TURBULENT GRAVITATIONAL CONVECTION FROM MAINTAINED AND INSTANTANEOUS SOURCES
TURBULENT GRAVITATIONAL CONVECTION FROM MAINTAINED AND INSTANTANEOUS SOURCES
复制标题
DOI：
10.1098/rspa.1956.0011
复制
发表时间：
1956-01-01
影响因子：
--
通讯作者：
TURNER, JS
中科院分区：
文献类型：
--
作者：
MORTON, BR;TAYLOR, G;TURNER, JS
使用适用于密度随高度变化的分层体液的方法，发展了来自维持和瞬时浮力源的对流理论；针对具有线性密度梯度的稳定分层流体的情况，提出了详细的解决方案。涉及的三个主要假设是（i）垂直速度和浮力的分布在所有高度上都相似，（ii）任何高度处的流体夹带速率与该高度处的特征速度成正比，以及（iii）流体不可压缩并且在混合时不会改变体积，并且整个运动中密度的局部变化与某些参考密度相比很小。根据体积、动量和浮力守恒的条件以无量纲形式导出控制方程，并获得维持源情况的数值解。这导致了对轻流体羽流在稳定分层流体中上升的最终高度的预测。通过将该理论与先前在均匀流体中的一些结果以及在分层盐溶液中进行的新实验的结果进行比较，对控制夹带速率的常数进行了估计。对于瞬时浮力源的情况，有一个精确的解；夹带常数再次根据分层流体的实验室结果进行估计。最后，通过用潜在温度代替温度，将分析应用于（可压缩）大气。预测了在各种条件下，在静止、稳定分层的大气中，来自典型热源的烟羽应上升的高度。
Theories of convection from maintained and instantaneous sources of buoyancy are developed, using methods which are applicable to stratified body fluids with any variation of density with height; detailed solutions have been presented for the case of a stably stratified fluid with a linear density gradient. The three main assumptions involved are (i) that the profiles of vertical velocity and buoyancy are similar at all heights, (ii) that the rate of entrainment of fluid at any height is proportional to a characteristic velocity at that height, and (iii) that the fluids are incompressible and do not change volume on mixing, and that local variations in density throughout the motion are small compared to some reference density. The governing equations are derived in non-dimensional form from the conditions of conservation of volume, momentum and buoyancy, and a numerical solution is obtained for the case of the maintained source, This leads to a prediction of the final height to which a plume of light fluid will rise in a stably stratified fluid. Estimates of the constant governing the rate of entrainment are made by comparing the theory with some previous results in uniform fluids, and with the results of new experiments carried out in a stratified salt solution. For the case of an instantaneous source of buoyancy there is an exact solution; the entrainment constant is again estimated from laboratory results for a stratified fluid Finally, the analysis is applied to the (compressible) atmosphere, by making the customary substitution of potential temperature for temperature. Predictions are made of the height to which smoke plumes from typical sources of heat should rise in a still, stably stratified atmosphere under various conditions.