开放剪切流空间全局动力学与空间相位斑图间的关系

开放流动空间动力学可基于两类全局能量关系式进行研究;而空间相位斑图则可通过互谱空间演化加以测定。全局能量关系式以时间Fourier系数的形式建立流场任意两点问速度脉动能量间的关系,籍此可定义全局意义上的线性、非线性和线性一非线性机制。基于轴对称剪切流、变密度轴对称圆射流以及平面对称剪切流的实验发现：轴对称旋涡结构的配对由线性、线性一非线性机制表征,对应有序空间相位斑图;并且能量可通过线性一非线性机制在具有相同相速度的扰动间传递。螺旋结构由线性机制表征,对应有序相位斑图。全局自激励振荡由非线性的能量共振表征,对应无序相位斑图。籍此,有序空间相位斑图对应线性和线性一非线性机制;而混沌相位斑图则对应非线性机制。     

Development of a Shear Instability in Nodal Zones of a Standing Internal Wave

The results of experimentally investigating the initial stage of development of shear instability of the interface between two immiscible fluids relatively oscillating during the parametric excitation of standing internal waves are presented. Three stages of distortion of the sinusoidal wave profile are distinguished: the formation of short secondary waves, their breaking, and transition to large-scale vortex formations. It is shown that in the nodal zones of a standing wave quasi-stationary wave perturbations start to develop at wave steepnesses Γ ～ 0.08–0.13 and critical Reynolds numbers of the laminar boundary layer R ～ 90–300. The experimental data are compared with the classical Kelvin-Helmholtz theory.     

Modeling the Dynamics of Ensemble-Averaged Linear Disturbances in Homogeneous Shear Flow

In order to expand the predictive capability of single-point turbulence closure models to account for the early-stage transition regime, a methodology for the formulation and calibration of model equations for the ensemble-averaged disturbance kinetic energy and energy dissipation rate is presented. The calibration is based on homogeneous shear flow where disturbances can be described by rapid distortion theory (RDT). The relationship between RDT and linear stability theory is exploited in order to obtain a closed set of modeled equations. The linear disturbance equations are solved directly so that the numerical simulation yields a database from which the closure coefficients in the ensemble-averaged disturbance equations can be determined. This revised version was published online in July 2006 with corrections to the Cover Date.     

On the Interaction of Turbulent Shear Layers with Harmonic Perturbations

The problem of coherent perturbations in a turbulent shear layer is considered for the purpose of developing a mathematical model based on a triple decomposition that extracts the coherent components of random fluctuations. The governing equations for the mean and the coherent parts of flow are derived, assuming the eddy-viscosity equivalence for the random part of flow, and solved by iterations to provide a coupled solution of the problem as a whole. Calculations agree well with experimental data in the upstream part of the layer where the mean–coherent flow interaction is the most important. In this region, the interaction changes the mean flow velocity distribution in such a manner that the neutral stability curve is shifted upstream relative to its position in the undisturbed layer and the perturbation intensity decreases further downstream. Experiments show that the coherent waves suppress the turbulent Reynolds stress production downstream of this region, but the model fails to predict the layer spreading correctly probably due to an inadequate turbulence closure of the mean flow. For the case of a turbulent mixing layer, we suggest a new closure relation that takes into account this coherent-random interaction.     

Spatial Stationary Long Waves in Shear Flows

The system of integrodifferential equations describing the spatial stationary freeboundary shear flows of an ideal fluid in the shallowwater approximation is considered. The generalized characteristics of the model are found and the hyperbolicity conditions are formulated. A new class of exact solutions of the governing equations is obtained which is characterized by a special dependence of the desired functions on the vertical coordinate. The system of equations describing this class of solutions in the hyperbolic case is reduced to Riemann invariants. New exact solutions of the equations of motion are found.     

Thin‐tube vortex simulations for sinusoidal instability in a counter‐rotating vortex pair

A thin‐tube vortex method is developed to investigate the intrinsic instability within a counter‐rotating vortex pair system and the effects from the core size and the wavenumbers (or wavelengths). The numerical accuracy and the advantages of the scheme are theoretically estimated. A nearest‐neighbour‐image method is employed in this three‐dimensional vortex simulation. Agreement with Crow's instability analysis has been achieved numerically for the long‐wave cases. A short‐wave instability for the zeroth radial mode of bending instability has also been found using the thin‐tube vortex simulations. Then, the combinations of long‐ and short‐wave instability are investigated to elucidate the non‐linear effects due to the interactions of two different modes. It is shown that instability is enhanced if both long‐ and short‐wave instabilities occur simultaneously. Although the method used in the paper is not capable of including effects such as axial flow, vortex core deformation and other complicated viscous effects, it effectively predicts and clarifies the first‐order factor that dominates the sinusoidal instability behaviour in a vortex pair. Copyright © 2002 John Wiley & Sons, Ltd.     

Dynamics of the outflow and its effect on the hydraulics of two-layer exchange flows in a channel

This paper reports that an experimental study is conducted to examine the dynamics of the outflow in two-layer exchange flows in a channel connecting between two water bodies with a small density difference. The experiments reveal the generation of Kelvin-Helmholtz (KH) instabilities within the hydraulically sub-critical flow region of the channel. During maximal exchange, those KH instabilities develops into large-amplitude KH waves as they escape the channel exit into the reservoir. The propagation speed of those waves, their generation frequency and their amplitudes are studied. The dynamics of the outflow and these waves are directly linked to the hydraulic conditions of the exchange flow within the channel.     

Investigation of Mechanisms of Excitation and Growth of Unstable Perturbations in Pulsating Flows

General laws of the processes of generation and amplification of secondary perturbations in oscillating viscous fluid flows are studied theoretically. The stability and receptivity are analyzed with reference to perturbations generated by fluctuations of the flow rate of Poiseuille flow induced by small two-dimensional roughnesses of the channel walls. It is shown that the presence of roughness leads to excitation in the flow of perturbations at all multiples of the main flow oscillation frequency. Using the Fourier transform along the streamwise coordinate, the problem of calculating the frequency harmonics is reduced to a system of equations of the Orr-Sommerfeld type interrelated via the oscillatory component of the main flow. On the basis of an investigation of the analytic properties of the Fourier-image it is shown that upstream and downstream of the roughness the perturbation can be represented in the form of a superposition of modes of the time-dependent Poiseuille flow. The modes are classified and their spectrum is calculated. The structure of the mean-square fluctuations generated by free perturbations is investigated. Examples of calculating the evolution of forced perturbations are given for cases in which the scattering of the oscillations of the main flow on the roughness leads to the generation of one or two modes growing downstream.     

Linear stability analysis in compressible, flat-plate boundary-layers

The stability problem of two-dimensional compressible flat-plate boundary layers is handled using the linear stability theory. The stability equations obtained from three-dimensional compressible Navier–Stokes equations are solved simultaneously with two-dimensional mean flow equations, using an efficient shoot-search technique for adiabatic wall condition. In the analysis, a wide range of Mach numbers extending well into the hypersonic range are considered for the mean flow, whereas both two- and three-dimensional disturbances are taken into account for the perturbation flow. All fluid properties, including the Prandtl number, are taken as temperature-dependent. The results of the analysis ascertain the presence of the second mode of instability (Mack mode), in addition to the first mode related to the Tollmien–Schlichting mode present in incompressible flows. The effect of reference temperature on stability characteristics is also studied. The results of the analysis reveal that the stability characteristics remain almost unchanged for the most unstable wave direction for Mach numbers above 4.0. The obtained results are compared with existing numerical and experimental data in the literature, yielding encouraging agreement both qualitatively and quantitatively.      

Mathematical Modeling of Flows Inside Rotating Bodies Made of Cellular-Porous Materials

A physicomathematical model is developed, which describes gas flows inside rapidly rotating bodies made of cellular-porous materials. Asymptotic and numerical solutions are obtained for some problems of forced centrifugal convection inside cylindrical cellular-porous bodies. The effect of the governing parameters (drag coefficient and dimensionless length of the cylinder) on characteristics and types of flows is considered. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 6, pp. 78–85, November–December, 2005.     

Dynamics and Stability of a Liquid Triaxial Ellipsoid

The problem of the dynamics of a liquid triaxial ellipsoid confined inside a uniformly rotating rigid shell is formulated and solved within the framework of the Poincare-Joukovski problem. The system of three non-linear first-order differential equations has kinetic energy and circulation integrals representing two ellipsoids with displaced centers in parameter space. All the steady-state and time-dependent solutions are studied; time-dependent solutions exist in four zones, where they are represented by elliptic Jacobi functions, and on three zone boundary interval (represented in terms of elementary functions). On the three other boundary intervals there exist liquid steady-state ellipsoids for which the vortex vector either coincides with one of the principal axes of the ellipsoid or lies in one of its principal planes of symmetry.     

Structure of Time-Dependent Transonic Flows in Plane Channels

The evolution and interaction of supersonic zones and the shock waves closing them are considered on the basis of the Lin-Reissner-Tsien equation for flow in plane channels with a local bottleneck.__________Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 2, 2005, pp. 168–179.Original Russian Text Copyright © 2005 by Bibik, Duesperov, and Popov.     

Properties and Averaged Equations for Flows of Bubbly Liquids

Averaged properties of bubbly liquids in the limit of large Reynolds and small Weber numbers are determined as functions of the volume fraction, mean relative velocity, and velocity variance of the bubbles using numerical simulations and a pair interaction theory. The results of simulations are combined with those obtained recently for sheared bubbly liquids [19] and the mixture momentum and continuity equations to propose a complete set of averaged equations and closure relations for the flows of bubbly liquids at large Reynolds and small Weber numbers.     

A Direct Numerical Study of Transport and Anisotropy in a Stably Stratified Turbulent Flow with Uniform Horizontal Shear

Direct numerical simulations of homogeneous turbulence in stably stratified shear flow have been performed to aid the understanding of turbulence and turbulent mixing in geophysical flow. Two cases are compared. In the first case, which has been studied in the past, the mean velocity has vertical shear and the mean density is vertically stably stratified. In the second case, which has not been studied systematically before, the mean velocity has horizontal shear and the mean density is again vertically stably stratified. The critical value of the gradient Richardson number, for which a constant turbulence level is obtained, is found to be an order of magnitude larger in the horizontal shear case. The turbulent transport coefficients of momentum and vertical mass transfer are also an order of magnitude larger in the horizontal shear case. The anisotropy of the turbulence intensities are found to be in the range expected of flows with mean shear with no major qualitative change in the range of Richardson numbers studied here. However, the anisotropy of the turbulent dissipation rate is strongly affected by stratification with the vertical component dominating the others. This revised version was published online in July 2006 with corrections to the Cover Date.     

Dynamics of a Fluid in a Rotating Horizontal Cylinder

The behavior of a low-viscosity fluid in a rotating horizontal circular cylinder is investigated experimentally. The stability of the centrifuged layer, the motion of the fluid with respect to the cavity, the excitation of inertial waves on the fluid surface, and the effect of the waves on the stability and flow structure are studied over a wide region of relative occupancy of the cavity. The results are analyzed from the viewpoint of vibrational mechanics in which the motion is generated by the oscillations of the fluid with respect to the cavity and the gravity force plays the role of the force oscillating in the cavity reference system.     

Localization of Shear Waves Near Layers Separating Two Regularly Laminated Half-Spaces

The existence conditions for surface and normal shear waves in finite and infinite periodically laminated structures with broken translational symmetry are studied theoretically and numerically. The problems posed are reduced to systems of linear algebraic equations. The existence condition for their nontrivial solutions yield dispersion relations. Conditions for the existence of surface and normal shear waves are established. Some results are plotted. The dependence of the dispersion spectrum on the physical and geometrical properties of the symmetry breaker is studied__________Translated from Prikladnaya Mekhanika, Vol. 41, No. 1, pp. 128–134, January 2005.     

Propagation of Magnetoelastic Shear Waves Through a Regularly Laminated Medium with Metallized Interfaces

An exact solution is found for magnetoelastic shear waves in an infinite structure consisting of three metallized layers. The core layer is ferrite and the face layers are nonmagnetic dielectrics. The wave process in the layers is described by a linearized system of magnetoelastic equations. The problem posed is reduced to a system of linear algebraic equations. The existence conditions for an undamped solution to this system yield the existence conditions for magnetoelastic bulk waves. The dispersion relations derived are analyzed in detail     

Shear flow disturbances due to interaction with convective rolls

The two-dimensional stationary problem of convection in a two-component stratified medium (for example, humid air) over a nonuniformly heated horizontal surface is solved in the linear approximation. In the case in which the surface temperature is harmonically dependent on the horizontal coordinate, convective rolls are formed above the surface. Depending on the background temperature stratification, situations characterized by temperature response sign reversal can occur (for example, a decrease in the temperature of the medium as a response to heating from beneath, or “negative” heat capacity of the medium). The disturbances arising in the background horizontal flow with vertical shear directed along the convective rolls are also calculated.     

多肢墙的线性方程解

本文去掉了R.Rossman方法中连梁连续化这一基本假定,给出了一种更符合实际的解法,该方法可以直接处理多肢墙,进而解决了R.Rossman方法中弯矩分配系数的确定问题。