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

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