At the Start of Third Round

    Title : Curvature Instability
   Author : Yuji Hattori
Affiliation : Institute of Fluid Science, Tohoku University
Keywords : vortex ring, helical vortex, curvature instability

Abstract

 Curvature instability was first found for Kelvin’s vortex ring by Fukumoto and Hattori (2005) and Hattori and Fukumoto (2003). It is due to parametric resonance of two neutral inertial waves coupled by the self-induced dipolar field of the vortex ring. Since then, it has been shown to exist for helical vortices and Hill’s spherical vortices. Recently, it was shown to exist for a vortex ring having continuous vorticity distribution like Gaussian distribution. However, the characteristics of the curvature instability are different between Kelvin’s vortex ring and the Gaussian vortex ring. Theoretical and numerical studies on the curvature instability are reviewed and recent results by direct numerical simulation are presented.

    Title : Prediction of crossflow-induced boundary-layer transition and its control by wall roughness
   Author : Makoto Hirota⁽¹⁾, Yuki Ide⁽²⁾, Takahisa Hayashida^(1),(3) and Yuji Hattori⁽¹⁾
Affiliation : (1) Institute of Fluid Science, Tohoku University
      (2) Japan Aerospace Exploration Agency
      (3) Graduate School of Information Sciences, Tohoku University
Keywords : boundary layer transition, drag reduction, Kelvin-Helmholtz instability,
       direct numerical simulation

Abstract

 On widely-used swept wings of aircrafts, laminar-to-turbulent transition of three-dimensional boundary layer is mainly caused by the crossflow instability, which increases friction drag on wings significantly. It is therefore important to correctly predict the transition location and try to shift it downstream in some way. We tackle this problem by multiple approaches; direct numerical simulation (DNS), linear and nonlinear stability analysis and theoretical modeling. In fact, the transition occurs only when low-speed streaks (that is induced by the primary crossflow mode) becomes further subject to a high-frequency secondary instability. By generalizing Rayleigh's inflection-point theorem for 1d parallel shear flow to 2d one, we predict the stability of low-speed streaks semitheoretically. When a crossflow mode is free from secondary instability, it tends to stabilize the velocity profile of the boundary layer nonlinearly. By intentionally exciting such a subcritical mode by wall roughness, the transition is demonstrated to delay in downstream direction.

    Title : Recent Development of Theory of Gases in Rational Extended Thermodynamics
   Author : Takashi Arima
Affiliation : National Institute of Technology, Tomakomai College
Keywords : Nonequilibrium thermodynamics, Extended thermodynamics, Dense gas,
       Polyatomic gas, Bulk viscosity

Abstract

 Rational extended thermodynamics provides a theoretical framework of a nonequilibrium system of continuum medium. Under the requirement of the symmetric hyperbolic system with the convex entropy, the theory adopts dissipative fluxes as fields in addition to the usual thermodynamic fields.
 In this talk, the theory of gases beyond the assumption of the local equilibrium is presented. In particular, I discuss the dynamics of the energy exchange among the internal modes of a molecule which provides the origin of the bulk viscosity related to the nonequilibrium pressure. In addition, from the aspect of the energy exchange, the theories for rarefied monatomic gases, rarefied polyatomic gases, dense monatomic gases and dense polyatomic gases are comprehensively summarized. The discussion includes the validity of the theory through the numerical analysis of the sound waves and steady flows in gases with large bulk viscosity such as hydrogen and carbon dioxide.

    Title : Strongly stratified limit for the 3D inviscid Boussinesq equations
   Author : Ryo Takada
Affiliation : Faculty of Mathematics, Kyushu University
Keywords : the 3D inviscid Boussinesq equations, stable stratification, strongly stratified limit

Abstract

 In this talk, we consider the initial value problem of the 3D inviscid Boussinesq equations under the effect of stable stratification. We prove the long time existence of classical solutions for large initial data when the buoyancy frequency is sufficiently high. Furthermore, we consider the singular limit of the strong stratification, and show that the long time classical solution converges to that of 2D incompressible Euler equations in some space-time norms.