彎曲河流擬序擾動的邊界效應(yīng)及其非線性動力理論研究
發(fā)布時間：2019-06-02 21:29
【摘要】：彎曲河流作為一個非線性系統(tǒng),壓力梯度和邊界引起的離心力可看作外在驅(qū)動。系統(tǒng)的非線性特征使得河流不僅呈現(xiàn)驅(qū)動力對應(yīng)的特征,還會呈現(xiàn)河流自身的固有特征,以及由二者相互作用產(chǎn)生的新特征,比如共振現(xiàn)象、分岔混沌等。擬序擾動對邊界特征的響應(yīng)是彎曲河流的固有特征。河道水流內(nèi)部存在一種大尺度的擬序結(jié)構(gòu),這種水流結(jié)構(gòu)是塑造河流平面形態(tài)的主要動力,形態(tài)的起伏會影響水流內(nèi)部的擬序結(jié)構(gòu),擬序結(jié)構(gòu)又進一步塑造河流形態(tài)。因此,本文認為使擬序擾動最穩(wěn)定的平面形態(tài)即為河流的穩(wěn)定平面形態(tài)。通過計算分析,我們發(fā)現(xiàn)當(dāng)邊界波數(shù)為0.39-0.41時擬序擾動最穩(wěn)定,其對應(yīng)的平面形態(tài)與Leopold and Wolman,Yalin、Julien等人的統(tǒng)計結(jié)果很相近。邊界直接導(dǎo)致的水動力和地形特征的力學(xué)實質(zhì)是河流系統(tǒng)的受迫振動。本文采用攝動方法,得到了彎曲河流全域動平衡下的弱非線性攝動解,各物理量均可由三個基本函數(shù)族組合而成,及縱向分布基本函數(shù)族ri(s)、橫向分布基本函數(shù)族gj(n)、垂向分布基本函數(shù)族fk(ξ)。根據(jù)縱向分布基本函數(shù)族的不同特征,可將攝動解分為線性同步部分、線性相位差部分和非線性耗散部分。前兩部分為色散項(rDp)僅使得河段物理量重分布,并不改變河段的整體特征量;非線性耗散部分(rDs),是河流平面形態(tài)阻力(彎曲阻力和伸縮阻力)產(chǎn)生的內(nèi)在機理,使得河段產(chǎn)生附加坡降和阻力。因此,河道的平面形狀彎曲、伸縮也是一種阻力。岸線擺動對強彎水流呈現(xiàn)明顯的時空特征影響很大,彎頂斷面分別在靠近凹岸上部和凸岸下部形成兩個大的環(huán)流,二者分別由Naot,Rodi(1982)的凹岸上環(huán)流和凸岸下環(huán)流經(jīng)彎曲作用發(fā)展而來。相鄰兩彎環(huán)流對強弱的相互轉(zhuǎn)換,使得曲率為零的過渡斷面附近流場急劇變化,流體微團發(fā)生急劇的旋轉(zhuǎn)、變形。槽壁擺動引起瞬時水流不僅空間分布不均,在長時間尺度上也呈現(xiàn)波動變化。近水面處主要受水面波動的影響,高于1 Hz的高頻部分即進入Kolmogorov-5/3衰減區(qū),而近底處水流紊動主要受條帶結(jié)構(gòu)的影響,需要在更高的頻段才能進入Kolmogorov區(qū)域。
[Abstract]:As a nonlinear system, the centrifugal force caused by pressure gradient and boundary can be regarded as external drive. The nonlinear characteristics of the system make the river not only present the characteristics of the driving force, but also the inherent characteristics of the river itself, as well as the new characteristics caused by the interaction between the two, such as resonance phenomenon, bifurcation chaos and so on. The response of quasi-ordered disturbance to boundary characteristics is an inherent feature of curved rivers. There is a large scale quasi-order structure in the river flow, which is the main driving force to shape the plane shape of the river. The fluctuation of the shape will affect the quasi-order structure inside the flow, and the quasi-order structure will further shape the river shape. Therefore, this paper holds that the plane form that makes the quasi-order disturbance the most stable is the stable plane form of the river. Through calculation and analysis, we find that the quasi-ordered disturbance is the most stable when the boundary wavenumber is 0.39-0.41, and the corresponding plane shape is very close to the statistical results of Leopold and Wolman,Yalin,Julien et al. The mechanical essence of hydrodynamic and topographic characteristics caused directly by boundary is the forced vibration of river system. In this paper, the perturbation method is used to obtain the weak nonlinear perturbation solution under the global dynamic equilibrium of curved rivers. Each physical quantity can be composed of three basic function families, and the longitudinal distribution basic function family ri (s),. Transverse distribution basic function family gj (n), vertical distribution basic function family fk (Zeta). According to the different characteristics of the basic function family of longitudinal distribution, the perturbation solution can be divided into linear synchronization part, linear phase difference part and nonlinear dissipation part. The first two parts are dispersion term (rDp), which only redistributes the physical quantity of the reach and does not change the overall characteristic quantity of the reach. The nonlinear dissipative part (rDs), is the internal mechanism of the plane form resistance (bending resistance and telescopic resistance) of the river, which makes the river reach produce additional slope drop and resistance. Therefore, the plane shape of the river is curved and telescopic is also a kind of resistance. The swinging of the shoreline has a great influence on the spatial and temporal characteristics of the strong curved flow. The curved top section forms two large circulation systems near the upper part of the concave bank and the lower part of the convex bank, respectively, which are caused by Naot,. The concave and subbank circulation of Rodi (1982) developed through bending. The transformation of the strength and strength of the adjacent two curved circulation makes the flow field near the transition section with zero curvature change sharply, and the fluid micromass rotates and deforms sharply. The instantaneous flow caused by the swing of the trough wall not only has uneven spatial distribution, but also fluctuates on a long time scale. The high frequency part above 1 Hz is mainly affected by the fluctuation of the water surface, while the turbulence near the bottom is mainly affected by the strip structure, so it is necessary to enter the Kolmogorov region in a higher frequency band.
【學(xué)位授予單位】：天津大學(xué)
【學(xué)位級別】：博士
【學(xué)位授予年份】：2015
【分類號】：TV147
本文編號：2491436
[Abstract]:As a nonlinear system, the centrifugal force caused by pressure gradient and boundary can be regarded as external drive. The nonlinear characteristics of the system make the river not only present the characteristics of the driving force, but also the inherent characteristics of the river itself, as well as the new characteristics caused by the interaction between the two, such as resonance phenomenon, bifurcation chaos and so on. The response of quasi-ordered disturbance to boundary characteristics is an inherent feature of curved rivers. There is a large scale quasi-order structure in the river flow, which is the main driving force to shape the plane shape of the river. The fluctuation of the shape will affect the quasi-order structure inside the flow, and the quasi-order structure will further shape the river shape. Therefore, this paper holds that the plane form that makes the quasi-order disturbance the most stable is the stable plane form of the river. Through calculation and analysis, we find that the quasi-ordered disturbance is the most stable when the boundary wavenumber is 0.39-0.41, and the corresponding plane shape is very close to the statistical results of Leopold and Wolman,Yalin,Julien et al. The mechanical essence of hydrodynamic and topographic characteristics caused directly by boundary is the forced vibration of river system. In this paper, the perturbation method is used to obtain the weak nonlinear perturbation solution under the global dynamic equilibrium of curved rivers. Each physical quantity can be composed of three basic function families, and the longitudinal distribution basic function family ri (s),. Transverse distribution basic function family gj (n), vertical distribution basic function family fk (Zeta). According to the different characteristics of the basic function family of longitudinal distribution, the perturbation solution can be divided into linear synchronization part, linear phase difference part and nonlinear dissipation part. The first two parts are dispersion term (rDp), which only redistributes the physical quantity of the reach and does not change the overall characteristic quantity of the reach. The nonlinear dissipative part (rDs), is the internal mechanism of the plane form resistance (bending resistance and telescopic resistance) of the river, which makes the river reach produce additional slope drop and resistance. Therefore, the plane shape of the river is curved and telescopic is also a kind of resistance. The swinging of the shoreline has a great influence on the spatial and temporal characteristics of the strong curved flow. The curved top section forms two large circulation systems near the upper part of the concave bank and the lower part of the convex bank, respectively, which are caused by Naot,. The concave and subbank circulation of Rodi (1982) developed through bending. The transformation of the strength and strength of the adjacent two curved circulation makes the flow field near the transition section with zero curvature change sharply, and the fluid micromass rotates and deforms sharply. The instantaneous flow caused by the swing of the trough wall not only has uneven spatial distribution, but also fluctuates on a long time scale. The high frequency part above 1 Hz is mainly affected by the fluctuation of the water surface, while the turbulence near the bottom is mainly affected by the strip structure, so it is necessary to enter the Kolmogorov region in a higher frequency band.
【學(xué)位授予單位】：天津大學(xué)
【學(xué)位級別】：博士
【學(xué)位授予年份】：2015
【分類號】：TV147
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