Linear Dynamics of Perturbations in Flows with Constant Horizontal Shear

The dynamics of perturbations in shallow water and incompressible stratified fluid flows with constant horizontal shear are described using the nonmodal analysis. It is shown that the shear flow perturbations can be divided into two classes on the basis of the potential vorticity: rapidly oscillating wave perturbations with zero potential vorticity and slow vortex perturbations with nonzero potential vorticity. In the cases of weak and strong shear the main features of the dynamics of wave and vortex perturbations are studied analytically (using the WKBG method) and numerically. It is shown that for large times the wave perturbation energy increases linearly, i.e., the shear flow is algebraically unstable due to the growth of rapid wave perturbations. This instability can be of importance in processes of turbulence development and surface and internal wave generation.     

Vorticity addition method

It is shown that in the general case it is not possible to propose the Lagrangian viewpoint on the vorticity evolution, which would be unique for the entire flow, using the existing analogs of the Helmholtz theorems. This is related to the fact that, as distinct from the Helmholtz theorem oneself, these analogs are valid only for nonzero vorticity zones. New analogs of the Helmholtz theorems are proposed for the general case of flows (from incompressible fluid to viscous gas). They describe the vorticity evolution at all the points including the points of nonzero vorticity.     

Cross-Stream Vorticity Field Induced by Streamwise Vortices in Unbounded and Wall-Bounded Shear Flows

This computational study examines the unsteady cross-stream vorticity structures that form when one or more streamwise vortices are immersed in homogeneous and boundary-layer shear flows. A quasi-two-dimensional limit is considered in which the velocity and vorticity fields, while still possessing three nonzero components, have vanishing gradient in the streamwise direction. This idealization is suitable to applications such as streamwise vortices that occur along a ship hull or airplane fuselage and it can be used as an idealized representation of the quasi-streamwise vortices in the near-wall region of a turbulent boundary layer. In this quasi-two-dimensional idealization, the streamwise velocity has no effect on the cross-stream velocity associated with the vortex. However, the vortex acts to modify the cross-stream vorticity component, resulting in regions of the flow with strong deviations in streamwise velocity. This paper examines the complex structures that form as the cross-stream vorticity field is wrapped up by the vortex and the effect of these structures on the streamwise velocity field, first for vortices immersed in homogeneous shear flow and then for vortices immersed in a boundary layer along a flat wall. Received 2 January 2002 and accepted 13 August 2002 Published online 3 December 2002 RID="*" ID="*" This project was supported by the Office of Naval Research under Grant Number N00014-01-1-0015. Dr. Thomas Swain is the program manager. Communicated by T.B. Gatski     

Numerical and experimental investigation of wave dynamic processes in high-speed train/tunnels

Numerical and experimental investigation on wave dynamic processes induced by high-speed trains entering railway tunnels are presented. Experiments were conducted by using a 1:250 scaled train-tunnel simulator. Numerical simulations were carried out by solving the axisymmetric Euler equations with the dispersion-controlled scheme implemented with moving boundary conditions. Pressure histories at various positions inside the train-tunnel simulator at different distance measured from the entrance of the simulator are recorded both numerically and experimentally, and then compared with each other for two train speeds. After the validation of nonlinear wave phenomena, detailed numerical simulations were then conducted to account for the generation of compression waves near the entrance, the propagation of these waves along the train tunnel, and their gradual development into a weak shock wave. Four wave dynamic processes observed are interpreted by combining numerical results with experiments. They are: high-speed trains moving over a free terrain before entering railway tunnels; the abrupt-entering of high-speed trains into railway tunnels; the abrupt-entering of the tail of high-speed trains into railway tunnels; and the interaction of compression and expansion waves ahead of high-speed trains. The effects of train-tunnel configuration, such as the train length and the train-tunnel blockage ratio, on these wave processes have been investigated as well.     

Interaction of shear flows of an ideal incompressible fluid in a channel

The problem of the decay of an arbitrary discontinuity for the equations describing plane-parallel shear flows of an ideal fluid in a narrow channel is considered. The class of particular solutions corresponding to fluid flows with piecewise constant vorticity is studied. In this class, the existence of self-similar solutions describing all possible unsteady wave configurations resulting from the nonlinear interaction of the specified shear flows is established. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 6, pp. 34–47, November–December, 2006.     

Vorticity in plane parallel, axially symmetrical or spherical flows of viscous fluid

For viscous (barotropic or incompressible) fluids it is shown that, if the vorticity and the viscous force are orthogonal, vortex lines are convected by a vector field which fits with the velocity field when viscosity vanishes (extension of Helmholtz theorem); it is also found that energy remains constant along the field lines of this vector field (extension of Bernoulli theorem).If, moreover, vorticity and velocity are orthogonal too, the magnitude of the vorticity then behaves as the density of a fluid which flows along streamsheets according to this very same vector field. These properties are mainly encountered for plane parallel flows, axially symmetrical flows, spherical flows, but also for some other miscellaneous flow geometries such as unidirectional or radial flows. The set of the former three flows can even be characterized by these properties; that enhances this set of important flow geometries, avails a general view on vorticity behavior, and explains the great simplicity of vorticity equations in these cases. Numerous examples and comments are given for illustrating.     

Solitary wave trains in a cold plasma

The existence of traveling solitary waves, the products of modulation instability in a cold quasi-neutral plasma, is considered. Solitary waves of this type (solitary wave trains) are formed as a result of bifurcation from a nonzero wave number of the linear wave spectrum. It is shown that the complete system of equations describing the wave process in a cold plasma has solutions of the solitary wave train type, at least when the undisturbed magnetic field is perpendicular to the wave front. Sufficient conditions of existence of solitary wave trains in weakly dispersive media are also formulated.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, pp. 154–161, September–October, 1996.     

Simulation of surface gravity waves in the Dyachenko variables on the free boundary of flow with constant vorticity

Waves in deep water with constant vorticity in the region bounded by the free surface and the infinitely deep plane bottom are considered. Using the conformal variables and the conformal transform technique, a system of exact integro-differential equations solved relative to the derivatives with respect to time is derived and the equivalent system of equations is obtained in the Dyachenko variables. The efficiency of using the obtained system in the Dyachenko variables for investigating surface wave dynamics on the current of infinite depth with constant vorticity is demonstrated with reference to numerical experiments.     

Stability of bichromatic gravity waves on deep water

The stability of bichromatic gravity waves with small but finite amplitudes propagating in two directions on deep water is considered. Starting from the Zakharov equation, elementary quartet interactions are isolated and stability criteria are formulated. Results are illustrated for various combinations of bichromatic wave trains, from long-crested to standing waves. Two generic mechanisms operate: the first one is a modulational instability of one of the two components of the bichromatic wave train; the second mechanism is a modulation which couples both components of the wave train. However a third mechanism eventually comes into play: the resonant interaction of Phillips and Longuet-Higgins which leads initially to the linear growth of a third wave. When this latter is active, in particular for wave trains with wave vectors close together, it is shown by numerical integration that the long-time recurrence is destroyed.     

Instantaneous structure and statistical feature of unsteady flow in a channel obstructed by a square rod

A two-dimensional numerical computation has been made for an unsteady flow in a channel obstructed by an inserted square rod. The results of the computation made for the flow with a parabolic inlet velocity profile at a specific value of channel Reynolds number are analyzed in detail. The obtained results reveal that momentum transfer is enhanced due to the apparent shear stress resulting from the nonzero value of cross-correlation between the streamwise and normal components of fluctuating velocity, , just as in turbulent shear flows, although the studied flow is quite different from turbulent flows in the sense that it is highly periodical and therefore free from randomness. This periodicity leads to a quick recovery of the velocity defect in some region of the wake of the rod. Special attention is paid to the time variation of flow structure. The crisscross motion of the Karman vortex previously found to occur is discussed again, and how it appears is explained in terms of the interaction between the Karman vortex and the disturbed wall shear layer. In the discussion of this relationship, wavering motion of the separation vorticity layers formed on both sides of the rod and the periodic formation of an isolated vortex island from the lifted tip of the wall vorticity layer are analyzed. The vortex island is found to play an important role not only for the occurrence of the crisscross motion of Karman vortex but also for the generation of the nonzero value of .     

Vorticity produced by shock wave diffraction

Numerical simulations with a monotonicity preserving flow solver have been performed to study shock diffraction phenomena and shock wave generated vorticity. The computations were performed using the conservative Finite Element Method-Flux Corrected Transport (FEM-FCT) scheme, which has been shown to have an excellent predictive capability for various compressible flows with both strong and weak shocks. An adaptive unstructured methodology based on adapting to high density and entropy gradients was used in conjunction with a conservative shock-capturing scheme to adequately resolve strong and weak flowfield gradients. The chief interest was the formation of vorticity arising from shock wave propagation over a sharp corner and the high accuracy and resolution of the interacting compressible wave features. Numerical simulations were compared with previous experimental results and exhibited remarkably good agreement in terms of compressible wave propagation, as well as vorticity development and transport. The computations also allowed insight into the fundamental fluid dynamics, specifically shock diffraction, vortex convection and shock-vortex interactions.     

Influences of marshalling length on the flow structure of a maglev train

In this paper, transient numerical simulations of maglev trains of different marshalling lengths (2, 4, and 8-car group trains) were conducted in the open air and without wind. This was done by solving the three-dimensional incompressible Navier-Stokes equations using an SST K-ω double-equation IDDES turbulence model. The results were compared with the results of wind tunnel experiments to verify the feasibility of numerical simulation. The results show an increase in the marshalling lengths of the train affects the flow above and below the train. With the increase of the marshalling length, the position of the flow separation in the tail car is advanced. The turbulence generated by the average shear on the x, y-plane and the x, z-plane as a component of the turbulence of the wake region increases. The region that produces non-vorticial vorticity in the main vortex becomes narrow and moves towards tail car. The structural analysis of the wake indicates that the wake structure of the 8-car group train is quite different from the other two groups. Both the time-averaged slipstream and the gust analysis show that the maximum expected slipstream velocity at the track-side increases as the train marshalling length increases. At the platform height, the change in vertical position of the wake vortex structure of the 2, 4, and 8-car group trains caused the difference of the shear flow regions. This is why the maximum expected slipstream velocity generated by the 4-car group train at this position is largest. As the marshalling length of the train increases, the time-average drag and lift force coefficient of the tail car have a significant negative correlation.     

Rotational inviscid flow with circulation zones in a channel of variable cross section

The development of the theory of rotational motion of inviscid fluids for the purposes of describing channel flow encounters certain difficulties in connection with the appearance of viscosity effects near the walls. In the potential-rotational model [1], in which the vorticity is nonzero only in a closed circulation zone surrounded by potential flow, it is assumed that the separation and attachment points are known in advance. For example, for flow around a cavity these points coincide with the extreme corner points of the contour. The problem of determining the vorticity in a closed zone for the potential-rotational model has been investigated in a number of studies [2, 3], etc. In the case of an incompressible fluid the vorticity in the circulation zone is constant for two-dimensional flow and proportional to the distance from the axis for axisymmetric flow. The value of the constant is found from the steady-state condition for the adjoining viscous layers. If the channel walls have a smooth profile without corner points, then for determining the boundaries of the circulation zones additional conditions must be used. This study employs another scheme, in which the vorticity is formed outside the region of flow and in a particular problem is specified in the form of a boundary condition. An analytic solution describing the rotational flow of an inviscid fluid in a channel with a slightly varying cross section is obtained. Three types of entrance flow nonuniformity are considered: 1) uniform shear flow, 2) wake-type flow, and 3) potential flow with a narrow wall boundary layer. Streamline patterns with circulation zones are constructed for flows in diffuser channels with the above-mentioned types of entrance nonuniformity. A model of flow separation in a channel with a turbulent boundary layer on the walls is discussed.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 31–37, March–April, 1985.In conclusion the author wishes to thank E. Yu. Shal'man, A. N. Kraiko, and A. B. Vatazhin for useful discussions and advice.     

Theory of nonstationary vortices in an ideal fluid

Equations that describe the evolution of a region with nonzero vorticity are formulated. These equations are solved on a bounded time interval for regions having the shape of a sphere or a circular cylinder at the initial time. It is shown that a spherical vortex formed in a medium at rest begins to move, and is stretched in the direction of the motion; a cylindrical vortex, under the influence of the nonuniform intensity of the vorticity on its boundary, changes both the magnitude and direction of its velocity, and describes a curvilinear trajectory. Expressions are obtained which describe the initial evolution of a fluid sphere of one density in a fluid medium of another density.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 3–11, November–December, 1980.     

流场非均匀性对非平面激波诱导的Richtmyer-Meshkov不稳定性影响的数值研究

基于Navier-Stokes方程组,采用可压缩多介质黏性流动和湍流大涡模拟程序MVFT (multi-viscousflow and turbulence),模拟了均匀流场与初始密度呈现高斯函数分布的非均匀流场中马赫数为1.25的非平面激波加载初始扰动air/SF6界面的Richtmyer-Meshkov (RM)不稳定性现象。数值模拟结果表明,初始流场非均匀性将会影响非平面激波诱导的RM不稳定性演化过程。反射激波加载前,非平面激波导致的界面扰动振幅随着流场非均匀性增强而增大;反射激波加载后,非均匀流场与均匀流场条件下的界面扰动振幅差异有所减小。进一步,定量分析流场中环量分布及脉动速度统计量揭示了前述规律的原因。此外,还与平面激波诱导的RM不稳定性进行了简单对比,发现由于非平面激波波阵面区域的涡量与激波冲击界面时产生的涡量的共同作用,使得非平面激波与平面激波诱导的界面失稳过程存在差异。     

Exponential shear flow of branched polymer melts

  The behavior of a low-density polyethylene melt in exponential shear strain histories is examined and compared to its behavior in constant rate planar elongation. A new set of shear stress and first normal stress difference data in exponential shear are presented and used in several different material functions that have been previously proposed. Viscosities composed of principal stress differences for the two flows showed no correspondence suggesting that, contrary to previous assertions, exponential shear and constant rate planar elongation flows are fundamentally different. It is further suggested that the presence of vorticity makes exponential shear a weak, rather than strong, flow. Received: 5 March 1999/Accepted: 1 September 1999     

Phase velocity effects of the wave interaction with exponentially sheared current

The nonlinear interaction between the unidirectional bichromatic wave-train and exponentially sheared current in water of an infinite depth is investigated. The model is based on the vorticity transport equation and the exact free surface conditions, without any assumptions for the existence of small physical parameters. Earlier works of the wave–current interaction were mainly restricted to either current acted on the monochromatic wave or irregular waves limited to irrotational current. Different from these previous works, no constraint is made in our model for amplitudes of the primary wave, and the current owns an exponential type profile along the vertical line. To ensure that the effect of vorticity on the phase velocity is consistent with earlier derivation, the case of a small amplitude wave traveling on the exponentially sheared current is examined firstly. Then the effect of nonlinearity on the phase velocity of primary waves in a bichromatic wave-train is considered. Accurate high-order approximations of the phase velocity are obtained under consideration of both the nonlinear wave self–self and mutual interactions. Finally, the combined effect of vorticity and nonlinearity on the phase velocity is investigated through the case of a bichromatic wave-train propagating on an exponentially sheared current. It is found that the characteristic current slope determines the effect of vorticity on the phase velocity caused by nonlinear wave self–self and mutual interactions, and the surface current strength may amplify/reduce this effect.     

The analysis of power circulation and the simplified expression of the transmission efficiency of 2K-H closed epicyclic gear trains

Transmission efficiency is a principal index for estimating the performance of 2K-H closed epicyclical gear trains. To calculate transmission efficiency, it must confirm the power flow direction in transformation gear train and verify if there is power circulation in closed epicyclical gear train firstly. In this paper, a simple algorithm is proposed to confirm the power flow direction and estimate if there exist the power circulation based on transmission ratio of basic links in differential gear train and transformation gear train. The simplified equations are deduced to calculate the transmission efficiency and some examples are given finally.     

Derivation of a higher order nonlinear Schrödinger equation for weakly nonlinear Rossby waves

In the paper, with the help of a perturbation expansion method a new higher order nonlinear Schrödinger (HNLS) equation is derived to describe nonlinear modulated Rossby waves in the geophysical fluid. Using this equation, the modulational wave trains are discussed. It is found that the higher order terms favor the instability growth of modulational disturbances superimposed on uniform Rossby wave trains, but the instability region becomes narrower. In addition, the latitude and uniform background basic flow are found to affect the instability growth rate and instability region of uniform Rossby wave train. However, for a geostrophic flow the background basic flow does not affect the modulational instability of uniform Rossby wave train.     

On aerodynamic noises radiated by the pantograph system of high-speed trains

Pantograph system of high-speed trains become significant source of aerodynamic noise when travelling speed exceeds 300 km/h. In this paper, a hybrid method of non-linear acoustic solver （NLAS） and Ffowcs Williams-Hawkings （FW-H） acoustic analogy is used to predict the aerodynamic noise of pantograph system in this speed range. When the simulation method is validated by a benchmark problem of flows around a cylinder of finite span, we calculate the near flow field and far acoustic field surrounding the pantograph system. And then, the frequency spectra and acoustic attenuation with distance are analyzed, showing that the pantograph system noise is a typical broadband one with most acoustic power restricted in the medium-high frequency range from 200 Hz to 5 kHz. The aerodynamic noise of pantograph systems radiates outwards in the form of spherical waves in the far field. Analysis of the overall sound pressure level （OASPL） at different speeds exhibits that the acoustic power grows approximately as the 4th power of train speed. The comparison of noise reduction effects for four types of pantograph covers demonstrates that only case 1 can lessen the total noise by about 3 dB as baffles on both sides can shield sound wave in the spanwise direction. The covers produce additional aerodynamic noise themselves in the other three cases and lead to the rise of OASPLs.