Perturbation analysis of baroclinic torque in low-Mach-number flows

Zhang，Shengqi1; Xia，Zhenhua2; Chen，Shiyi1,3

2022-01-10

10.1017/jfm.2021.896

JOURNAL OF FLUID MECHANICS   影响因子和分区

0022-1120

1469-7645

In this paper, we propose a series expansion of the baroclinic torque in low-Mach-number flows, so that the accuracy and universality of any buoyancy term could be examined analytically, and new types of buoyancy terms could be constructed and validated. We first demonstrate that the purpose of introducing a buoyancy term is to approximate the baroclinic torque, and straightforwardly the error of any buoyancy term could be defined with the deviation of its curl from the corresponding baroclinic torque. Then a regular perturbation method is introduced for the elliptic equation of the hydrodynamic pressure in low-Mach-number flows, resulting in a sequence of Poisson equations, whose solutions lead to the series representation of the baroclinic torque and the new types of buoyancy terms. It is found that the frame invariance of the momentum equation is maintained with one of the new types of buoyancy terms. With the error definition of buoyancy terms and the series representation of the baroclinic torque, the validity and accuracy of previous and new buoyancy terms are examined. Finally, numerical simulations confirm that, with a decreasing density variation or an increasing order of our new buoyancy term, the simplified equations can converge to the original low-Mach-number equations.

compressible flows convection

SCI ; EI

英语

通讯

National Science Foundation of China (NSFC)[11988102,11822208,11772297,91852205] ; Shenzhen Science and Technology Programme[KQTD20180411143441009]

Mechanics ; Physics

Mechanics ; Physics, Fluids & Plasmas

WOS:000721319500001

CAMBRIDGE UNIV PRESS

20214611153099

Aerodynamics ; Buoyancy ; Mach number ; Perturbation techniques ; Torque

Aerodynamics, General:651.1 ; Mathematics:921 ; Calculus:921.2 ; Physical Properties of Gases, Liquids and Solids:931.2 ; Mechanical Variables Measurements:943.2

ENGINEERING

2-s2.0-85118863740

Scopus

1.State Key Laboratory for Turbulence and Complex Systems,Peking University,Beijing,100871,China
2.State Key Laboratory of Fluid Power and Mechatronic Systems,Department of Engineering Mechanics,Zhejiang University,Hangzhou,310027,China
3.Department of Mechanics and Aerospace Engineering,Southern University of Science and Technology,Shenzhen,518055,China

Zhang，Shengqi,Xia，Zhenhua,Chen，Shiyi. Perturbation analysis of baroclinic torque in low-Mach-number flows[J]. JOURNAL OF FLUID MECHANICS,2022,930.

Zhang，Shengqi,Xia，Zhenhua,&Chen，Shiyi.(2022).Perturbation analysis of baroclinic torque in low-Mach-number flows.JOURNAL OF FLUID MECHANICS,930.

Zhang，Shengqi,et al."Perturbation analysis of baroclinic torque in low-Mach-number flows".JOURNAL OF FLUID MECHANICS 930(2022).