利用旋转平台产生定常涡旋的一种方法及其三维结构测量
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摘要
自然界中绝大部分运动都是有旋的,涡旋现象是流体力学研究的一个重要方向。本文通过实验室实验中对涡旋现象进行研究,具有参数可控、现象直观可见、可获取三维数据场等优势。但是考虑到真实海洋中存在的的海洋层结、地转效应,通常使用的实验室造涡方法存在着破坏层结、涡旋结构不稳定等缺陷。本实验提出了一种定常涡旋的生成方法,可以在旋转层结流体中生成一个稳定的涡旋。通过此种方法生成的涡旋,速度与涡度分布径向分布遵循不同的规律,垂向上都沿统一的指数规律衰减,且涡度径向分布可以用一简单解析函数拟合。
Most motion of the fluid in the nature is rotational,and vortex phenomenon is an important direction in the study of fluid mechanics.The research on the vortex phenomenon via laboratory experiment allow us to adjust the experimental parameters within the allowable range,easily access to visual phenomena,and have the advantages of being able to obtain three-dimensional data fields.However,considering the fact that the existence of stratification and geostrophic effects in the real ocean,the commonly used laboratory vortex induced methods have some defects such as the destruction of stratification and the instability of vortex structure.When it comes to apply experimental results to real ocean simulation,those defects may be hard to ignore.A steady vortex generation method is proposed in this paper,which can generate a steady vortex in a rotating stratified fluid.Vortex generated by this method,its radial distributions of velocity and vorticity follow different rules,and the vertical distributions of those decrease along the uniform exponential law.The vorticity radial distribution can be fitted by a simple analytic function.
Most motion of the fluid in the nature is rotational,and vortex phenomenon is an important direction in the study of fluid mechanics.The research on the vortex phenomenon via laboratory experiment allow us to adjust the experimental parameters within the allowable range,easily access to visual phenomena,and have the advantages of being able to obtain three-dimensional data fields.However,considering the fact that the existence of stratification and geostrophic effects in the real ocean,the commonly used laboratory vortex induced methods have some defects such as the destruction of stratification and the instability of vortex structure.When it comes to apply experimental results to real ocean simulation,those defects may be hard to ignore.A steady vortex generation method is proposed in this paper,which can generate a steady vortex in a rotating stratified fluid.Vortex generated by this method,its radial distributions of velocity and vorticity follow different rules,and the vertical distributions of those decrease along the uniform exponential law.The vorticity radial distribution can be fitted by a simple analytic function.
引文
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[15] Karch A,Tong D.Particle-vortex duality from 3dbosonization[J].Physical Review X,2016,6.
[16]陈琛.水平温差驱动环流的机制探讨及实验研究[D].青岛:中国海洋大学,2009.Chen C.Lab Experiment and Theoretical Model for Horizontal Convection[M].Qingdao:Ocean University of China.2009.
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[18] Economidou M,Hunt G R.Density stratified environments:the double-tank method[J].Experiments in Fluids,2009,46(3):453-466.
[19] Fincham A and Delerce G,Advanced optimization of correlation imaging velocimetry algorithms[J].Exp Fluids,2000,29(1):13-22.
[20] Trieling R R,Heijst G J F V.Decay of monopolar vortices in a stratified fluid[J].Fluid Dynamics Research,1998,23(1):27-43.
[21]万伟,屈玲,周生启.双扩散对流中台阶结构的实验研究[J].力学学报,2014,46(2):217-223.Wan W,Qu L,Zhou S.Laboratory studies on the staircase structure of double-diffusive convection[J].Chinese Journal of Theoretical and Applied Mechanics,2014,46(2):217-223.
[22] Illingworth S J.Model-based control of vortex shedding at low Reynolds numbers[J].Theoretical&Computational Fluid Dynamics,2016,30(5):1-20.
[2] Kloosterziel R C,Carnevale G F,Phillippe D.Propagation of barotropic dipoles over topography in a rotating tank[J].Dynamics of Atmospheres&Oceans,1993,19(233):65-100.
[3] Billant P,Chomaz J M.Experimental evidence for a new instability of a vertical columnar vortex pair in a strongly stratified fluid[J].Journal of Fluid Mechanics,2000(418):167-188.
[4] Andersen A,Bohr T,Stenum B,et al.Anatomy of a bathtub vortex[J].Physical Review Letters,2003,91(10):104502.
[5] Heijst G J F V,Clercx H J H.Laboratory modeling of geophysical Vortices[J].Annual Review of Fluid Mechanics,2009,41(1):143-164.
[6]张正光.中尺度涡[D].青岛:中国海洋大学,2014.Zhang Z.Mesoscale Eddy[D].Qingdao:Ocean University of China,2014.
[7]张晓爽,吕红民.利用旋转平台模拟Rossby波现象的实验研究[J].中国海洋大学学报(自然科学版),2010,40(S1):9-15.Zhang X,Lyu H,The experimental study of simulation of rossby wave by using rotating platform[J].Periodical of Ocean University of China,2010,40(S1):9-15.
[8] Kloosterziel,Carnevale,Orlandi.Inertial instability in rotating and stratified fluids:barotropic vortices[J].Journal of Fluid Mechanics,2007,583(583):379-412.
[9] Stegner A,Zeitlin V.From quasi-geostrophic to strongly nonlinear monopolar vortices in a paraboloidal shallow-water-layer experiment[J].Journal of Fluid Mechanics,2000,356(356):1-24.
[10] Mittal S,Raghuvanshi A.Control of vortex shedding behind circular cylinder for flows at low Reynolds numbers[J].International Journal for Numerical Methods in Fluids,2015,35(4):421-447.
[11] Scolan H,Su S,Wright S,et al.Numerical and experimental study of flows in a rotating annulus with local convective forcing[C].//EGU General Assembly Conference.[s.1.]:EGU General Assembly Conference Abstracts,2016.
[12] Scolan H,Read P L.A rotating annulus driven by localized convective forcing:a new atmosphere-like experiment[J].Experiments in Fluids,2017,58(6):75-81.
[13] Terhaar S,Reichel T G,Schr9dinger C,et al.Vortex breakdown types and global modes in swirling combustor flows with axial injection[J].Journal of Propulsion&Power,2015,31(1):219-229.
[14] Vega L.The dynamics of vortex filaments with corners[J].Communications on Pure&Applied Analysis,2017,14(4):1581-1601.
[15] Karch A,Tong D.Particle-vortex duality from 3dbosonization[J].Physical Review X,2016,6.
[16]陈琛.水平温差驱动环流的机制探讨及实验研究[D].青岛:中国海洋大学,2009.Chen C.Lab Experiment and Theoretical Model for Horizontal Convection[M].Qingdao:Ocean University of China.2009.
[17] Wain D.Laboratory Experiments on the Effect of Baroclinic Eddies on a Dense Plume in a Rotating Stratified Fluid[R].[s.l.]:Woods Hole Oceanog.Inst Tech Rept,WHOI-2005-08:239-259.
[18] Economidou M,Hunt G R.Density stratified environments:the double-tank method[J].Experiments in Fluids,2009,46(3):453-466.
[19] Fincham A and Delerce G,Advanced optimization of correlation imaging velocimetry algorithms[J].Exp Fluids,2000,29(1):13-22.
[20] Trieling R R,Heijst G J F V.Decay of monopolar vortices in a stratified fluid[J].Fluid Dynamics Research,1998,23(1):27-43.
[21]万伟,屈玲,周生启.双扩散对流中台阶结构的实验研究[J].力学学报,2014,46(2):217-223.Wan W,Qu L,Zhou S.Laboratory studies on the staircase structure of double-diffusive convection[J].Chinese Journal of Theoretical and Applied Mechanics,2014,46(2):217-223.
[22] Illingworth S J.Model-based control of vortex shedding at low Reynolds numbers[J].Theoretical&Computational Fluid Dynamics,2016,30(5):1-20.