Transonic inviscid disc flows in the Schwarzschild metric - I

Metric structures of inviscid flows

An intrinsic metric tensor, a flat connexion and the corresponding distance-like function are constructed in the configuration space formed by the velocity field and the thermodynamic variables of an inviscid fluid. The kinetic-energy norm is obtained as a limiting case; all physical quantities are Galilean invariant. Explicit expressions are given for the case of an ideal gas. The flat connexi...

Application of viscous-inviscid interaction methods to transonic turbulent flows

Control of Underwater Vehicles in Inviscid Fluids. I: Irrotational Flows

In this paper, we investigate the controllability of an underwater vehicle immersed in an infinite volume of an inviscid fluid whose flow is assumed to be irrotational. Taking as control input the flow of the fluid through a part of the boundary of the rigid body, we obtain a finite-dimensional system similar to Kirchhoff laws in which the control input appears through both linear terms (with t...

Quasi-Simultaneous Viscous-Inviscid Interaction for Transonic Airfoil Flow

Following Prandtl, a viscous-inviscid interaction (VII) method is presented, where the flow field is divided into a viscous shear layer and an inviscid outer region. Their coupling is performed with the quasi-simultaneous approach, making use of an appropriately chosen interaction law. Firstly, an engineering example of transonic airfoil flow is presented, in which the interaction law is based ...

On the Energy of Inviscid Singular Flows

ABSTRACT. It is known that the energy of a weak solution to the Euler equation is conserved if it is slightly more regular than the Besov space B 3,∞. When the singular set of the solution is (or belongs to) a smooth manifold, we derive various L-space regularity criteria dimensionally equivalent to the critical one. In particular, if the singular set is a hypersurface the energy of u is conser...