V. A. Vladimirov

An experimental study on hurricane mesovortices

Mesovortices in the eyewall region of a hurricane are intriguing elements of the hurricane engine. In-situ measurements of them are sparse, however, and our understanding of their overall role in the physics of a hurricane is incomplete. To further understand their dynamics an experimental apparatus using a homogeneous fluid (water) has been constructed to emulate the lower tropospheric flow of the hurricane eye/eyewall region. For experimental configurations possessing a central aspect ratio less than unity, a primary and secondary circulation similar to the in flow layer of an intense hurricane, and a similar radius-to-width ratio of the curvilinear shear layer bordering the eye and eyewall region, the flow supports two primary quasi-steady vortices and secondary intermittent vortices. The vortices form through Kelvin–Helmholtz instability of the curvilinear shear layer bordering the slowly upwelling fluid in the centre and the converging fluid from the periphery. The primary vortices are maintained by convergence of circulation from the periphery and merger of secondary vortices spawned along the shear layer. The horizontal flow field is measured using a particle image velocimeter. Despite the relatively strong secondary circulation through the parent vortex the horizontal flow is found to be approximately uniform in the direction parallel to the rotation axis. The peak tangential velocity is found to occur in the mesovortices and is roughly 50% greater than the parent vortex that supports them. The measurements provide insight into recent observations of excessive wind damage in landfalling storms and support the hypothesis that intense storms contain coherent vortex structures in the eyewall region with higher horizontal wind speeds locally than the parent hurricane.

Algal motility measured by a laser-based tracking method

The velocities of individual actively swimming cells of the green alga Chlamydomonas nivalis can be measured with the use of spatial displacements of their successive images (by a ‘tracking’ method). This paper proposes a new tracking method based on the use of laser light; it is common for the tracking of passive particles, but the case of actively swimming cells presents specific problems. The first problem is the potential influence of the laser light on the behaviour of the cells. A key result of the study is that for carefully chosen parameters the effect of the laser light on the algal swimming is negligible (below the measurement error). Hence, the self-swimming velocities can be measured; sample results are given. The proposed method permits a large measurement volume, and thus allows the velocities of several hundreds of cells to be measured simultaneously. From these data an approximation for the probability distribution function of the velocities of the cells can be derived; this function is crucial for the construction of mathematical models of algal motility. The laser-based tracking method is applicable and useful for measurements of algal motion in still fluid. The method thus presents new opportunities in this area of research.

On the self-propulsion of an N-sphere micro-robot

The aim of this paper is to describe the self-propulsion of a micro-robot (or micro-swimmer) consisting of

Planar inviscid flows in a channel of finite length: washout, trapping and self-oscillations of vorticity

N

The stability of steady magnetohydrodynamic flows with current-vortex sheets

spheres moving along a fixed line. The spheres are linked to each other by arms with their lengths changing periodically. We use the asymptotic procedure containing the two-timing method and a distinguished limit. We show that self-propulsion velocity appears (in the main approximation) as a linear combination of velocities of all possible triplets of spheres. Velocities and efficiencies of three-, four- and five-sphere swimmers are calculated.

Energy principle for magnetohydrodynamic flows and Bogoyavlenskij's transformation

The paper addresses the nonlinear dynamics of planar inviscid incompressible flows in the straight channel of a finite length. Our attention is focused on the effects of boundary conditions on vorticity dynamics. The renowned Yudovichs boundary conditions (YBC) are the normal component of velocity given at all boundaries, while vorticity is prescribed at an inlet only. The YBC are fully justified mathematically: the well posedness of the problem is proven. In this paper we study general nonlinear properties of channel flows with YBC. There are 10 main results in this paper: (i) the trapping phenomenon of a point vortex has been discovered, explained and generalized to continuously distributed vorticity such as vortex patches and harmonic perturbations; (ii) the conditions sufficient for decreasing Arnolds and enstrophy functionals have been found, these conditions lead us to the washout property of channel flows; (iii) we have shown that only YBC provide the decrease of Arnolds functional; (iv) three criteria of nonlinear stability of steady channel flows have been formulated and proven; (v) the counterbalance between the washout and trapping has been recognized as the main factor in the dynamics of vorticity; (vi) a physical analogy between the properties of inviscid channel flows with YBC, viscous flows and dissipative dynamical systems has been proposed; (vii) this analogy allows us to formulate two major conjectures (C1 and C2) which are related to the relaxation of arbitrary initial data to C1: steady flows, and C2: steady, self-oscillating or chaotic flows; (viii) a sufficient condition for the complete washout of fluid particles has been established; (ix) the nonlinear asymptotic stability of selected steady flows is proven and the related thresholds have been evaluated; (x) computational solutions that clarify C1 and C2 and discover three qualitatively different scenarios of flow relaxation have been obtained.

Dumbbell micro-robot driven by flow oscillations

The stability of steady magnetohydrodynamic flows of an inviscid incompressible fluid with current-vortex sheets to small three-dimensional perturbations is studied. The energy method of Frieman and Rotenberg is extended to the case of steady flows with surfaces of tangential discontinuities across which the tangent velocity or the tangent magnetic field or both of them have jump discontinuities. Sufficient conditions for linear stability of some classes of steady flows with parallel velocity and magnetic field are obtained. Also, a sufficient condition for instability of a tubular current-vortex sheet is given.

Dynamics of a Solid Affected by a Pulsating Point Source of Fluid

The stability of steady magnetohydrodynamic flows of an inviscid incompressible fluid is studied using the energy method. It is shown that certain symmetry transformations of steady solutions of the equations of ideal magnetohydrodynamics have an important property: if a given steady magnetohydrodynamic flow is stable by the energy method, then certain infinite-dimensional families of steady flows obtained from the given flow by these transformations are also stable. This result is used to obtain new sufficient conditions for linear stability. In particular, it is shown that certain classes of steady magnetohydrodynamic flows in which both the magnetic field and the velocity depend on all three spatial coordinates are stable.

Dynamics of a rolling robot

In this paper we study the self-propulsion of a dumbbell micro-robot submerged in a viscous fluid. The micro-robot consists of two rigid spherical beads connected by a rod or a spring; the rods/springs length is changing periodically. The constant density of each sphere differs from the density of a fluid, while the whole micro-robot has neutral buoyancy. An effective oscillating gravity field is created via rigid-body oscillations of the fluid. Our calculations show that the micro-robot undertakes both translational and rotational motion. Using an asymptotic procedure containing a two-timing method and a distinguished limit, we obtain analytic expressions for the averaged self-propulsion velocity and averaged angular velocity. The important special case of zero angular velocity represents rectilinear self-propulsion with constant velocity.

An asymptotic model in acoustics: acoustic drift equations.

This paper provides a new insight to the classical Bjorknes’s problem. We examine a mechanical system “solid+fluid” consisted of a solid and a point source (singlet) of fluid, whose intensity is a given function of time. First we show that this system is governed by the least action (Hamilton’s) principle and derive an explicit expression for the Lagrangian in terms of the Green function of the solid. The Lagrangian contains a linear in velocity term. We prove that it does not produce a gyroscopic force only in the case of a spherical solid. Then we consider the periodical high-frequency pulsations (vibrations) of the singlet. In order to construct the high-frequency asymptotic solution we employ a version of the multiple scale method that allows us to obtain the “slow” Lagrangian for the averaged motions directly from Hamilton’s principle. We derive such a “slow” Lagrangian for a general solid. In details, we study the “slow” dynamics of a spherical solid, which can be either homogeneous or inhomogeneous in density. Finally, we discuss the “Bjorknes’s dynamic buoyancy” for a solid of general form.