In　this　paper,　we　investigate　some　new　properties　of　the　incompressible　Euler　and　Navier-Stokes　equations　by　studying　a　3D　model　for　axisymmetric　3D　incompressible　Euler　and　Navier-Stokes　equations　with　swirl.　The　3D　model　is　derived　by　reformulating　the　axisymmetric　3D　incompressible　Euler　and　Navier-Stokes　equations　and　then　neglecting　the　convection　term　of　the　resulting　equations.　Some　properties　of　this　3D　model　are　reviewed.　Finally,　some　potential　features　of　the　incompressible　Euler　and　Navier-Stokes　equations　such　as　the　stabilizing　effect　of　the　convection　are　presented.