Finer fractal geometry for analytic families of conformal dynamical systems

We prove several results establishing real analyticity of Hausdorff dimensions of limit sets of analytic families of conformal graph directed Markov systems. With this tool and with iterated function systems resulting from the existence of nice sets in the sense of Rivera-Letelier, we prove that the canonical Hausdorff measure restricted to the radial Julia set of a tame meromorphic function (can be rational) is σ-finite and that the Hausdorff dimension of the radial Julia sets for fairly general families of meromorphic functions (can be rational) is real analytic.     

Stuart vortices in a stratified mixing layer: the Holmboe model

Asymptotic techniques are used to model the quasi-steady state vortices that have been observed in two-dimensional simulations of vortex roll-up in stratified shear layers. A time-independent nonlinear critical layer analysis is used to find a family of steady-state finite amplitude vortices in the Holmboe model of an inviscid stratified shear layer, with the vorticity inside closed streamlines based on the Stuart vortex. The vortices are compared to results of simulations and also an alternative model where the vorticity was constant inside closed streamlines.     

On the geometry of radiative and thermally conducting gas flows

After formulation of the various dynamical and kinematical relations connecting the flow quantities with the geometrical parameters of the streamline trajectories, the expressions for the tangent, principal normal and binormal vectors and the curvature and torsion of the streamlines have been obtained in terms of the velocity components, pressure, density, thermal conductivity and radiation variables. This is followed by the determination of the pressure gradient along the streamlines, their principal normals and binormals. It has been shown that the radiating character of the gas decreases the pressure gradient whereas thermal conductivity increases it along the streamlines but the pressure remains constant along the binormals and if the streamlines are straight lines, the trajectories of the principal normals lie on the surface of the constant pressure. Finally, the expressions for the vorticity components in terms of the curvature of the streamline and the velocity gradients along the streamline, their principal normals and binormals have been obtained.     

MHD flow past a sphere at low and moderate Reynolds numbers

The steady incompressible magnetohydrodynamic (MHD) flow past a sphere with an applied magnetic field parallel to the main flow is studied for the Reynolds number, Re, up to 100 and interaction parameter, N, up to 0.7. The magnetic Reynolds number is assumed to be small. It is observed that drag coefficient increases as N increases. The Finite difference method is used to solve the vorticity-stream function form of the non-linear Navier-Stokes equations. The multigrid method is used to solve the finite difference equations. The fifth decimal place convergent solutions are obtained upto the finest grid of 1024×512. Graphs of the streamlines, vorticity lines, surface vorticity and drag coefficient are presented.The authors are grateful to the Principal, Pondicherry Engineering College and Head, Department of Mathematics, Pondicherry Engineering College for providing the necessary facilities. The authors are thankful to Dr. Umamaheswara Rao, Department of Applied Mathematics, Andhra University, Visakhapatnam and Dr. R. Sivakumar, Department of Physics, Pondicherry Engineering College, for their encouragement.     

On rotational water waves with surface tension

The purpose of this paper is to present some recent advances in the study of water waves with vorticity and surface tension. These are periodic, two-dimensional waves over a flat bottom and the surface profiles are symmetric and monotone between crest and trough. The proofs rely on bifurcation theory.     

DRBEM solution of natural convection flow of nanofluids with a heat source

This paper presents the dual reciprocity boundary element method (DRBEM) solution of the unsteady natural convective flow of nanofluids in enclosures with a heat source. The implicit Euler scheme is used for time integration. All the convective terms are evaluated in terms of DRBEM coordinate matrix. The vorticity boundary conditions are obtained from the Taylor series expansion of stream function equation. The results report that the average Nusselt number increases with the increase in both volume fraction and Rayleigh number. It is also observed that an increase in heater length reduces the heat transfer. The average Nusselt number of aluminum oxide-water based nanofluid is found to be smaller than that of copper-water based nanofluid. Results are given in terms of streamlines, isotherms, vorticity contours, velocity profiles and tables containing average Nusselt number for several values of Rayleigh number, heater length, volume fraction, and number of iterations together with CPU times.     

Regularity of rotational travelling water waves

Several recent results on the regularity of streamlines beneath a rotational travelling wave, along with the wave profile itself, will be discussed. The survey includes the classical water wave problem in both finite and infinite depth, capillary waves and solitary waves as well. A common assumption in all models to be discussed is the absence of stagnation points.     

Dynamic Analysis of Wind Power Turbine's Tower under the Combined Action of Winds and Waves

To deal with the dynamic response problem of offshore wind power tower under the combined action of winds and waves,finite element method is used to analyze the structure and flow field around the outside flange of the segmentation part. The changes of pressure distribution and vorticity about the outside flange are obtained.Focused on the analysis on the change of hydrostatic pressure and temperature of the tower cut surface,contour lines under the combined action of winds and waves are depicted. Results show that the surface of the offshore wind turbine tower presents instable temperature field when it suffers the action of winds and waves loads,the static pressure increases nonlinearly with the increase of altitude,the fluid vorticity around the outside flange follows an parabolic curve approximately. Results provide a reference for the actual monitoring data of the offshore wind turbine tower under the combined action of winds and waves,so as to ensure the normal operation of tower.     

Certain inverse solutions of the plane creeping flow of a second-order fluid

Summary Inverse solutions for the plane steady creeping flow of a second-order fluid are obtained by assuming certain forms of vorticity and its Laplacian. Expressions for streamlines are given explicitly in each case.     

基于PIV技术的平屋盖表面分离泡流动结构研究

该文利用粒子图像测速技术,通过风洞流场显示试验,观察了大跨平屋盖表面的分离泡现象,给出了不同来流工况下多个可视化平面的旋涡流线和涡量场分布。试验结果表明,当风向垂直于平屋盖迎风前缘时,屋盖顶面将出现典型的分离泡现象,涡量场的负向峰值出现在迎风前缘处,屋面风压力随离迎风前缘距离的增加而减小。均匀流场下流动将在迎风边缘产生分离而后再附,再附长度近乎横跨整个屋盖;而湍流场中的小尺度湍流促使分离剪切层较早地再附形成分离泡,且湍流度越大,旋涡再附长度越短。运用FLUENT模拟了平屋盖表面的分离泡,与流动显示试验结果吻合较好。通过多个可视化平面的综合分析得到分离泡的三维形态特征,建立了旋涡的演化、涡核位置与建筑物表面压力分布的内在联系,获得了若干有价值的结论。     

Variational wave-scattering theory for a sinusoidal reflection grating

Abstract

Scattering calculations via the Schwinger variational principle are exemplified for the canonical model of E _∥ plane waves incident on a planarsinusoidal perfect-reflector surface. The complete solution is obtained in terms of a contour integral from which analytic limits are derived that agree with exact results. The contour integral is then evaluated by principal-value and asymptotic techniques, furnishing an explicit solution in Bessel and digamma functions. The variational solution is cast finally into the form of a linear algebraic system, whence we derive various analytic expansions that reproduce further exact results and confirm the efficacy of a simple form of our trial functions. Computations employing this trial function are compared with other approximations and the exact solution. Alternative variational solution representations involving incomplete Anger–Weber or half-range Anger functions are appended.     

Scattering of first and second sound waves by quantum vorticity in superfluid helium

We study the scattering of first and second sound waves by quantum vorticity in superfluid Helium using two-fluid hydrodynamics. The vorticity of the superfluid component and the sound interact because of the nonlinear character of these equations. Explicit expressions for the scattered pressure and temperature are worked out in a first Born approximation, and care is exercised in delimiting the range of validity of the assumptions needed for this approximation to hold. An incident second sound wave will partly convert into first sound, and an incident first sound wave will partly convert into second sound. General considerations show that most incident first sound converts into second sound, but not the other way around. These considerations are validated using a vortex dipole as an explicitely worked out example.     

Surface vorticity modeling of flow around airfoils

A surface vorticity method based on the new Kutta condition has been developed for solving the steady flow around an airfoil and unsteady separated flow past airfoil with a spoiler. In a discussion of the Kutta condition, it is argued that the appropriate Kutta condition is required to obtain a satisfactory solution. In this paper, two new methods of satisfying the Kutta condition incorporated in the surface vorticity method are described. The first method, which is based on results from flow visualization, is to introduce an additional control point at a short distance downstream of the trailing edge. In order to account for the fact that the velocity above the trailing edge is different from that below as in the real flow, the second method is to add a finite segment of vortex sheet downstream of the trailing edge. The present Kutta conditions are incorporated into the surface vorticity method and extend to solve unsteady flow around an airfoil with a spoiler. The computational results are in reasonable agreement with other computation as well as experiments.     

Numerical simulation of unsteady viscous flow around a circular cylinder

A finite difference solution is obtained for the time-dependent viscous incompressible 2-dimensional flow past a circular cylinder by direct integration of the Navier-Stokes equations expressed in a general curvilinear coordinate system. The solution describes the development of the vortex street developed behind the cylinder. Evolution of flow configuration is studied by means of streamlines, pressure contours, and vorticity contours for different Reynolds numbers. The time-dependent lift and drag coefficients are also obtained.     

Moving phreatic surface in a porous slab: an analytical solution

Transient Darcian flow in an inclined rigid fully saturated porous layer is studied. A phreatic surface of fixed shape driven by uniformly increasing (but generally not equal) water levels in the contiguous reservoirs moves upward with a constant velocity. In a system of coordinates travelling with the reservoir water level the real and imaginary parts of the complex potential (an analytic function) and complex coordinate are linearly interconnected along the boundary of the flow domain that allows implementing the Polubarinova-Kochina method. An explicit analytic equation of the free surface is derived and shown to result in non-trivial configurations including the saturated zone overhanging dry areas.     

Surface acoustic breathers of self-induced transparency in semiconductors

A theory of the nonlinear surface acoustic waves in semiconductors containing paramagnetic impurities is constructed. The formation of surface acoustic breathers under the conditions of self-induced transparency is considered. Explicit analytic expressions for the breathers of Rayleigh waves are obtained. It is shown that the interaction of an acoustic wave with conduction electrons leads to a weak damping of the wave amplitude and a change in the breather parameters.     

Boundary element analysis of wave-current interaction around a large structure

A numerical approach for wave-current interaction around a large structure is investigated, based on potential flow theory, linear waves and small current velocity approximation. The velocity potential in a wave-current coexisting field is separated into a steady current potential and an unsteady wave potential. The boundary element method was then employed to compute the unsteady wave potential with effects of both a uniform current and a large body taken into consideration. It is demonstrated that the steady current potential can be expressed as the sum of a uniform current and a steady disturbance due to the presence of the object. The variation of current velocity in the vicinity of the object is then calculated by using a surface vorticity boundary integral meethod. Boundary element analysis is also used for the numerical solutions of the surface vorticity method. Substituting both unsteady wave potential and current velocity into the first-order dynamic surface boundary condition, the water surface elevation around a large structure in a wave-current coexisting field can then be obtained. Comparisons of numerical predictions with experimental results ar also made; qualitative good agreements are obtained.     

On the uniform vorticity in a high Reynolds number flow

A method is proposed for determining the value of the uniform vorticity (₀) in the inviscid region of a high Reynolds number (Re) flow with closed streamlines. An asymptotic treatment of the area integral of the Navier-Stokes equations over the enclosed region leads to a constraint involving the core vorticity; this requires the solution of the momentum equations at O(1) and O(Re ^{–% MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaGymaiaac+% cacaaIYaaaaa!3816!\[1/2\]}) both in the core and in the surrounding boundary layers, although we are subsequently able to show that, under the assumption that the core vorticity at O() is also constant, the value of ₀ depends only on the flow at O(1). The analysis is verified numerically for the case where the boundary is an ellipse, and is also shown to be in agreement with the only case for which an analytic solution is available, namely when the enclosing boundary is circular. The validity of the above-mentioned assumption is also discussed.     

Complete point symmetry group of the barotropic vorticity equation on a rotating sphere

The complete point symmetry group of the barotropic vorticity equation on a rotating sphere is determined. The method we use relies on the invariance of megaideals of the maximal Lie invariance algebra of a system of differential equations under automorphisms generated by the associated point symmetry group. A convenient set of megaideals is found for the maximal Lie invariance algebra of the spherical vorticity equation. We prove that there are only two independent (up to composition with continuous point symmetry transformations) discrete symmetries for this equation.