A universal variational formulation for two dimensional fluid mechanics

A universal variational formulation for two dimensional fluid mechanics is obtained. which is subject to the so-called parameter-constrained equations (the relationship between parameters in two governing equations). By eliminating the constraints the generalized variational principle (GVPs) can be readily derived from the formulation The formulation can be applied to any conditions in case the governing equations can be converted into conservative forms. Some illustrative examples are given to testify the effectiveness and simplicity of the method.