扩散对流温盐台阶结构的数值模拟
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摘要
热盐驱动下的扩散对流现象是海洋中高纬度海域普遍存在的一种现象,对其进行数值模拟可更细致地研究海洋小尺度动力过程。文章分析了扩散对流的形成机制,建立了二维方腔模型,通过有限体积法求解控制方程,对其分层现象进行了数值模拟。研究给出了流场的温度及盐度随时间演化的关系,展现了流场中速度的涡旋结构,分析了温盐台阶结构的生成、合并的演化过程,并对其物质和能量的输运进行了初步的理论解释。另外,对不同热流密度情况下的扩散对流现象进行了对比研究,发现随着热流密度的增加,台阶结构的演变速率变快,而且上边界冷却对其演化速率具有促进作用,但热流密度的改变并没有对台阶结构的演变趋势产生明显的影响。
Diffusive convection driven by temperature and salinity is a ubiquitous phenomenon in the mid and high latitudes of the ocean. Numerical simulation of diffusive convection can be used to study small-scale dynamic processes of the ocean. In this study, we analyze the formation mechanism of diffusive convection and establish a two-dimensional cavity model. The governing equation of the model is solved by the finite volume method, and the process of layering phenomenon is simulated numerically. The temporal evolution of temperature and salinity of the flow field is given, and the vortex structure of the velocity field is simulated. The processes of the formation and merging of diffusive convection staircases are analyzed, and a theoretical explanation for mass and energy transport processes is given. In addition, the diffusive convection under different heat flux density is discussed. It is found that the growth rate of diffusive convection staircases increases with the increase of heat flux density, and the cooling from the upper boundary plays an important role in accelerating its growth. The variation of heat flux density does not have a significant impact on the evolution of diffusive convection staircases.
Diffusive convection driven by temperature and salinity is a ubiquitous phenomenon in the mid and high latitudes of the ocean. Numerical simulation of diffusive convection can be used to study small-scale dynamic processes of the ocean. In this study, we analyze the formation mechanism of diffusive convection and establish a two-dimensional cavity model. The governing equation of the model is solved by the finite volume method, and the process of layering phenomenon is simulated numerically. The temporal evolution of temperature and salinity of the flow field is given, and the vortex structure of the velocity field is simulated. The processes of the formation and merging of diffusive convection staircases are analyzed, and a theoretical explanation for mass and energy transport processes is given. In addition, the diffusive convection under different heat flux density is discussed. It is found that the growth rate of diffusive convection staircases increases with the increase of heat flux density, and the cooling from the upper boundary plays an important role in accelerating its growth. The variation of heat flux density does not have a significant impact on the evolution of diffusive convection staircases.
引文
鲍征宇,1989.双扩散对流理论简介及国外研究现状[J].地质科技情报,8(4):35-42.BAO ZHENGYU,1989.Brief double-diffusive convection theory and its recent development abroad[J].Geological Science and Technology Information,8(4):35-42(in Chinese with English abstract).
赖锡军,2004.温盐分层流的非结构网格数值模拟[D].南京:河海大学.LAI XIJUN,2004.Numerical simulation of stratified flows with combined temperature and salinity on unstructured grids[D].Nanjing:Hohai University(in Chinese with English abstract).
卢玉华,詹杰民,2006.三维方腔温盐双扩散的格子Boltzmann方法数值模拟[J].物理学报,55(9):4774-4782.LUYUHUA,ZHAN JIEMIN,2006.Three-dimensional numerical simulation of thermosolutal convection in enclosures using lattice Boltzmann method[J].Acta Physica Sinica,55(9):4774-4782(in Chinese with English abstract).
屈玲,2014.海洋扩散对流温盐台阶机理及演化的研究[D].北京:中国科学院大学.QU LING,2014.The fundamental study of diffusive convection staircase and its evolution in the ocean[D].Beijing:University of Chinese Academy of Sciences(in Chinese with English abstract).
万伟,屈玲,周生启,2014.双扩散对流中台阶结构的实验研究[J].力学学报,46(2):217-223.WAN WEI,QU LING,ZHOU SHENGQI,2014.Laboratory studies on the staircase structure of double-diffusive convection[J].Chinese Journal of Theoretical and Applied Mechanics,46(2):217-223(in Chinese with English abstract).
邢元明,杨磊,管玉平,2013.海表扩散层中气体行为的分子动力学模拟[J].热带海洋学报,32(2):82-87.XINGYUANMING,YANG LEI,GUAN YUPING,2013.Molecular dynamics simulation of gas behaviors in seawater diffusive layer beneath the air-sea interface[J].Journal of Tropical Oceanography,32(2):82-87(in Chinese with English abstract).
詹杰民,李毓湘,2002.温盐双扩散均衡场中的振荡现象[J].物理学报,51(4):828-834.ZHAN JIEMIN,LI YUXIANG,2002.Oscillation phenomena in a thermohaline double-diffusive convection system[J].Acta Physica Sinica,51(4):828-834(in Chinese with English abstract).
郑珺婷,詹杰民,2002.双扩散对流系统问题的研究进展[J].力学进展,32(3):415-424.ZHENG JUNTING,ZHAN JIEMIN,2002.A review on double-diffusive convection[J].Advances in Mechanics,32(3):415-424(in Chinese with English abstract).
BEBIEVA Y,TIMMERMANS M L,2016.An examination of double diffusive processes in a mesoscale eddy in the Arctic Ocean[J].Journal of Geophysical Research:Oceans,121(1):457-475.
CARPENTER J R,SOMMER T,WüEST A,2012.Simulations of a double-diffusive interface in the diffusive convection regime[J].Journal of Fluid Mechanics,711:411-436.
DURRAN D R,1991.The third-order Adams-Bashforth method:An attractive alternative to leapfrog time differencing[J].Monthly Weather Review,119(3):702-720.
FENG GUOLIN,CAO HONGXING,DONG WENJIE,et al,2001.A new difference scheme with multi-time levels[J].Chinese Physics,10(11):1004-1010.
GUO SHUANGXI,ZHOU SHENGQI,QU LING,et al,2016.Laboratory experiments on diffusive convection layer thickness and its oceanographic implications[J].Journal of Geophysical Research:Oceans,121(10):7517-7529.
GUTHRIE J D,FER I,MORISON J,2015.Observational validation of the diffusive convection flux laws in the Amundsen Basin,Arctic Ocean[J].Journal of Geophysical Research:Oceans,120(12):7880-7896.
GUTHRIE J D,FER I,MORISON J H,2017.Thermohaline staircases in the Amundsen Basin:Possible disruption by shear and mixing[J].Journal of Geophysical Research:Oceans,122(10):7767-7782.
HUPPERT H E,TURNER J S,1972.Double-diffusive convection and its implications for the temperature and salinity structure of the ocean and Lake Vanda[J].Journal of Physical Oceanography,2(4):456-461.
HUPPERT H E,LINDEN P F,1979.On heating a stable salinity gradient from below[J].Journal of Fluid Mechanics,95(3):431-464.
KELLEY D E,1990.Fluxes through diffusive staircases:A new formulation[J].Journal of Geophysical Research:Oceans,95(C3):3365-3371.
KELLEY D E,FERNANDO H J S,GARGETT A E,et al,2003.The diffusive regime of double-diffusive convection[J].Progress in Oceanography,56(3-4):461-481.
KIMURA S,NICHOLLS K W,VENABLES E,2015.Estimation of ice shelf melt rate in the presence of a thermohaline staircase[J].Journal of Physical Oceanography,45(1):133-148.
LEWIS W T,INCROPERA F P,VISKANTA R,1982.Interferometric study of stable salinity gradients heated from below or cooled from above[J].Journal of Fluid Mechanics,116:411-430.
MARMORINO G O,CALDWELL D R,1976.Heat and salt transport through a diffusive thermohaline interface[J].Deep Sea Research and Oceanographic Abstracts,23(1):59-67.
NEAL V T,NESHYBA S,DENNER W,1969.Thermal stratification in the Arctic Ocean[J].Science,166(3903):373-374.
SCHMITT R W,1994.Double diffusion in oceanography[J].Annual Review of Fluid Mechanics,26:255-285.
SHIBLEY N C,TIMMERMANS M L,CARPENTER J R,et al,2017.Spatial variability of the Arctic Ocean's double diffusive staircase[J].Journal of Geophysical Research:Oceans,122(2):980-994.
TURNER J S,1965.The coupled turbulent transports of salt and and heat across a sharp density interface[J].International Journal of Heat and Mass Transfer,8(5):759-767.
TURNER J S,STOMMEL H,1964.A new case of convection in the presence of combined vertical salinity and temperature gradients[J].Proceedings of the National Academy of Sciences of the United States of America,52(1):49-53.
TURNER J S,1968.The behaviour of a stable salinity gradient heated from below[J].Journal of Fluid Mechanics,33(1):183-200.
XIE LINGLING,LI MINGMING,LI MIN,2015.Observational analysis of the double-diffusive convection in the deep Canada Basin[J].Acta Oceanologica Sinica,34(11):71-79.
ZHOU SHENGQI,LU YUANZHENG,SONG XUELONG,et al,2016.New layer thickness parameterization of diffusive convection in the ocean[J].Dynamics of Atmospheres and Oceans,73:87-97.
赖锡军,2004.温盐分层流的非结构网格数值模拟[D].南京:河海大学.LAI XIJUN,2004.Numerical simulation of stratified flows with combined temperature and salinity on unstructured grids[D].Nanjing:Hohai University(in Chinese with English abstract).
卢玉华,詹杰民,2006.三维方腔温盐双扩散的格子Boltzmann方法数值模拟[J].物理学报,55(9):4774-4782.LUYUHUA,ZHAN JIEMIN,2006.Three-dimensional numerical simulation of thermosolutal convection in enclosures using lattice Boltzmann method[J].Acta Physica Sinica,55(9):4774-4782(in Chinese with English abstract).
屈玲,2014.海洋扩散对流温盐台阶机理及演化的研究[D].北京:中国科学院大学.QU LING,2014.The fundamental study of diffusive convection staircase and its evolution in the ocean[D].Beijing:University of Chinese Academy of Sciences(in Chinese with English abstract).
万伟,屈玲,周生启,2014.双扩散对流中台阶结构的实验研究[J].力学学报,46(2):217-223.WAN WEI,QU LING,ZHOU SHENGQI,2014.Laboratory studies on the staircase structure of double-diffusive convection[J].Chinese Journal of Theoretical and Applied Mechanics,46(2):217-223(in Chinese with English abstract).
邢元明,杨磊,管玉平,2013.海表扩散层中气体行为的分子动力学模拟[J].热带海洋学报,32(2):82-87.XINGYUANMING,YANG LEI,GUAN YUPING,2013.Molecular dynamics simulation of gas behaviors in seawater diffusive layer beneath the air-sea interface[J].Journal of Tropical Oceanography,32(2):82-87(in Chinese with English abstract).
詹杰民,李毓湘,2002.温盐双扩散均衡场中的振荡现象[J].物理学报,51(4):828-834.ZHAN JIEMIN,LI YUXIANG,2002.Oscillation phenomena in a thermohaline double-diffusive convection system[J].Acta Physica Sinica,51(4):828-834(in Chinese with English abstract).
郑珺婷,詹杰民,2002.双扩散对流系统问题的研究进展[J].力学进展,32(3):415-424.ZHENG JUNTING,ZHAN JIEMIN,2002.A review on double-diffusive convection[J].Advances in Mechanics,32(3):415-424(in Chinese with English abstract).
BEBIEVA Y,TIMMERMANS M L,2016.An examination of double diffusive processes in a mesoscale eddy in the Arctic Ocean[J].Journal of Geophysical Research:Oceans,121(1):457-475.
CARPENTER J R,SOMMER T,WüEST A,2012.Simulations of a double-diffusive interface in the diffusive convection regime[J].Journal of Fluid Mechanics,711:411-436.
DURRAN D R,1991.The third-order Adams-Bashforth method:An attractive alternative to leapfrog time differencing[J].Monthly Weather Review,119(3):702-720.
FENG GUOLIN,CAO HONGXING,DONG WENJIE,et al,2001.A new difference scheme with multi-time levels[J].Chinese Physics,10(11):1004-1010.
GUO SHUANGXI,ZHOU SHENGQI,QU LING,et al,2016.Laboratory experiments on diffusive convection layer thickness and its oceanographic implications[J].Journal of Geophysical Research:Oceans,121(10):7517-7529.
GUTHRIE J D,FER I,MORISON J,2015.Observational validation of the diffusive convection flux laws in the Amundsen Basin,Arctic Ocean[J].Journal of Geophysical Research:Oceans,120(12):7880-7896.
GUTHRIE J D,FER I,MORISON J H,2017.Thermohaline staircases in the Amundsen Basin:Possible disruption by shear and mixing[J].Journal of Geophysical Research:Oceans,122(10):7767-7782.
HUPPERT H E,TURNER J S,1972.Double-diffusive convection and its implications for the temperature and salinity structure of the ocean and Lake Vanda[J].Journal of Physical Oceanography,2(4):456-461.
HUPPERT H E,LINDEN P F,1979.On heating a stable salinity gradient from below[J].Journal of Fluid Mechanics,95(3):431-464.
KELLEY D E,1990.Fluxes through diffusive staircases:A new formulation[J].Journal of Geophysical Research:Oceans,95(C3):3365-3371.
KELLEY D E,FERNANDO H J S,GARGETT A E,et al,2003.The diffusive regime of double-diffusive convection[J].Progress in Oceanography,56(3-4):461-481.
KIMURA S,NICHOLLS K W,VENABLES E,2015.Estimation of ice shelf melt rate in the presence of a thermohaline staircase[J].Journal of Physical Oceanography,45(1):133-148.
LEWIS W T,INCROPERA F P,VISKANTA R,1982.Interferometric study of stable salinity gradients heated from below or cooled from above[J].Journal of Fluid Mechanics,116:411-430.
MARMORINO G O,CALDWELL D R,1976.Heat and salt transport through a diffusive thermohaline interface[J].Deep Sea Research and Oceanographic Abstracts,23(1):59-67.
NEAL V T,NESHYBA S,DENNER W,1969.Thermal stratification in the Arctic Ocean[J].Science,166(3903):373-374.
SCHMITT R W,1994.Double diffusion in oceanography[J].Annual Review of Fluid Mechanics,26:255-285.
SHIBLEY N C,TIMMERMANS M L,CARPENTER J R,et al,2017.Spatial variability of the Arctic Ocean's double diffusive staircase[J].Journal of Geophysical Research:Oceans,122(2):980-994.
TURNER J S,1965.The coupled turbulent transports of salt and and heat across a sharp density interface[J].International Journal of Heat and Mass Transfer,8(5):759-767.
TURNER J S,STOMMEL H,1964.A new case of convection in the presence of combined vertical salinity and temperature gradients[J].Proceedings of the National Academy of Sciences of the United States of America,52(1):49-53.
TURNER J S,1968.The behaviour of a stable salinity gradient heated from below[J].Journal of Fluid Mechanics,33(1):183-200.
XIE LINGLING,LI MINGMING,LI MIN,2015.Observational analysis of the double-diffusive convection in the deep Canada Basin[J].Acta Oceanologica Sinica,34(11):71-79.
ZHOU SHENGQI,LU YUANZHENG,SONG XUELONG,et al,2016.New layer thickness parameterization of diffusive convection in the ocean[J].Dynamics of Atmospheres and Oceans,73:87-97.