Landau solutions are special to the stationary incompressible Navier-Stokes equations in three dimensional space excluding origin. They self-similar and axisymmetric with no swirl. In fact, any smooth solution must be a solution. effort of extending this result one for class pointwise scale-invariant bound $|u(x)|\leq C_0|x|^{-1}$ some $C_0>0$, we consider discretely solutions, investigate exis...

The development of combustion systems to minimize the emission of pollutants and to increase the system’s efficiency involves modifications of the combustion process using premixed systems and highly turbulent swirl stabilized flames. However, these modifications of the combustion process usually lead to stability problems caused by the appearance of combustion-driven oscillations. Therefore, i...

Topological methods are used to establish global and to extract local structure properties of vector fields in axi-symmetric and 3-d flows as function of time. The notion of topological skeleton is applied to the interpretation of vector fields generated numerically by the Navier-Stokes equations. The flows considered are swirling jets with super-critical swirl numbers that show low Reynolds nu...

Consider a three-dimensional vortex sheet in inviscid, incompressible flow which is irrotational away from the sheet. We derive an equation for the evolution of a vortex sheet in Lagrangian coordinates, i.e. an equation that is restricted to the sheet itself and is analogous to the Birkhoff-Rott equation for a two-dimensional (planar) sheet. This general equation is specialized to sheets with a...

Vortex breakdown (VB) in unconfined swirling jets occurs as either a bubble form of vortex (BVB) or conical (CVB). This computational study examines flow features these forms for Reynolds number at which VB is accompanied by transition to turbulence ( $Re = 1000$ , based on inflow jet radius and centreline velocity). Large eddy simulations were performed with the condition Maxworthy profile mod...