學(xué)依據(jù)。

1 研究方法

1.1 一維潮波傳播解析模型

忽略斜壓梯度(即密度梯度)的影響, 一維動(dòng)量守恒方程表示為:

式中的、、、、分別表示斷面平均流速、重力加速度、水深、自由水面高程和Manning-Strickler摩擦系數(shù)(即曼寧系數(shù)的倒數(shù))。

式中1/為潮波頻率(為潮波周期)，0和的定義分別為:

1.2 不同分潮之間的非線性相互作用

為探討不同分潮之間的非線性相互作用, 采用Chebyshev多項(xiàng)式分解方法線性化二次流速項(xiàng)并與僅考慮單一主要分潮的潮波傳播解析模型相結(jié)合, 二次流速項(xiàng)可用如下Chebyshev多項(xiàng)式進(jìn)行展開(Godin, 1991, 1999):

對(duì)于個(gè)(≥2)分潮情況, 二次流速項(xiàng)可擴(kuò)展為:

1.3 半封閉河口潮波傳播解析解

根據(jù)Toffolon 等(2011)半封閉河口潮波傳播解析模型, 潮波振幅和相位的解析解如下:

經(jīng)過一系列的代數(shù)運(yùn)算((詳細(xì)推導(dǎo)見Toffolon等(2011)和Cai等(2016)), 方程(21)和(22)中未知變量的解析解為:

此外, 在半封閉河口中, 潮波振幅的反射系數(shù)可定義為:

2 解析模型在Guadiana河口的應(yīng)用

2.1 研究區(qū)域

圖1 Guadiana河口位置圖

2.2 半封閉河口解析模型的率定與驗(yàn)證

2.3 河口主要潮波變量對(duì)平均水深變化的響應(yīng)過程

各個(gè)分潮流速振幅參數(shù)隨距離和平均水深變化的等值線分布圖如圖2所示,值越大表明河口流速振幅相對(duì)無摩擦矩形河口的流速振幅越大(見公式9)。在河口下游(=0~60km), 隨著平均水深的增加, 半日分潮族(M2、S2和N2)的流速振幅參數(shù)逐漸增大, 而全日分潮族(K1和O1)呈現(xiàn)先增大后減小的變化規(guī)律。而在河口上游(=60~78km), 各個(gè)分潮的流速振幅參數(shù)幾乎不受平均水深變化的影響, 且均為較小值(上游封閉端0)。此外, 由圖2還可知, 平均水深的變化對(duì)半日分潮族的影響大于全日分潮族, 這是由于全日分潮族的流速振幅與潮波振幅之比(即/)遠(yuǎn)小于半日分潮族。

圖3為各個(gè)分潮的潮波振幅增大/衰減率參數(shù)隨距離和平均水深變化的等值線分布圖。>0表示潮波振幅沿程增大,<0表示潮波振幅沿程衰減, 而=0表示潮波振幅沿程不變(見公式10)。由圖可見, 隨著平均水深增加, 半日分潮族和全日分潮族的潮波振幅增大/衰減率參數(shù)逐漸增大, 但在河口上游(=60~78km), 潮波振幅增大/衰減率參數(shù)基本趨于不變。圖3中藍(lán)色實(shí)線下部為負(fù)值(表示潮波振幅沿程衰減), 而藍(lán)色實(shí)線上部為正值(表示潮波振幅沿程增大)。隨著平均水深的增大, 圖3中藍(lán)色實(shí)線與紅色實(shí)線的交點(diǎn)橫坐標(biāo)逐漸減小, 表明各個(gè)分潮沿程振幅最小值在河口沿程出現(xiàn)的位置逐漸向海方向推移, 但當(dāng)水深增加超過某臨界值后(如平均水深大于7m時(shí),M2=0), 河口潮波振幅沿程增大, 此時(shí)口門處潮波振幅最小。

圖3 Guadiana河口主要天文分潮(M2、S2、N2、K1、O1)衰減率參數(shù)δ隨平均水深變化的等值線分布圖紅色實(shí)線代表河口實(shí)際平均水深=5.5m; 藍(lán)色線條為δ=0

圖4 Guadiana河口主要天文分潮(M2、S2、N2、K1、O1)波速參數(shù)λ隨平均水深變化的等值線分布圖紅色實(shí)線代表河口實(shí)際平均水深=5.5m。藍(lán)色線條為λ=1

2.4 河口主要潮波變量的沿程平均變化量及變化率

平均水深引起的河口主要潮波變量(即流速參數(shù)、潮波振幅衰減率參數(shù)、波數(shù)參數(shù)以及流速與水位之間的相位差)的沿程變化量以及變化率可用如下公式計(jì)算:

表1 Guadiana河口主要天文分潮(M2、S2、N2、K1、O1)無量綱潮波變量參數(shù)相對(duì)河口實(shí)際平均水深條件下的變化量ψ(單位: m)和變化率σ(單位: %)

注: “*”表示倍數(shù)關(guān)系。

2.5 平均水深變化對(duì)不同分潮潮波傳播的影響機(jī)制

圖6 Guadiana河口主要天文分潮(M2、S2、N2、K1、O1)沿程的平均形狀參數(shù)γ (a)和摩擦參數(shù)χ (b)隨平均水深增大的變化圖

圖7 Guadiana河口主要天文分潮(M2、S2、N2、K1、O1)反射系數(shù)ΨA在河口上游(x=78km)(a) 和沿程平均值 (b) 隨平均水深增大的變化圖

3 結(jié)論

全球氣候變化背景下強(qiáng)人類活動(dòng)(如航道疏浚)對(duì)河口環(huán)境將產(chǎn)生顯著影響, 而河口在受到強(qiáng)人類活動(dòng)干擾后, 河口區(qū)域的潮汐動(dòng)力格局可能會(huì)發(fā)生較大變化。本文選取葡萄牙Guadiana河口作為研究區(qū)域, 應(yīng)用解析模型分析河口平均水深變化對(duì)主要天文分潮的傳播過程, 并揭示其響應(yīng)機(jī)制, 主要得出以下幾點(diǎn)結(jié)論:

1) 平均水深變化對(duì)潮汐動(dòng)力的影響主要體現(xiàn)在河口中下游段(=0~60km), 而對(duì)河口上游段(=60~78km)的影響較弱。平均水深的增加導(dǎo)致各分潮流速振幅、潮波振幅、潮波的傳播速度以及流速和水位之間的相位差增大。

2) 相同水深變化引起的主要潮波變量變化幅度, 主要半日分潮(M2、S2、N2)大于全日分潮(K1、O1)。

4) 當(dāng)水深小于實(shí)際水深時(shí)(模擬河道淤積), 各個(gè)分潮流速振幅、潮波振幅、潮波傳播速度以及流速和水位之間的相位差減小, 說明河道淤積會(huì)導(dǎo)致河口潮汐動(dòng)力減弱。

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Response of tidal dynamics to the variation of water depth: case study of Guadiana estuary in Portugal

ZHANG Ping1,2,3,4, XIE Meifang1,2,3,4, YANG Hao1,2,3,4, CAI Huayang1,2,3,4, Ou Suying1,2,3,4, YANG Qingshu1,2,3,4

1. Institute of Estuarine and Coastal Research, School of Marine Sciences, Sun Yat-sen University, Guangzhou 510275 China; 2. State and Local Joint Engineering Laboratory of Estuarine Hydraulic Technology, Guangzhou 510275 China;3. Guangdong Provincial Engineering Research Center of Coasts, Islands and Reefs, Guangzhou 510275 China; 4. Southern Laboratory of Ocean Science and Engineering, Zhuhai 519082, China

Quantifying the impacts of human-induced (such as dredging for navigational channels) or natural (such as global sea level rise) interventions on estuarine environment is an important issue for estuary and coastal studies. For given simplified geometry and dynamics, analytical models are capable of rapidly identify the influence of human-induced or natural interventions on estuarine environment, which are invaluable tools for exploring response of tidal dynamics to external forcing. In this study, a one-dimensional hydrodynamic analytical model was used to explore the response of tidal dynamics in terms of different constituents to variation of tidally averaged water depth (mimicking the channel dredging and deposition) in the Guadiana estuary in Portugal, building on previous studies on nonlinear frictional interaction between different tidal constituents. The results show that the influence of variable depth on tidal dynamics in the seaward reach (=0–60 km) is stronger compared to that in the landward reach (=60–78 km). In particular, the influence of variable depth on the predominant semi-diurnal tides (M2, S2, N2) is larger than that on diurnal tides (K1, O1). Analytical results also indicate that the basic tidal dynamic pattern along the estuary is more or less the same for a less intensive dredging of less than 2 m, while the pattern may substantially change for an intensive dredging activity. In addition, the channel bed deposition will weaken the tidal dynamics with a decrease of tidal amplitude, velocity amplitude, tidal wave celerity, and the phase lag between velocity and the elevation also decreases.

tidal dynamics; channel dredging; channel deposition; analytical model; Guadiana estuary

2019-04-09;

2019-05-31.

National Key Research and Development Program of China(2016YFC0402600); National Natural Science Foundation of China (5170928); Open Research Found of State Key Laboratory of Estuarine and Coastal Research (SKLEC-KF201809); Guangdong Provincial Natural Science Foundation of China (2017A030310321); the Water Resource Science and Technology Innovation Program of Guangdong Province (2016-20)

CAI Huayang, E-mail: caihy7@mail.sysu.edu.cn

P731

A

1009-5470(2020)01-0001-11

2019-04-09;

2019-05-31。

孫淑杰編輯

國家重點(diǎn)研發(fā)計(jì)劃項(xiàng)目(2016YFC0402600); 國家自然科學(xué)基金項(xiàng)目(5170928); 河口海岸學(xué)國家重點(diǎn)實(shí)驗(yàn)室開放課題基金資助項(xiàng)目(SKLEC-KF201809); 廣東省自然科學(xué)基金項(xiàng)目(2017A030310321); 廣東省水利科技創(chuàng)新項(xiàng)目(2016-20)

張萍(1995—), 女, 廣東省韶關(guān)市人, 碩士研究生, 主要從事河口海岸動(dòng)力學(xué)研究。E-mail: zhangp256@ mail2.sysu.edu.cn

*感謝所有對(duì)本文付出努力的人, 感謝各位審稿專家對(duì)本文提出的寶貴建議。

Editor: SUN Shujie

10.11978/2019037