Nonlinear vortex dynamo in a rotating stratified moist atmosphere

We have found a new type of large-scale instability in a rotating stratified moist atmosphere with small-scale turbulence. The turbulence is excited by an external small-scale force with a low Reynolds number. We have constructed the theory based on the method of multiscale asymptotic expansions. The nonlinear equations for large-scale motion have been derived in the third order of the perturbation theory. We have investigated the linear instability and stationary nonlinear regimes. Solutions in the form of localized vortex structures or kinks of a new type have been obtained.     

Anatomy of a bathtub vortex

We present experiments and theory for the "bathtub vortex," which forms when a fluid drains out of a rotating cylindrical container through a small drain hole. The fast down-flow is found to be confined to a narrow and rapidly rotating "drainpipe" from the free surface down to the drain hole. Surrounding this drainpipe is a region with slow upward flow generated by the Ekman layer at the bottom of the container. This flow structure leads us to a theoretical model similar to one obtained earlier by Lundgren [J. Fluid Mech. 155, 381 (1985)]], but here including surface tension and Ekman upwelling, comparing favorably with our measurements. At the tip of the needlelike surface depression, we observe a bubble-forming instability at high rotation rates.     

On the influence of a horizontal magnetic field on the Rosensweig instability of a nonlinear magnetizable ferrofluid

The Rosensweig instability induced by magnetic forces of the flat free surface of the layer of a stationary nonlinearly magnetizable ferrofluid is considered. The fluid covers a horizontal plate of a nonmagnetic material, located in a tilted magnetic field. The critical value of the vertical component of the magnetization vector is calculated in the linear formulation for a deep magnetic fluid for any physically admissible magnetization law. The influence of the horizontal component of the applied magnetic field on the onset of instability upon the modified Langevin magnetization is analyzed.     

Free surface flow between two horizontal concentric cylinders

Results are reported on a combined experimental and numerical investigation of a free surface flow at small Reynolds numbers. The flow is driven by the rotation of the inner of two horizontal concentric cylinders, with an inner to outer radius ratio of 0.43. The outer cylinder is stationary. The annular gap is partially filled, from 0.5 to 0.95 full, with a viscous liquid leaving a free surface. When the fraction of the annular volume filled by liquid is 0.5, a thin liquid film covers the rotating inner cylinder and reenters the liquid pool. For relatively low rotation speeds, the evolution of the film thickness is consistent with the theory for a plate being withdrawn from an infinite liquid pool. The overall liquid flow pattern at this condition consists of two counter-rotating cells: one is around the inner cylinder and the other with weaker circulation rate is in the bottom part of the annulus and nearly symmetric about the vertical axis. With increasing rotation rate, the free surface becomes more deformed, and the dynamics of the stagnation line and the cusp line dividing the cells are tracked as quantitative measures of the interface shape. In addition, the recirculating flow cells lose symmetry and the cusp deforms the free surface severely. A comparison of numerically computed flow which describes the interface by a phase-field method confirms the dynamics of the two cells and the interface deformation. For filling fraction 0.75, the liquid level is slightly above the inner cylinder and a significant decrease in size of the bottom cell with increasing rotation rate is found. For filling fractions approaching unity, the liquid flow consists of one single cell and the surface deformation remains small.     

Influence of the surface deformability and variable viscosity on buoyant - thermocapillary instability in a liquid layer

The primary stationary and oscillatory Bénard-Marangoni instability is investigated in a fluid layer of infinite horizontal extent, bounded below by a rigid plane and above by a deformable upper surface, subjected to a vertical temperature gradient. Since the viscosity is temperature-dependent the consequences of relaxing Oberbeck-Boussinesq approximation and free surface deformability are theoretically examined by means of small disturbance analysis. The problem has been solved numerically by the Taylor series expansion method. The results obtained confirm that when the free surface is undeformable, stationary convection develops in the form of polygonal cells, and oscillatory motion cannot be detected. When the surface deformability is considered, stationary convection sets in, either as a short-wavelength hexagonal instability or as a long-wavelengh mode or as both, and oscillatory convection is also possible. The stability threshold for the short-wavelength mode depends mainly on the viscosity variation while the long-wavelength mode is determined by the surface deformation. Numerically, it is found that the neutral oscillatory Marangoni numbers are only negative. When a variable-viscosity model is used the theoretical and experimental results are in better agreement. Received 15 May 1997     

Morphological stability analysis of partial wetting

We develop a macroscopic static theory of the morphological stability of partial wetting. The system we studied consist of a smooth horizontal solid surface and some non-volatile liquid on it. A necessary condition for the stable equilibrium of such systems is known as the Young condition on the contact angle made at the contact line where the free surface of liquid meets the solid surface. But this condition is local and is not sufficient for the stability. We present a formulation for studying the stability of systems which satisfy the Young condition. Then we apply this to several morphologies of wetting. We find that there are at least two fundamental morphologies that we call a hole and a ridge, which are thermodynamically unstable against certain infinitesimal deformations of the contact lines. The hole type instability has also been found recently [D. J. Srolovitz and S. A. Safran, J. Appl. Phyys., 60 (1986), 1]. We also derived a reduced expression for the wetting energy as a functional of the contact line positions under the assumption of almost flat free surface of the liquid. This serves us to understand the characteristic length scale which appears in the ridge type instability. Besides these instabilities there is another category of morphological instability in which the system becomes unstable against an infinitesimal deformation of the free surface of liquid. We show this by an illustrating example in which the instability is described as the so-called tangent bifureation in nonlinear systems.     

Meniscus instability in a thin elastic film

A new kind of meniscus instability leading to the formation of stationary fingers with a well-defined spacing has been observed in experiments with elastomeric films confined between a plane rigid glass and a thin curved glass plate. The wavelength of the instability increases linearly with the thickness of the confined film, but it is remarkably insensitive to the compliance and the energetics of the system. However, lateral amplitude (length) of the fingers depends on the compliance of the system and on the radius of curvature of the glass plate. A simple linear stability analysis is used to explain the underlying physics and the key observed features of the instability.     

Radiometric measurement on rotating object

The important attribute of infrared radiometer is its ability to measure temperature from a distance without physical contact. Radiometric measurements conducted on a continuously heated stationary and rotating plate are discussed here along with computation of surface temperature from the data obtained. The temperature has been measured remotely with an accuracy of 2%.     

On the influence of the Reynolds number on the intensity of vortex sound flowing around a cylindrical profile

Regularities of the emission of vortex sound (eolian tone) during air flow around stationary and rotating cylindrical profiles have been investigated. The influence of the flow Reynolds number on the intensity of vortex sound emission has been estimated from results of measuring the pressure fluctuation distribution on the surface of stationary cylindrical rods flowed around by air, as well as in the wake behind them. It is shown that the emission intensity depends on the location of the point of flow detachment from the profile surface and the track width near the profile. The ranges of the flow Reynolds numbers where the emission intensity increases with different flow velocities have been determined by analyzing the dependence of the profile lift coefficient on the Reynolds number. An independent way of determining the profile lift coefficient by measuring the vortex sound intensity is proposed. The results explain contradictions between the results of some authors, who experimentally observed different dependences of emission intensity on the flow velocity. The influence of the profile diameter on the vortex sound emission intensity has been investigated. The boundary Reynolds number above which the profile diameter does not affect emission has been established for stationary and rotating cylindrical profiles. It is shown that deposition of rough coatings on the rod surface may reduce the vortex sound emission intensity by affecting the point of flow detachment from the surface.     

Experimental study of the multipolar vortex instability

The instability of a vortex subjected to a stationary dipolar or tripolar constraint is studied experimentally by using a rotating deformable cylinder on which two or three rollers are applied. As the Reynolds number and the aspect ratio of the cylinder are varied, different modes of instability are observed and their wavelength and frequency are compared to theoretical predictions. Secondary instability and cyclic breakup are also evidenced in the elliptic geometry.     

Emergence and decay of turbulence in stirred atomic Bose-Einstein condensates

We show that "weak" elliptical deformation of an atomic Bose-Einstein condensate rotating at close to the quadrupole instability frequency leads to turbulence with a Kolmogorov energy spectrum. The turbulent state is produced by energy transfer to condensate fragments that are ejected by the quadrupole instability. This energy transfer is driven by breaking the twofold rotational symmetry of the condensate. Subsequently, vortex-sound interactions damp the turbulent state leading to the crystallization of a vortex lattice.     

Rosensweig instability of ferrogel thin films or membranes

We derive the dispersion relation of surface waves for magnetic gel membranes or thin films at the interface between two fluids in the presence of an external magnetic field normal to the free surface. Above a critical field strength surface waves become linearly unstable with respect to a stationary pattern of surface protuberances. This linear stability criterion generalizes that of the Rosensweig instability for ferrofluid and ferrogel free surfaces to take into account bending elasticity and intrinsic elastic and magnetic surface properties of the film or membrane, additionally. The latter is of interest for uniaxial ferrogel film or membranes, which show a locked-in permanent magnetization.     

Generation of a stationary train of chaotic soliton-like microwave pulses in self-oscillating ring systems with a ferromagnetic thin film

The generation of a stationary train of chaotic soliton-like microwave pulses has been observed in an isolated self-oscillating ring system with a ferromagnetic thin-film and a resonator. The pulses have been formed owing to three-wave parametric processes and modulation instability of a surface magnetostatic wave. The soliton-like character of the microwave pulses is indicated by the time dependence of the instantaneous phase of the signal envelope.     

Large-Biot-number non-isothermal flow of a thin film on a stationary or rotating cylinder

Using the lubrication approximation we investigate two-dimensional steady flow of a thin film of fluid with temperature-dependent viscosity on a uniformly heated or cooled horizontal cylinder, which may be stationary or rotating about its axis, in the case when the Biot number (a measure of heat transfer at the free surface) is large.We show that the film thickness (but not the fluid velocity) may be obtained from that in the isothermal case by a simple re-scaling.     

Synchrotron X-ray study of the q-fold quasicrystalline symmetry of the smectic C twist grain boundary phase (TGBC)

We report the first X-ray scattering investigation of spatial variations of the q-fold quasicrystalline symmetry (so-called commensurability) of well-aligned samples. A spatial resolution of was achieved using the ESRF microfocus beamline. The liquid crystal samples, contained between glass plates which were either parallel or in a wedge geometry, were scanned in order (i) to probe the mosaicity and (ii) to continuously change the balance between surface and volume effects. In the case of parallel plate cells, commensurability was observed everywhere throughout the sample, hence ruling out possible effects of mosaicity to explain the q-fold symmetry of the diffraction patterns previously reported when probed with a spatial resolution of mm² in rotating anode experiments. In the case of wedge cells, the evolution of X-ray patterns with thickness suggested that commensurate lockin occurs for sufficiently thick samples with a width that is statistical. Received 18 January 1999     

Observation of a free-Shercliff-layer instability in cylindrical geometry

We report on observations of a free-Shercliff-layer instability in a Taylor-Couette experiment using a liquid metal over a wide range of Reynolds numbers, Re～10(3)-10(6). The free Shercliff layer is formed by imposing a sufficiently strong axial magnetic field across a pair of differentially rotating axial end cap rings. This layer is destabilized by a hydrodynamic Kelvin-Helmholtz-type instability, characterized by velocity fluctuations in the r-θ plane. The instability appears with an Elsasser number above unity, and saturates with an azimuthal mode number m which increases with the Elsasser number. Measurements of the structure agree well with 2D global linear mode analyses and 3D global nonlinear simulations. These observations have implications for a range of rotating MHD systems in which similar shear layers may be produced.     

滑动椭球凹面约束下的物体运动解析

本文首先分析导出光滑平面上能自由滑动的静止旋转椭球凹面理想约束下静释放小球的运动轨迹，然后求出静释放小球（可视为质点）的运动速度表达式和加速度表达式，最后用Excel取特定数值作出了小球的速度和加速度与x的函数图像，可直观反映小球的速度和加速度变化的规律。     

具有微型沟槽结构旋转圆盘减阻的实验研究

建立了开式旋转圆盘系统减阻实验平台,对圆盘螺线沟槽减阻进行实验研究,并可以结合数值研究手段对微型沟槽减阻的机理进行研究。实验结果表明圆盘开槽面积为7.4%时,螺线微型沟槽使得旋转圆盘的最大减阻率达6.1%,V型沟槽两侧的压力差所产生的正扭矩是其减阻的主要原因。沟槽还能起到提高圆盘内径与外径处的静压差的效果。研究结果还表明,采用和平板减阻相同的无量纲尺寸的沟槽会引起圆盘表面的剪应力较大增加。     

Motion of clusters of weakly coupled two-dimensional cavity solitons

An analysis of clusters of weakly coupled two-dimensional spatial optical solitons in a large-aperture class A laser with a saturable absorber is developed. The symmetries that control the transverse motion of the clusters are described. Numerical solutions of the governing generalized complex Ginzburg-Landau equation demonstrate the existence of four types of clusters of weakly coupled cavity solitons that correspond to symmetries of transverse intensity distributions and energy flows: (1) stationary (with two mirror symmetry axes), (2) rotating about a stationary center of mass (invariant under rotation), (3) translating without rotation (with a single mirror symmetry axis), and (4) asymmetric ones rotating about a center of mass that moves around a circle (with equal periods of rotation and circular motion).     

Point charge in the vicinty of a Kerr black hole

We derive the expression for the electromagnetic field of a point charge at rest on the symmetry axis near a rotating Kerr black hole. This is a generalization of the previously obtained solution for the field of a point charge near a nonrotating Schwarzschild black hole. Unlike the Schwarzschild case the charge is found to give rise to magnetic fields as seen by a stationary or locally nonrotating observer.