不同涡粘性湍流底边界层特征量研究
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摘要
湍流底边界层的物理性质和动力过程十分复杂，其水动力特征对于海洋工程、海洋生物等学科具有重要的研究意义和应用价值。但是由于其特殊的地理位置和复杂的动力系统，观测数据和理论模型非常难获得，一直是物理海洋学、海洋环境工程及生物学研究的热点之一。本论文主要的工作：一方面从理论上研究了海底悬浮液的有效粘性的消减机制；另一方面通过建立两种新的涡粘性参数化形式，建立湍流底边界层动力系统的理论模式并得到其解析解。研究内容可分为三个方面：
1.在高浓度悬浮液的条件下，利用变换场理论，根据Stokes方程，研究了悬浮液的有效粘性随颗粒尺度的变化特征。统计结果表明：一定的颗粒浓度下（中或高），在一个元胞内增加颗粒的尺度或者减少单位体积内的颗粒数量，可大幅度地减小固体悬浮液的有效粘性。本工作揭示了固体颗粒尺度的变化可控制悬浮液的有效粘性的机制。
2.给出新的参数化垂直涡粘性的三次多项式形式az2(1z/d)，基于简化的Navier–Stokes方程，利用超几何函数的方法，得到了湍流粗糙底边界层的动力系统的解析解。另外，推导出湍流底边界层的其他的动力参数，如底剪应力，Ekman传输，Ekman抽吸及近底部速度分布场，从理论上研究了湍流底边界层特征量的分布特征。进一步，通过数值结果的分析，得出底边界层的总速度，亏损速度及其剪应力受平均流的角频率和地球自转影响比较大；而底边界层的动力结构对于底边界层顶部粗糙度不敏感。
3.推导出在另一个新的涡粘性形式az (1z/d)2下的湍流底边界层的动力系统的解析解。并且通过数值分析得到：湍流底边界层的速度剖面同样对于平均流的角频率和地球自转影响之比依赖性较大；但是对于底边界层顶部粗糙度不敏感。通过和潮流的实际观测数据对比，在速度的振幅上拟合基本一致。
本论文的工作从理论上研究了湍流边界层涡粘性的影响机制和参数化形式，是研究底边界层的动力影响因素重要的手段和方法。
The physical properties and dynamic processes of the oscillatory bottom boundarylayer that is a typical and important boundary layer are very complicated. Thehydrodynamic properties of turbulent bottom boundary layer are important researchand application value in marine engineering, marine biology and so on. However, theestablishment of the theory model of the ocean bottom boundary layer and itsanalytical solution are seldom. Observation experiment and theoretical research of theocean bottom boundary layer have also been the research hot spot for the physicaloceanography, marine environmental engineering and biology. In this paper, the mainwork is structured following: on the one hand, discusses the effective viscosityreduction behavior model of solid suspension in ocean bottom boundary layer; On theother hand, establish two different new forms of turbulent viscosity and research thedynamic of the turbulent bottom boundary layer theoretically. This paper is organizedinto three parts as follows.
In the first part of the paper the transformation field method is used to model thereduction behaviour of effective viscosity of solid suspensions theoretically byenlarging the particle size at a given high concentration of particles based on theStokes equation. Under a simple shearing flow, the effective viscosity of solidsuspensions can be reduced by controlling the inclusion particle size or the number ofinclusion particles in a unit volume. With a lot of samples of random cubic particles ina unit cell, our statistical results show that at the same higher concentration, theeffective viscosity of solid suspensions can be reduced by increasing the particle sizeor reducing the number of inclusion particles in a unit volume. This work disclosesthe viscosity reduction mechanism of increasing particle size, which is observedexperimentally.
In the second part of the paper the analytical solutions of the velocity distributionwithin the turbulent bottom boundary layer are deduced by supposed a new eddyviscosity of cubic polynomial form az2(1z/d). Based on the simplifiedNavier-Stokes equations, the property of the hypergeometric function is used to thismodel. Moreover, other dynamic parameters of bottom boundary layer are alsoobtained, such as the bottom shear stress, the Ekman transport, Ekman pumping and the velocity fields near the bottom. Thus the dynamic characteristics of well-mixedturbulent bottom boundary are discussed theoretically. Furthermore, numerical resultsshow that the total velocity profile, Ekman velocity and shear stress are sensitivenessto the ratio of the tidal frequency and the Coriolis parameter, but have been lessinfluenced on the roughness heights at the top of the bottom boundary layer.
In the third part of the paper, we give another eddy viscosity of cubic polynomialform az (1z/d)2, and derive an analytical solution of velocity for turbulentrough bottom boundary layer. Furthermore, numerical results show that the velocityprofile in the bottom boundary layer is influenced strongly by the ratio of the tidalfrequency and the Coriolis parameter but is not sensitive to the roughness heights atthe top of the bottom boundary layer. Comparing with measured data of a tidal currentwithin bottom boundary layer, it indicates that the analytical model agrees well withobservation of the tidal current velocity magnitude.
In this paper, we research theoretically the effective viscosity reduction behaviourof solid suspension and eddy viscosity parametric forms. They are important meansand methods in researching dynamic influence factors of bottom boundary layer.
1.在高浓度悬浮液的条件下，利用变换场理论，根据Stokes方程，研究了悬浮液的有效粘性随颗粒尺度的变化特征。统计结果表明：一定的颗粒浓度下（中或高），在一个元胞内增加颗粒的尺度或者减少单位体积内的颗粒数量，可大幅度地减小固体悬浮液的有效粘性。本工作揭示了固体颗粒尺度的变化可控制悬浮液的有效粘性的机制。
2.给出新的参数化垂直涡粘性的三次多项式形式az2(1z/d)，基于简化的Navier–Stokes方程，利用超几何函数的方法，得到了湍流粗糙底边界层的动力系统的解析解。另外，推导出湍流底边界层的其他的动力参数，如底剪应力，Ekman传输，Ekman抽吸及近底部速度分布场，从理论上研究了湍流底边界层特征量的分布特征。进一步，通过数值结果的分析，得出底边界层的总速度，亏损速度及其剪应力受平均流的角频率和地球自转影响比较大；而底边界层的动力结构对于底边界层顶部粗糙度不敏感。
3.推导出在另一个新的涡粘性形式az (1z/d)2下的湍流底边界层的动力系统的解析解。并且通过数值分析得到：湍流底边界层的速度剖面同样对于平均流的角频率和地球自转影响之比依赖性较大；但是对于底边界层顶部粗糙度不敏感。通过和潮流的实际观测数据对比，在速度的振幅上拟合基本一致。
本论文的工作从理论上研究了湍流边界层涡粘性的影响机制和参数化形式，是研究底边界层的动力影响因素重要的手段和方法。
The physical properties and dynamic processes of the oscillatory bottom boundarylayer that is a typical and important boundary layer are very complicated. Thehydrodynamic properties of turbulent bottom boundary layer are important researchand application value in marine engineering, marine biology and so on. However, theestablishment of the theory model of the ocean bottom boundary layer and itsanalytical solution are seldom. Observation experiment and theoretical research of theocean bottom boundary layer have also been the research hot spot for the physicaloceanography, marine environmental engineering and biology. In this paper, the mainwork is structured following: on the one hand, discusses the effective viscosityreduction behavior model of solid suspension in ocean bottom boundary layer; On theother hand, establish two different new forms of turbulent viscosity and research thedynamic of the turbulent bottom boundary layer theoretically. This paper is organizedinto three parts as follows.
In the first part of the paper the transformation field method is used to model thereduction behaviour of effective viscosity of solid suspensions theoretically byenlarging the particle size at a given high concentration of particles based on theStokes equation. Under a simple shearing flow, the effective viscosity of solidsuspensions can be reduced by controlling the inclusion particle size or the number ofinclusion particles in a unit volume. With a lot of samples of random cubic particles ina unit cell, our statistical results show that at the same higher concentration, theeffective viscosity of solid suspensions can be reduced by increasing the particle sizeor reducing the number of inclusion particles in a unit volume. This work disclosesthe viscosity reduction mechanism of increasing particle size, which is observedexperimentally.
In the second part of the paper the analytical solutions of the velocity distributionwithin the turbulent bottom boundary layer are deduced by supposed a new eddyviscosity of cubic polynomial form az2(1z/d). Based on the simplifiedNavier-Stokes equations, the property of the hypergeometric function is used to thismodel. Moreover, other dynamic parameters of bottom boundary layer are alsoobtained, such as the bottom shear stress, the Ekman transport, Ekman pumping and the velocity fields near the bottom. Thus the dynamic characteristics of well-mixedturbulent bottom boundary are discussed theoretically. Furthermore, numerical resultsshow that the total velocity profile, Ekman velocity and shear stress are sensitivenessto the ratio of the tidal frequency and the Coriolis parameter, but have been lessinfluenced on the roughness heights at the top of the bottom boundary layer.
In the third part of the paper, we give another eddy viscosity of cubic polynomialform az (1z/d)2, and derive an analytical solution of velocity for turbulentrough bottom boundary layer. Furthermore, numerical results show that the velocityprofile in the bottom boundary layer is influenced strongly by the ratio of the tidalfrequency and the Coriolis parameter but is not sensitive to the roughness heights atthe top of the bottom boundary layer. Comparing with measured data of a tidal currentwithin bottom boundary layer, it indicates that the analytical model agrees well withobservation of the tidal current velocity magnitude.
In this paper, we research theoretically the effective viscosity reduction behaviourof solid suspension and eddy viscosity parametric forms. They are important meansand methods in researching dynamic influence factors of bottom boundary layer.
引文
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