Stability of Rotating Viscous and Inviscid flows
نویسنده
چکیده
Flow instability and turbulent transition can be well explained using a new proposed theory--Energy gradient theory [1]. In this theory, the stability of a flow depends on the relative magnitude of energy gradient in streamwise direction and that in transverse direction, if there is no work input. In this note, it is shown based on the energy gradient theory that inviscid nonuniform flow is unstable if the energy in transverse direction is not constant. This new finding breaks the classical linear theory from Rayleigh that inviscid flow is unstable if the velocity profile has an inflection point in parallel flows and inviscid flow is stable if the velocity profile has no inflection point in parallel flow. Then, stability of rotating viscous and inviscid flows is studied, and two examples of rotating flows (rotating rigid body motion and free vortex motion) are shown, respectively.
منابع مشابه
Stability and bifurcations of two-dimensional zonal jet flows on a rotating sphere
In planetary atmospheres in Jupiter or Saturn, for example, strong zonal jets have been observed. The existence of the zonal jet flow has been considered as one of the robust properties of planetary atmospheres. The two-dimensional incompressible Navier-Stokes flow on a rotating sphere is considered to be one of the simplest and most fundamental models of the atmospheric motions taking into acc...
متن کاملA Composite Finite Difference Scheme for Subsonic Transonic Flows (RESEARCH NOTE).
This paper presents a simple and computationally-efficient algorithm for solving steady two-dimensional subsonic and transonic compressible flow over an airfoil. This work uses an interactive viscous-inviscid solution by incorporating the viscous effects in a thin shear-layer. Boundary-layer approximation reduces the Navier-Stokes equations to a parabolic set of coupled, non-linear partial diff...
متن کاملSimulation of Pitching and Heaving Airfoil with Oscillation of Flow Boundary Condition
A pressure based implicit procedure to solve the Euler and Navier-Stokes equation is developed to predict transonic viscous and inviscid flows around the pitching and heaving airfoils with a high reslution scheme. In this process, nonorthogonal and non moving mesh with collocated finite volume formulation are used. In order to simulate pitching or heaving airfoil, oscillation of flow boundary c...
متن کاملNon-linear asymptotic stability for the through-passing flows of inviscid incompressible fluid
The paper addresses the dynamics of inviscid incompressible fluid confined within bounded domain with the inflow and outflow of fluid through certain parts of the boundary. This system is non-conservative essentially since the fluxes of energy and vorticity through the flow boundary are not equal to zero. Therefore, the dynamics of such flows should demonstrate the generic non-conservative phen...
متن کاملStability of Two-Dimensional Viscous Incompressible Flows under Three-Dimensional Perturbations and Inviscid Symmetry Breaking
In this article we consider weak solutions of the three-dimensional incompressible fluid flow equations with initial data admitting a one-dimensional symmetry group. We examine both the viscous and inviscid cases. For the case of viscous flows, we prove that Leray-Hopf weak solutions of the threedimensional Navier-Stokes equations preserve initially imposed symmetry and that such symmetric flow...
متن کامل