| Abstrakt: |
The plume slope Graph $\text {d} z c / \text {d} x$ correlated strongly with the ratio of the total vertical to horizontal integral buoyancy flux Graph $(F z+F z')/(F x+F x')$, and further analysis showed that the difference between Graph $w m/(U+u m)$ and Graph $(F z+F z')/(F x+F x')$ was determined by the vertical turbulent buoyancy flux. The characteristic radius Graph $r m$ is defined as Graph $r m=(Q/U s)^{1/2}$ (i.e. using the definition of Graph $Q$; (2.9a)), which encapsulates both the pure plume definition Graph $r m = Q/M z^{1/2}$ for Graph $U\ll w m$, Graph $u m \ll w m$, and the bent-over solution Graph $r m = (Q/U)^{1/2}$ for Graph $U\gg u m, U \gg w m$. Denoting the distance from the beginning of the nudging region as Graph $x^*$, we adjusted the velocity according to Graph $\boldsymbol {u}^* = (1 - x^*/L n) \boldsymbol {u} + (x^*/L n) \boldsymbol {u} a$, where Graph $\boldsymbol {u}$ is the original DNS velocity and Graph $\boldsymbol {u} a = (U,0,0)$ is the ambient environmental velocity. Equation (2.9a-d) implicitly provides the definition of Graph $u m$, Graph $w m$ and Graph $b m$ as Graph $M x/Q$, Graph $M z/Q$ and Graph $F/Q$, respectively. Zero-flux Neumann boundary conditions were used for buoyancy at Graph $z = 0$ and Graph $z = L z$, with the exception of a circular region of radius Graph $r 0$, centred at Graph $(0,0,0)$, through which a constant buoyancy flux was imposed. [Extracted from the article] |
