The Nusselt numbers of horizontal convection
The Nusselt numbers of horizontal convection
复制标题
水平对流的努塞尔数
DOI：
10.1017/jfm.2020.269
复制
发表时间：
2020
影响因子：
3.7
通讯作者：
Young, William R.
中科院分区：
文献类型：
--
作者：
Rocha, Cesar B.;Constantinou, Navid C.;Llewellyn Smith, Stefan G.;Young, William R.
In the problem of horizontal convection a non-uniform buoyancy,, is imposed on the top surface of a container and all other surfaces are insulating. Horizontal convection produces a net horizontal flux of buoyancy,, defined by vertically and temporally averaging the interior horizontal flux of buoyancy. We show that $\overline {\boldsymbol {J}\boldsymbol {\cdot}\unicode [STIX]{x1D735} b_ {s}}=-\unicode [STIX]{x1D705}\langle|\unicode [STIX]{x1D735} b|^{2}\rangle $; the overbar denotes a space–time average over the top surface, angle brackets denote a volume–time average and $\unicode [STIX]{x1D705} $ is the molecular diffusivity of buoyancy. This connection betweenand $\unicode [STIX]{x1D705}\langle|\unicode [STIX]{x1D735} b|^{2}\rangle $ justifies the definition of the horizontal-convective Nusselt number,, as the ratio of $\unicode [STIX]{x1D705}\langle|\unicode [STIX]{x1D735} b|^{2}\rangle $ to the corresponding quantity produced by molecular diffusion alone. We discuss the advantages of this definition ofover other definitions of horizontal-convective Nusselt number. We investigate transient effects and show that $\unicode [STIX]{x1D705}\langle|\unicode [STIX]{x1D735} b|^{2}\rangle $ equilibrates more rapidly than other global averages, such as the averaged kinetic energy and bottom buoyancy. We show that $\unicode [STIX]{x1D705}\langle|\unicode [STIX]{x1D735} b|^{2}\rangle $ is the volume-averaged rate of Boussinesq entropy production within the enclosure. In statistical steady state, the interior entropy production is balanced by a flux through the top surface. This leads to an equivalent ‘surface Nusselt number’, defined as the surface average of vertical buoyancy flux through the top surface times the imposed surface buoyancy. In experimental situations it is easier to evaluate the surface entropy flux, rather than the volume integral of $|\unicode [STIX]{x1D735} b|^{2} $ demanded by $\unicode [STIX]{x1D705}\langle|\unicode [STIX]{x1D735} b|^{2}\rangle $.
In the problem of horizontal convection a non-uniform buoyancy,, is imposed on the top surface of a container and all other surfaces are insulating. Horizontal convection produces a net horizontal flux of buoyancy,, defined by vertically and temporally averaging the interior horizontal flux of buoyancy. We show that $\overline {\boldsymbol {J}\boldsymbol {\cdot}\unicode [STIX]{x1D735} b_ {s}}=-\unicode [STIX]{x1D705}\langle|\unicode [STIX]{x1D735} b|^{2}\rangle $; the overbar denotes a space–time average over the top surface, angle brackets denote a volume–time average and $\unicode [STIX]{x1D705} $ is the molecular diffusivity of buoyancy. This connection betweenand $\unicode [STIX]{x1D705}\langle|\unicode [STIX]{x1D735} b|^{2}\rangle $ justifies the definition of the horizontal-convective Nusselt number,, as the ratio of $\unicode [STIX]{x1D705}\langle|\unicode [STIX]{x1D735} b|^{2}\rangle $ to the corresponding quantity produced by molecular diffusion alone. We discuss the advantages of this definition ofover other definitions of horizontal-convective Nusselt number. We investigate transient effects and show that $\unicode [STIX]{x1D705}\langle|\unicode [STIX]{x1D735} b|^{2}\rangle $ equilibrates more rapidly than other global averages, such as the averaged kinetic energy and bottom buoyancy. We show that $\unicode [STIX]{x1D705}\langle|\unicode [STIX]{x1D735} b|^{2}\rangle $ is the volume-averaged rate of Boussinesq entropy production within the enclosure. In statistical steady state, the interior entropy production is balanced by a flux through the top surface. This leads to an equivalent ‘surface Nusselt number’, defined as the surface average of vertical buoyancy flux through the top surface times the imposed surface buoyancy. In experimental situations it is easier to evaluate the surface entropy flux, rather than the volume integral of $|\unicode [STIX]{x1D735} b|^{2} $ demanded by $\unicode [STIX]{x1D705}\langle|\unicode [STIX]{x1D735} b|^{2}\rangle $.
改进水平对流的界限
影响因子：
3.7
作者：
C. Rocha;Thomas Bossy;Stefan G. Llewellyn Smith;W. Young
通讯作者：
W. Young
空间周期性强迫下的湍流水平对流：由内部惯性控制的状态
影响因子：
3.7
作者：
M. G. Rosevear;B. Gayen;R. W. Griffiths
通讯作者：
R. W. Griffiths
影响因子：
4.2
作者：
Burns, Keaton J.;Vasil, Geoffrey M.;Brown, Benjamin P.
通讯作者：
Brown, Benjamin P.