**5. Conclusions**

In this work, we determined the one-dimensional optimal system for the two-dimensional ideal gas equations. The nonrotating system was found to be invariant under an eight-dimensional group of one-parameter point transformations. and there were twenty-three independent one-dimensional Lie algebras. One the other hand, when the Coriolis force was introduced, the dynamical admitted seven Lie point symmetries and twenty one-dimensional Lie algebras.

For all the independent Lie algebras, we determined all the invariant functions, which corresponded to all the independent similarity solutions.

In a future work, we plan to classify all the independent one-dimensional Lie algebras, which lead to analytic forms for the similarity solutions.

**Funding:** This research received no external funding.

**Acknowledgments:** The author wants to thank Kevin Duffy for gracious hospitality and P.G.L.Leach for a fruitful discussion on the subject.

**Conflicts of Interest:** The author declare no conflict of interest.
