Capturing the baroclinic effect in non-Boussinesq gravity currents  

作　　者：Shengqi Zhang Zhenhua Xia 

机构地区：[1]State Key Laboratory for Turbulence and Complex Systems,College of Engineering,Peking University,Beijing 100871,China [2]Department of Engineering Mechanics,Zhejiang University,Hangzhou 310027,China

出　　处：《Theoretical & Applied Mechanics Letters》2022年第1期10-16,共7页力学快报（英文版）

基　　金：supported by the National Natural Science Foundation of China(Grants 11822208,92152101,11772297,and 91852205)。

摘　　要：Direct numerical simulations of two-dimensional gravity currents with small and medium density variations are performed using different non-Boussinesq buoyancy approximations. Taking the full low-Machnumber approximation as the reference, the accuracy of several buoyancy terms are examined. It is found that all considered buoyancy terms performed well in the cases with small density variation. In the cases with medium density variation, the classical gravitational Boussinesq’s buoyancy term showed the lack of accuracy, and a simple correction did not make any improvement. In contrast, the recently introduced second-order buoyancy term showed a significantly higher accuracy. The present results and our previous derivations indicate that simple algebraic buoyancy approximations extended from the Boussinesq’s gravitational buoyancy are unlikely to achieve an accuracy beyond first order. Instead, it seems necessary to solve at least one extra Poisson equation for buoyancy terms to capture the higher-order baroclinic effect. An approximate analysis is also provided to show the leading term of the non-Boussinesq effect corresponding to gravity.

关 键 词：Baroclinic effect Gravity current 

分 类 号：O35[理学—流体力学]