Numerical studies of shock focusing induced by reflection of detonation waves within a hemispherical implosion chamber

The initiation and the propagation of detonation waves in a hemispherical chamber and the imploding shock waves that are the reflected detonation waves at the chamber wall are numerically investigated. The effects of the boundary layer and the non-uniformity of the flow field induced by the detonation wave on the imploding shock stability are examined. It is found that the effect of the boundary layer separation on the chamber wall has the strongest effect on the implosion focus.     

Influence of spatial modulation of the temperature field on the stability of two-dimensional steady flow in a horizontal layer of fluid

A study is made of the stability of the steady periodic regime that arises in a horizontal layer of fluid in the presence of spatial modulation of of the temperature on the solid bottom boundary. The upper free boundary of the layer is in contact with the atmosphere. The fundamental resonance values of the wave number of the modulation are found; there are five of them. If the temperature of the lower boundary of the layer is constant, and the temperature gradient is not too large, the fluid is in equilibrium. When the temperature gradient passes through the critical value, the equilibrium ceases to be stable, and steady convection develops in the fluid [1]. In the presence of spatial modulation of the temperature on the lower boundary of the layer the fluid cannot be in equilibrium, and a spatially periodic steady regime is established in it. The aim of the present paper is to find the critical values of the temperature gradient at which this fundamental steady regime becomes unstable and a secondary steady regime develops in the fluid. An analogous problem for the case when both boundaries of the layer are free surfaces and without allowance for the influence of the atmosphere has been solved by Vozovoi and Nepomnyashchii [2].     

Structuring of suspended sediments in periodic vortex flow over a vortex ripple

The formation of spatially ordered structures in a suspended sediment under the action of two-dimensional standing surface gravity waves is studied experimentally for the first time in a rectangular vessel oscillating in the vertical direction. The parameters of the structured regions in vessels with individual vortex ripples and groups of ripples are found for the first and second wave modes. Isolated structured regions of the suspended sediment appear over the bottom topography and gradually reach the free surface. The corresponding spatial horizontal scales are determined by the sand ripple dimensions, while the vertical scale of the clouds increases with time. In all experiments, the structures formed remained unchanged during the whole interval of the fluid wave motion and disappeared when the parametric excitation of the waves stopped.     

一种新的运动激波--非定常边界层相互干扰现象

本文探讨了一种新的激波－非定常边界层相互干扰现象，这种激波－边界层干扰现象既不同于定常激波－边界层干扰现象，又不同于激波在端面反射后与该激波所诱导的边界层之间的干扰现象，而是运动激波与稀疏波和第一激波所诱导的非这常边界层之间的干扰现象，本文对这种现象用微波动力学理论进行分析，并把这种干扰现象看成激波的绕射现象，同时在稀疏波破膜的双驱动激波管中进行实验观察，最后把理论分析与实验观察进行了比较。     

Large eddy simulation of boundary layer flow under cnoidal waves

Water waves in coastal areas are generally nonlinear, exhibiting asymmetric velocity profiles with different amplitudes of crest and trough. The behaviors of the boundary layer under asymmetric waves are of great significance for sediment transport in natural circumstances. While previous studies have mainly focused on linear or symmetric waves, asymmetric wave-induced flows remain unclear, particularly in the flow regime with high Reynolds numbers.Taking cnoidal wave as a typical example of asymmetric waves, we propose to use an infinite immersed plate oscillating cnoidally in its own plane in quiescent water to simulate asymmetric wave boundary layer. A large eddy simulation approach with Smagorinsky subgrid model is adopted to investigate the flow characteristics of the boundary layer. It is verified that the model well reproduces experimental and theoretical results. Then a series of numerical experiments are carried out to study the boundary layer beneath cnoidal waves from laminar to fully developed turbulent regimes at high Reynolds numbers, larger than ever studied before.Results of velocity profile, wall shear stress, friction coefficient, phase lead between velocity and wall shear stress, and the boundary layer thickness are obtained. The dependencies of these boundary layer properties on the asymmetric degree and Reynolds number are discussed in detail.     

Stability of the laminar boundary layer flow encountering a row of roughness elements: Biglobal stability approach and DNS

The stability of the laminar boundary layer developing on a flat plate in the presence of a periodic row of roughness elements is investigated. A Direct Numerical Simulation is performed to compute the steady flow downstream of the roughness elements, which contains a pair of two counter-rotating streamwise vortices per element, which can be considered as a “pre-streaky” structure. The linear stability of this base flow is analyzed by means of the so-called “biglobal” stability approach. Three-dimensional eigenmodes are found, which are shown to be the continuation of the Tollmien–Schlichting waves present in the case of an unperturbed boundary layer. Moreover, a stabilizing effect due to the roughness-induced vortices is found. A Direct Numerical Simulation of the interaction between a two-dimensional Tollmien–Schlichting wave and the roughness array is also performed. The computed perturbation traveling downstream of the roughness elements is shown to be a linear combination of the biglobal eigenmodes.     

Unsteady RANS method for surface ship boundary layer and wake and wave field

Results are reported of an unsteady Reynolds‐averaged Navier–Stokes (RANS) method for simulation of the boundary layer and wake and wave field for a surface ship advancing in regular head waves, but restrained from body motions. Second‐order finite differences are used for both spatial and temporal discretization and a Poisson equation projection method is used for velocity–pressure coupling. The exact kinematic free‐surface boundary condition is solved for the free‐surface elevation using a body‐fitted/free‐surface conforming grid updated in each time step. The simulations are for the model problem of a Wigley hull advancing in calm water and in regular head waves. Verification and validation procedures are followed, which include careful consideration of both simulation and experimental uncertainties. The steady flow results are comparable to other steady RANS methods in predicting resistance, boundary layer and wake, and free‐surface effects. The unsteady flow results cover a wide range of Froude number, wavelength, and amplitude for which first harmonic amplitude and phase force and moment experimental data are available for validation along with frequency domain, linear potential flow results for comparisons. The present results, which include the effects of turbulent flow and non‐linear interactions, are in good agreement with the data and overall show better capability than the potential flow results. The physics of the unsteady boundary layer and wake and wave field response are explained with regard to frequency of encounter and seakeeping theory. The results of the present study suggest applicability for additional complexities such as practical ship geometry, ship motion, and maneuvering in arbitrary ambient waves. Copyright © 2001 John Wiley & Sons, Ltd.     

Turbulent Dynamics of a Critically Reflecting Internal Gravity Wave

Results from computational fluid dynamics experiments of internal wave reflection from sloping boundaries are presented. In these experiments the incident wave lies in a plane normal to the slope. When the angle of wave energy propagation is close to the bottom slope the reflection causes wave breakdown into a quasi-periodic, turbulent boundary layer. Boundary layer energetics and vorticity dynamics are examined and indicate the importance of the three-dimensional turbulence. The boundary layer exhibits intermittent turbulence: approximately every 1.2 wave periods the boundary layer mixes energetically for a duration of about one-third of a wave period, and then it restratifies until the next mixing event. Throughout the wave cycle a strong thermal front is observed to move upslope at the phase speed of the incident waves. Simulations demonstrate that the net effects of turbulent mixing are not confined to the boundary layer, but are communicated to the interior stratified fluid by motions induced by buoyancy effects and by the wave field, resulting in progressive weakening of the background density gradient. Transition to turbulence is determined to occur at Reynolds numbers of approximately 1500, based upon the wavelength and maximum current velocity of the oncoming wave train. The boundary layer thickness depends on the Reynolds number for low Richardson numbers, with a characteristic depth of approximately one-half of the vertical wavelength of the oncoming wave. Received 21 May 1997 and accepted 14 October 1997     

Structurization and restructurization of a homogeneous suspension in a standing wave field

The process of formation of a spatially ordered fine structure in an originally uniform suspension of small-size particles in the field of two-dimensional standing surface gravity waves in a rectangular reservoir oscillating in the vertical direction is for the first time recorded in experiments. The parameters of structured regions are determined in reservoirs with both separate vortical ripples and their groups and with rough sandy and smooth regions of the bottom for the first and second wave modes. It is established that isolated structured regions are formed near the bottom or the free surface and gradually fill the fluid throughout its entire thickness. Minimum scales of the structures are on the Stokesian range, while maximum scales are determined by the geometry and the energy of the main flow. In all experiments performed the structurization was conserved during the entire interval of wave motion of the suspension and vanished during a few minutes after the parametric excitation of the waves has been stopped.     

Experimental investigation of secondary steady flows in Faraday surface waves

It is shown that in the two-dimensional Faraday surface waves excited in a vertically oscillating rectangular water-filled vessel there is a system of secondary circulatory flows that occupies the entire fluid volume between the vessel bottom and the free surface. In parallel with the oscillations at the wave frequency, the fluid particles are slowly displaced in accordance with these circulatory flows. The secondary flow velocity field is measured and the trajectories of individual fluid particles in the standing wave are determined. The experimental data are compared with the Longuet-Higgins model. It is shown that the initial stage of formation of regular structures on the surface of a sediment layer on the vessel bottom may be related with the presence of secondary circulatory flows.     

Acoustic Field Effect on Laminar Turbulent Transition on a Swept Wing in the Favorable Pressure Gradient Region

The development of disturbances in a three-dimensional boundary layer on a swept wing model is studied both under natural conditions and for artificial excitation of traveling waves by an acoustic field. It is found that steady-state streamwise structures are formed in the three-dimensional boundary layer; under natural conditions a wave packet leading to turbulence is detected. When the flow is exposed to the action of an acoustic field at a frequency from the wave packet, disturbances whose velocity along the streamwise structures is equal to 0.55 of the oncoming flow velocity are formed, while the laminar-turbulent transition is displaced upstream.     

Localized Coherent Structures in the Boundary Layer

A Blasius laminar boundary layer and a steady turbulent boundary layer on a flat plate in an incompressible fluid are considered. The spectral characteristics of the Tollmien—Schlichting (TS) and Squire waves are numerically determined in a wide range of Reynolds numbers. Based on the spectral characteristics, relations determining the three–wave resonance of TS waves are studied. It is shown that the three–wave resonance is responsible for the appearance of a continuous low–frequency spectrum in the laminar region of the boundary layer. The spectral characteristics allow one to obtain quantities that enter the equations of dynamics of localized perturbations. By analogy with the laminar boundary layer, the three–wave resonance of TS waves in a turbulent boundary layer is considered.     

Spatial Simple Waves on a Shear Flow

The paper studies simple waves of the shallowwater equations describing threedimensional wave motions of a rotational liquid in a freeboundary layer. Simple wave equations are derived for the general case. The existence of unsteady or steady simple waves adjacent continuously to a given steady shear flow along a characteristic surface is proved. Exact solutions of the equations describing steady simple waves were found. These solutions can be treated as extension of Prandtl–Mayer waves for sheared flows. For shearless flows, a general solution of the system of equations describing unsteady spatial simple waves was found.     

Breaking of waves of limiting amplitude over an obstacle

Homogeneous heavy fluid flows over an uneven bottom are studied in a long-wave approximation. A mathematical model is proposed that takes into account both the dispersion effects and the formation of a turbulent upper layer due to the breaking of surface gravity waves. The asymptotic behavior of nonlinear perturbations at the wave front is studied, and the conditions of transition from smooth flows to breaking waves are obtained for steady-state supercritical flow over a local obstacle. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 3, pp. 3–11, May–June, 2006.     

Application of unsteady mixing equations to some aerodynamic problems

Tangential discontinuities [1] are introduced in solving several transient and steady-state problems of gas dynamics. These discontinuities are unstable [2] as a result of the effects of viscosity and thermal conductivity. Therefore it is advisable to replace the tangential discontinuity by a mixing region and account for its interaction with the inviscid flows, establishing on the boundaries of this region the conditions of vanishing friction stress and equality of the velocity and temperature components to the corresponding velocity and temperature components of the inviscid flows. This formulation improves the accuracy of the solution of such problems by posing them as problems with irregular reflection and intersection of shock waves [1].The consideration of the interaction of unsteady turbulent mixing regions with the inviscid flow also permits the formulation of several problems in which the effects of viscosity lead to complete rearrangement of the flow pattern (the lambda-configuration) with the interaction of the reflected shock wave with the boundary layer in the shock tube [3,4], the formation of zones of developed separation ahead of obstacles, etc.).In this connection, §1 presents an analysis of the self-similar solutions of the unsteady turbulent mixing equations (a corresponding analysis of the laminar mixing equations which coincide with the boundary layer equations is presented in [1]). It is shown that these self-similar solutions describe, along with the several problems noted above, the problems of the formation of steady jets and mixing zones in the base wake.As an example, §2 presents, within the framework of the proposed schematization, an approximate solution of the problem of the interaction of a shock wave reflected from a semi-infinite wall with the boundary layer on a horizontal plate behind the incident shock wave. The results obtained are applied to the analysis of reflection in a shock tube. Computational results are presented which are in qualitative agreement with experiment [3, 4].     

Transient two‐layer thin‐film flow

The transient two‐layer thin‐film planar flow is investigated theoretically in this study. The interplay among inertia, viscous and surface/interfacial tension is emphasized. It is found that the film and interface profiles, as well as the flow field, are strongly influenced by the viscosity ratio, velocity and film thickness ratios at inception, and the surface‐to‐interfacial tension ratio. The nonlinear stability of the steady state reveals the formation of a solitary wave after flow inception, which propagates in the form of a convective instability, with the steady state recovered only in the tail (upstream) region of the wave. In the presence of surface/interfacial tension, surface modulation appears, which grows in wavelength and amplitude with position. The flow is found to be particularly stable for higher viscosity of the lower film layer. Copyright © 2010 John Wiley & Sons, Ltd.     

Shocklets in compressible flows

The mechanism of shocklets is studied theoretically and numerically for the stationary fluid, uniform compressible flow, and boundary layer flow. The conditions that trigger shock waves for sound wave, weak discontinuity, and Tollmien-Schlichting （T-S） wave in compressible flows are investigated. The relations between the three types of waves and shocklets are further analyzed and discussed. Different stages of the shocklet formation process are simulated. The results show that the three waves in compressible flows will transfer to shocklets only when the initial disturbance amplitudes are greater than the certain threshold values. In compressible boundary layers, the shocklets evolved from T-S wave exist only in a finite region near the surface instead of the whole wavefront.     

Three-wave interactions of disturbances in a hypersonic boundary layer on a porous surface

Interactions of disturbances in a hypersonic boundary layer on a porous surface are considered within the framework of the weakly nonlinear stability theory. Acoustic and vortex waves in resonant three-wave systems are found to interact in the weak redistribution mode, which leads to weak decay of the acoustic component and weak amplification of the vortex component. Three-dimensional vortex waves are demonstrated to interact more intensively than two-dimensional waves. The feature responsible for attenuation of nonlinearity is the presence of a porous coating on the surface, which absorbs acoustic disturbances and amplifies vortex disturbances at high Mach numbers. Vanishing of the pumping wave, which corresponds to a plane acoustic wave on a solid surface, is found to assist in increasing the length of the regions of linear growth of disturbances and the laminar flow regime. In this case, the low-frequency spectrum of vortex modes can be filled owing to nonlinear processes that occur in vortex triplets.     

Over-reflection and instabilities in shear flows of shallow water with bottom friction

In a two-dimensional shear flow of shallow water, the bottom friction relates uniquely the spanwise profile of the depth-averaged velocity to the bottom topography. If the basic flow varies weakly in the spanwise direction, the local analysis of stability at every spanwise position gives the region of the flow parameters for which the classic hydraulic instability due to the bottom friction cannot occur. In this region, the linear analyses of the waves scattering and instability due to the lateral shear can be performed effectively by means of the frictionless linearized equations if both the bottom slope and friction are equally small.The energy of the total perturbed flow can be split into three main parts that correspond to the basic flow, small amplitude wave motion and induced mean flow. The waves can be either amplified or damped near the critical layers, where their streamwise phase velocity equals the velocity of the basic flow. Two physical mechanisms of this amplification exist. The first one is similar to that suggested by Takehiro and Hayashi for a linear frictionless shallow water flow. The incident and transmitted waves carry energy of opposite signs, which results in an increase in the amplitude of the reflected wave compared to that of the incident one. This mechanism of over-reflection operates for any combination of the flow parameters. The other mechanism is similar to Landau damping in plasma flows; it is related to the energy exchange between the waves and fluid particles at the critical layers due to the velocity synchronism. It may lead to either additional amplification or damping of the waves for different flow conditions. In particular, its significance can be reduced by stronger bottom friction. If the basic flow has uniform potential vorticity, Landau damping is negligible, and over-reflection always occurs. If the feed-back is provided by another critical layer, the net over-reflection results in the formation of trapped modes.