Steady Euler Flows with Large Vorticity and Characteristic Discontinuities in Arbitrary Infinitely Long Nozzles

We establish the existence and uniqueness of smooth solutions with large vorticity and weak solutions with vortex sheets/entropy waves for the steady Euler equations for both compressible and incompressible fluids in arbitrary infinitely long nozzles. We first develop a new approach to establish the existence of smooth solutions without assumptions on the sign of the second derivatives of the horizontal velocity, or the Bernoulli and entropy functions, at the inlet for the smooth case. Then the existence for the smooth case can be applied to construct approximate solutions to establish the existence of weak solutions with vortex sheets/entropy waves by nonlinear arguments. This is the first result on the global existence of solutions of the multidimensional steady compressible full Euler equations with free boundaries, which are not necessarily small perturbations of piecewise constant background solutions. The subsonic-sonic limit of the solutions is also shown. Finally, through the incompressible limit, we establish the existence and uniqueness of incompressible Euler flows in arbitrary infinitely long nozzles for both the smooth solutions with large vorticity and the weak solutions with vortex sheets. The methods and techniques developed here will be useful for solving other problems involving similar difficulties.Comment: 43 pages; 2 figures; To be published in Advances in Mathematics (2019

Transonic shocks for three-dimensional axisymmetric flows in divergent nozzles

We prove the stability of three-dimensional axisymmetric solutions to the steady Euler system with transonic shocks in divergent nozzles under perturbations of the exit pressure and the supersonic solution in the upstream region. We first derive a free boundary problem with the newly introduced formulation of the Euler system for three-dimensional axisymmetric flows in divergent nozzles via the method of Helmholtz decomposition. We then construct an iteration scheme and use the Schauder fixed point theorem and weak implicit function theorem to solve the problem.Comment: 55 pages, 2 figure

Sloshing in a rotating liquid inside a closed sea cage for fish farming

Sloshing in a sea cage with a slowly rotating liquid is investigated. The cage is axisymmetric, and the liquid is subjected to a nearly uniform angular velocity about the vertical axis of the cage. Both experimental and theoretical investigations are presented. It is shown that rotation modifies the sloshing regimes of a non-rotating liquid by splitting the natural frequencies. Therefore, resonant sloshing regimes can be manipulated by varying the rotation rate of the liquid.acceptedVersio

Aeronautical Engineering: A Continuing Bibliography with indexes

This bibliography lists 426 reports, articles and other documents introduced into the NASA scientific and technical information system in August 1984. Reports are cited in the area of Aeronautical Engineering. The coverage includes documents on the engineering and theoretical aspects of design, construction, evaluation, testing operation and performance of aircraft (including aircraft engines) and associated components, equipment and systems

Aeronautical engineering: A continuing bibliography with indexes (supplement 253)

This bibliography lists 637 reports, articles, and other documents introduced into the NASA scientific and technical information system in May, 1990. Subject coverage includes: design, construction and testing of aircraft and aircraft engines; aircraft components, equipment and systems; ground support systems; and theoretical and applied aspects of aerodynamics and general fluid dynamics

Aeronautical engineering: A continuing bibliography with indexes (supplement 303)

This bibliography lists 211 reports, articles, and other documents introduced into the NASA scientific and technical information database. Subject coverage includes: design, construction, and testing of aircraft and aircraft engines; aircraft components, equipment, and systems; ground support systems; and theoretical and applied aspects of aerodynamics and general fluid dynamics

Aeronautical Engineering: a Continuing Bibliography with Indexes (Supplement 243)

This bibliography lists 423 reports, articles, and other documents introduced into the NASA scientific and technical information system in August 1989. Subject coverage includes: design, construction and testing of aircraft and aircraft engines; aircraft components, equipment and systems; ground support systems; and theoretical and applied aspects of aerodynamics and general fluid dynamics

Aeronautical engineering: A continuing bibliography with indexes (supplement 284)

This bibliography lists 974 reports, articles, and other documents introduced into the NASA scientific and technical information system in Oct. 1992. The coverage includes documents on design, construction, evaluation, testing, operation, and performance of aircraft (including aircraft engines) and associated components, equipment, and systems. It also includes research and development in aerodynamics, aeronautics, and ground support equipment for aeronautical vehicles