Discussion about the characteristics of flow in atmospheric airflow field using the complex function
|
摘要
气流经过不同地形时会产生不同程度的波动,研究其运动过程对天气和气候变化,以及航空和滑翔安全有重要意义。本文在假设大气为理想流体的前提下,从保角映照及复势的角度讨论两种情况下的气流流动。首先讨论了水平流经过圆弧形山包时的运动,分析了水平流速及山的大小对气流运动的影响,发现流速越大、山高与半宽的比例越大,气流波动越剧烈;然后讨论了点涡复合上水平流经过水平边界时的运动,由于涡心为极点,使得无论水流速度多大都无法改变涡心的位置,涡心周边粒子运动情况改变,但涡心保持不动。
Different levels of fluctuation occur when airflow passes over different terrain.It is important for weather and climate change,as well as aviation and glider safety,to study the motion of airflow.Based on conformal mapping and the complex potential,the motion of airflow in two different cases is discussed under the premise that the atmosphere is an ideal fluid.Firstly,the parallel flow movement through an arc-shaped mountain is studied,and the influence of horizontal velocity and of the angle between the mountain and the negative direction of horizontal ground on the airflow movement is analyzed.The results indicate that the influence on the motion increases with an increase in flow velocity and a decrease in the angle.Then,the motion of a parallel flow superimposed onto a point vortex when passing a linear boundary is discussed.Since the vortex core is an extreme point,its location cannot be changed,no matter how fast the flow velocity.That is,although the motion of the surrounding particles is changed,the vortex core remains motionless.
Different levels of fluctuation occur when airflow passes over different terrain.It is important for weather and climate change,as well as aviation and glider safety,to study the motion of airflow.Based on conformal mapping and the complex potential,the motion of airflow in two different cases is discussed under the premise that the atmosphere is an ideal fluid.Firstly,the parallel flow movement through an arc-shaped mountain is studied,and the influence of horizontal velocity and of the angle between the mountain and the negative direction of horizontal ground on the airflow movement is analyzed.The results indicate that the influence on the motion increases with an increase in flow velocity and a decrease in the angle.Then,the motion of a parallel flow superimposed onto a point vortex when passing a linear boundary is discussed.Since the vortex core is an extreme point,its location cannot be changed,no matter how fast the flow velocity.That is,although the motion of the surrounding particles is changed,the vortex core remains motionless.
引文
Burton,D.A.,J.Gratus,and R.W.Tucker.2004.“Hydrodynamic Forces on Two Moving Discs.”Theoretical and Applied Mechanics 31(2):153-188.doi:10.2298/TAM0402153B.
Cao,J.,Q.Xu,and S.T.Gao.2015.“Recent Developments in Computing Streamfunction and Velocity Potential in a Limited Domain.”Atmospheric and Oceanic Science Letters8(6):403-408.doi:10.3878/AOSL20150041.
Chao,J.P.,K.K.Chang,and S.M.Yan.1964.“A Preliminary Investigation for the Formation of Pressure Jump Produced by the Mountain in A Two-Layer Model(In Chinese).”Acta Meteorologica Sinica 34:109-117.doi:10.11676/qxxb1964.024.
Crowdy,D.,and J.Marshall.2006.“The Motion of a Point Vortex through Gaps in Walls.”Journal of Fluid Mechanics551:31-48.doi:10.1017/S0022112005008244.
Crowdy,D.G.2006.“Analytical Solutions for Uniform Potential Flow past Multiple Cylinders.”European Journal of Mechanics-B/Fluid 25(4):459-470.doi:10.1016/j.euromechflu.2005.11.005.
Galewsky,J.,and A.Sobel.2005.“Moist Dynamics and Orographic Precipitation in Northern and Central California during the New Year’s Flood of 1997.”Monthly Weather Review 133(6):1594-1612.doi:10.1175/MWR2943.1.
Johnson,E.R.,and N.R.McDonald.2004a.“The Motion of a Vortex near Two Circular Cylinder.”Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences460:939-954.doi:10.1098/rspa.2003.1193.
Johnson,E.R.,and N.R.McDonald.2004b.“The Motion of a Vortex near a Gap in a Wall.”Physics of Fluids 16(2):462-469.doi:10.1063/1.1637603.
Long,R.R.1953.“Some Aspects of the Flow of Stratified Fluids:I.A Theoretical Investigation.”Tellus 5(1):42-58.doi:10.1111/j.2153-3490.1953.tb01035.x.
Long,R.R.1954.“Some Aspects of the Flow of Stratified Fluids:II.Experiments with a Two-Fluid System.”Tellus 6(2):97-115.doi:10.1111/j.2153-3490.1954.tb01100.x.
Long,R.R.1955.“Some Aspects of the Flow of Stratified Fluids:III.Continuous Density Gradients.”Tellus 7(3):341-357.doi:10.1111/j.2153-3490.1955.tb01171.x.
Moore,S.A.,C.Wilson,and S.Bell.2005.“High Resolution Modeling of the Extreme Precipitation Event over Algiers in November 2001.”Advances in Geosciences 2:139-143.doi:10.5194/adgeo-2-139-2005.
Ryzhov,E.A.,Y.G.Izrailskii,and K.V.Koshel.2014.“Vortex Dynamics of a Fluid near a Boundary with a Circular Cavity.”Izvestiya Atmospheric and Oceanic Physics 50(4):420-425.doi:10.1134/S0001433814040203.
Scorer,R.S.1949.“Theory Of Waves in The Lee Of Mountains.”Quarterly Journal of the Royal Meteorological Society 75:41-56.doi:10.1002/(ISSN)1477-870X.
Scorer,R.S.,and H.Klieforth.1959.“Theory of Mountain Waves of Large Amplitude.”Quarterly Journal of the Royal Meteorological Society 85(364):131-143.doi:10.1002/qj.49708536406.
Taylor,P.A.,P.J.Mason,and E.F.Bradley.1987.“BoundaryLayer Flow over Low Hills.”Boundary-Layer Meteorology 39(1-2):107-132.doi:10.1007/BF00121870.
Torres,C.R.,E.E.Lanz,and S.I.Larios.2016.“Effect of Wind Direction and Orography on Flow Structures at Baja California Coast:A Numerical Approach.”Journal of Computational and Applied Mathematics 295:48-61.doi:10.1016/j.cam.2015.02.039.
Xiang,X.J.,K.K.Chen,and G.R.Spedding.2017.“Dynamic Mode Decomposition for Estimating Vortices and Lee Waves in a Stratified Wake.”Experiments in Fluids 58(5):56.doi:10.1007/s00348-017-2344-8.
Yeh,T.C.1956.“Topographical Effect on the Airflow(In Chinese).”Acta Meteorologica Sinica 27:243-262.doi:10.11676/qxxb1956.018.
Yu,E.T.,J.Q.Sun,and W.L.Xiang.2013.“High-Resolution Hindcast of Record-Breaking Rainfall in Beijing and Impact of Topography.”Atmospheric and Oceanic Science Letters 6(5):253-258.doi:10.3878/j.issn.1674-2834.13.0005.
Zang,Z.L.,and M.Zhang.2008.“A Study of the Environmental Influence on the Amplitude of Lee Waves.”Advances in Atmospheric Sciences 25(3):474-480.doi:10.1007/s00376-008-0474-x.
Zhong,Y.Q.2009.Complex Functions Theory(In Chinese).Beijing:Higher Education Press.
Zhu,M.,Z.H.Yu,and H.C.Lu.1999.“The Effect of Meso-Scale Lee Wave and Its Application(In Chinese).”Acta Meteorologica Sinica 57(6):705-714.doi:10.11676/qxxb1999.068.
Гутман,Л.Η.1976.The Nonlinear Theory of Mesoscale Meteorological Process(In Chinese).Beijing:Science Press.
Cao,J.,Q.Xu,and S.T.Gao.2015.“Recent Developments in Computing Streamfunction and Velocity Potential in a Limited Domain.”Atmospheric and Oceanic Science Letters8(6):403-408.doi:10.3878/AOSL20150041.
Chao,J.P.,K.K.Chang,and S.M.Yan.1964.“A Preliminary Investigation for the Formation of Pressure Jump Produced by the Mountain in A Two-Layer Model(In Chinese).”Acta Meteorologica Sinica 34:109-117.doi:10.11676/qxxb1964.024.
Crowdy,D.,and J.Marshall.2006.“The Motion of a Point Vortex through Gaps in Walls.”Journal of Fluid Mechanics551:31-48.doi:10.1017/S0022112005008244.
Crowdy,D.G.2006.“Analytical Solutions for Uniform Potential Flow past Multiple Cylinders.”European Journal of Mechanics-B/Fluid 25(4):459-470.doi:10.1016/j.euromechflu.2005.11.005.
Galewsky,J.,and A.Sobel.2005.“Moist Dynamics and Orographic Precipitation in Northern and Central California during the New Year’s Flood of 1997.”Monthly Weather Review 133(6):1594-1612.doi:10.1175/MWR2943.1.
Johnson,E.R.,and N.R.McDonald.2004a.“The Motion of a Vortex near Two Circular Cylinder.”Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences460:939-954.doi:10.1098/rspa.2003.1193.
Johnson,E.R.,and N.R.McDonald.2004b.“The Motion of a Vortex near a Gap in a Wall.”Physics of Fluids 16(2):462-469.doi:10.1063/1.1637603.
Long,R.R.1953.“Some Aspects of the Flow of Stratified Fluids:I.A Theoretical Investigation.”Tellus 5(1):42-58.doi:10.1111/j.2153-3490.1953.tb01035.x.
Long,R.R.1954.“Some Aspects of the Flow of Stratified Fluids:II.Experiments with a Two-Fluid System.”Tellus 6(2):97-115.doi:10.1111/j.2153-3490.1954.tb01100.x.
Long,R.R.1955.“Some Aspects of the Flow of Stratified Fluids:III.Continuous Density Gradients.”Tellus 7(3):341-357.doi:10.1111/j.2153-3490.1955.tb01171.x.
Moore,S.A.,C.Wilson,and S.Bell.2005.“High Resolution Modeling of the Extreme Precipitation Event over Algiers in November 2001.”Advances in Geosciences 2:139-143.doi:10.5194/adgeo-2-139-2005.
Ryzhov,E.A.,Y.G.Izrailskii,and K.V.Koshel.2014.“Vortex Dynamics of a Fluid near a Boundary with a Circular Cavity.”Izvestiya Atmospheric and Oceanic Physics 50(4):420-425.doi:10.1134/S0001433814040203.
Scorer,R.S.1949.“Theory Of Waves in The Lee Of Mountains.”Quarterly Journal of the Royal Meteorological Society 75:41-56.doi:10.1002/(ISSN)1477-870X.
Scorer,R.S.,and H.Klieforth.1959.“Theory of Mountain Waves of Large Amplitude.”Quarterly Journal of the Royal Meteorological Society 85(364):131-143.doi:10.1002/qj.49708536406.
Taylor,P.A.,P.J.Mason,and E.F.Bradley.1987.“BoundaryLayer Flow over Low Hills.”Boundary-Layer Meteorology 39(1-2):107-132.doi:10.1007/BF00121870.
Torres,C.R.,E.E.Lanz,and S.I.Larios.2016.“Effect of Wind Direction and Orography on Flow Structures at Baja California Coast:A Numerical Approach.”Journal of Computational and Applied Mathematics 295:48-61.doi:10.1016/j.cam.2015.02.039.
Xiang,X.J.,K.K.Chen,and G.R.Spedding.2017.“Dynamic Mode Decomposition for Estimating Vortices and Lee Waves in a Stratified Wake.”Experiments in Fluids 58(5):56.doi:10.1007/s00348-017-2344-8.
Yeh,T.C.1956.“Topographical Effect on the Airflow(In Chinese).”Acta Meteorologica Sinica 27:243-262.doi:10.11676/qxxb1956.018.
Yu,E.T.,J.Q.Sun,and W.L.Xiang.2013.“High-Resolution Hindcast of Record-Breaking Rainfall in Beijing and Impact of Topography.”Atmospheric and Oceanic Science Letters 6(5):253-258.doi:10.3878/j.issn.1674-2834.13.0005.
Zang,Z.L.,and M.Zhang.2008.“A Study of the Environmental Influence on the Amplitude of Lee Waves.”Advances in Atmospheric Sciences 25(3):474-480.doi:10.1007/s00376-008-0474-x.
Zhong,Y.Q.2009.Complex Functions Theory(In Chinese).Beijing:Higher Education Press.
Zhu,M.,Z.H.Yu,and H.C.Lu.1999.“The Effect of Meso-Scale Lee Wave and Its Application(In Chinese).”Acta Meteorologica Sinica 57(6):705-714.doi:10.11676/qxxb1999.068.
Гутман,Л.Η.1976.The Nonlinear Theory of Mesoscale Meteorological Process(In Chinese).Beijing:Science Press.