Yoshifumi Kimura

Diffusion in stably stratified turbulence

We examine results of direct numerical simulations (DNS) of homogeneous turbulence in the presence of stable stratification. We focus on the effects of stratification on eddy diffusion, and the distribution of pairs of particles released in the flow. DNS results are presented over a range of stratification, and at Reynolds numbers compatible with aliased free spectral results for a resolution of 128 mesh points. We compare results for particle dispersion to simple analytic theories such as that proposed by Csanady (1964) and Pearson et al. (1983) by adapting the basic Langevin model to decaying turbulence at low Reynolds numbers. Stable stratification is found to arrest both single particle displacements and pair separation in the direction of stratification, but it leaves these quantities nearly unaltered in the transverse direction. With respect to the dynamics of stratified flows, we find that regions of strong viscous dissipation are intermittently spaced, and are associated with large horizontal vorticity, consistent with recent experimental results by Fincham et al. (1994).

Vortex Motion on a Sphere

The theory of the vortex motion of two-dimensional incompressible inviscid flow on a sphere is presented. Vorticity and stream function, which are related by the Laplace-Beltrami operator, are initially outlined. Greens function of the equation is obtained in which the stream function is expressed as an integral form. The equations of motion for two vortex models on a sphere are derived. In particular, the equation for vortex patches with constant vorticity is given in terms of the contour integral appropriate for the contour dynamics.

Vortex motion on surfaces with constant curvature

Vortex motion on two–dimensional Riemannian surfaces with constant curvature is formulated. By way of the stereographic projection, the relation and difference between the vortex motion on a sphere (S2) and on a hyperbolic plane (H2) can be clearly analysed. The Hamiltonian formalism is presented for the motion of point vortices on S2 and H2. The set of first integrals for each Hamiltonian shows a corresponding algebraic property in terms of the Poisson bracket defined respectively for S2 andH2. As an example of analytic solutions, the motion of a vortex pair (dipole) is considered. It is shown that a dipole draws a geodesic curve as its trajectory on S2 and H2.

Statistics of an advected passive scalar

An elementary argument shows that non‐Gaussian fluctuations in the temperature at a point in space are induced by random advection of a passive temperature field that has a nonlinear mean gradient, whether or not there is molecular diffusion. This is corroborated by exact analysis for the nondiffusive case and by direct numerical simulation for diffusive cases. Eulerian mapping closure gives results close to the simulation data. Non‐Gaussian fluctuations of temperature at a point also are induced by a more subtle mechanism that requires both advection and molecular diffusion and is effective even when the statistics are strictly homogeneous. It operates through selectively strong dissipation of regions where intense temperature gradients have been induced by advective straining. This phenomenon is demonstrated by simulations and explored by means of an idealized analytical model.

Zero-helicity Lagrangian kinematics of three-dimensional advection

The toroidal–poloidal decomposition for divergenceless vector fields in three dimensions is used to classify incompressible steady velocity fields in three dimensions according to whether they have zero, or nonzero helicity, and whether they are integrable, or nonintegrable as dynamical systems. Linearized steady Rayleigh–Benard convection flows provide examples from each class. Computational techniques that preserve volume and helicity are developed and used to visualize the Lagrangian particle trajectories of three‐dimensional advection for two Rayleigh–Benard flows having zero helicity in a periodic domain.

Similarity Solution of Two-Dimensional Point Vortices

Theory of the similarity solution of two-dimensional point vortices in an unbounded region is presented. To get the solution, the time dependence of the solution for all vortex positions are assumed to be the same. It is shown that the system either rotates rigidly or collapses according to the initial position of vortices. Then numerical calculations are made especially for the system of three vortices. It is found that the rigid rotation corresponds to the regular triangle solution or the straight line solution, and that irrespective of the strengths of three vortices, the regular triangle solution always exists while the straight line solution is obtained by solving a certain cubic equation.

Parametric motion of complex-time singularity toward real collapse

Abstract Motion of complex-time singularities for solutions of a system of three interacting point vortices is studied, by varying initial conditions until collapse occurs. When collapse occurs, the complex-time singularities converge to a point on the real axis. A heuristic scaling law between the initial displacement of one vortex and the position of the nearest complex-time singularity to the origin is tested numerically. The exponent of the scaling law is related to one of the eigenvalues of the linearized stability problem for the motion of the vortices in a regularized (blown-up) frame.

Motion of a Pair of Vortices in a Semicircular Domain

Study of the motion of two point vortices in a semicircular domain is presented. Especially, the case of equal but opposite circulation is investigated. This system is of a nonintegrable Hamiltonian case according to the Liouville theorem, and may exhibit chaotic behaviors. With the aid of computer simulations, both regular and chaotic states are seen for a series of particular initial conditions.

Transport properties of waves on a vortexes filament

Abstract It is shown that a soliton on a vortex filament can transport linear and angular impulse in the direction of soliton propagation. That is the positive evidence that the soliton potentially is a mechanism for transport of physical quantities such as mass, excess energy, linear and angular momentum and helicity. As a direct application, the far-field sound pressure generated by the soliton is presented. It is shown that the pressure is a combination of two kinds of rotating quadrupoles translating in the same direction with the soliton.

Motion of Two Identical Point Vortices in a Simple Shear Flow

Motion of two identical point vortices in a simple shear flow is studied. According to the competition between the strength of the shear flow and that of the vortices, two vortices either separate being carried by the flow or rotate on a periodic orbit. The critical ratio of these strength is found, and computer simulations are made for various situations according to this criterion. The integrability of this system is also considered as a Hamiltonian system. Though the Hamiltonian is less symmetric than that of the case without a boundary or an external flow, the system is integrable according to the Liouville theorem.