Unstable Shear Research Articles

The effects of unstable stratification and mean shear on the chemical reaction in grid turbulence

The effects of unstable thermal stratification and mean shear on chemical reaction and turbulent mixing were experimentally investigated in reacting and non-reacting liquid mixing-layer flows downstream of a turbulence-generating grid. Experiments were carried out under three conditions: unsheared neutrally stratified, unsheared unstably stratified and sheared neutrally stratified. Instantaneous velocity and concentration were simultaneously measured using the combination of a laser-Doppler velocimeter and a laser-induced fluorescence technique. The results show that the turbulent mixing is enhanced at both large and small scales by buoyancy under unstably stratified conditions and therefore the chemical reaction is strongly promoted. The mean shear acts to enhance the turbulent mixing mainly at large scales. However, the chemical reaction rate in the sheared flow is not as large as in the unstably stratified case with the same turbulence level, since the mixing at small scales in the sheared neutrally stratified flow is weaker than that in the unsheared unstably stratified flow. The unstable stratification is regarded as a better tool to attain unsheared mixing since the shearing stress acting on the fluid is much weaker in the unstably stratified flow than in the sheared flow.

The Nonlinear Forcing of Large-Scale Internal Gravity Waves by Stratified Shear Instability

The forcing of large-scale internal gravity waves by shear-unstable stratified free shear layers is investigated. The gravity wave forcing mechanism considered arises from the nonlinear interaction of unstable modes of differing horizontal wavenumber as they reach finite amplitude in the shear layer. The analysis assumes an initially plane-parallel shear flow and no preferred horizontal scales in the perturbations that initiate instability. Therefore, the large-scale gravity wave forcing mechanism considered arises only from the dynamical action of eddies in the shear layer. One of the primary goals of this study is to estimate the vertical flux of horizontal momentum of propagating gravity waves forced by this mechanism. A numerical model is used to simulate the Kelvin‐Helmholtz instability of the shear layer, and the induced large-scale gravity wave radiation. Owing to the large horizontal scale of the radiated waves, numerical simulations are practical only in two spatial dimensions. Therefore, to make a physically meaningful estimate of the vertical momentum flux, a diagnostic procedure is developed to identify the gravity wave radiation that arises from the early nonlinear evolution of the shear layer. This early evolution is well modeled by the simulations, because it occurs prior to the time at which three-dimensional motions would develop in a three-dimensional unstable shear layer. The results of this study are applied to the real atmosphere to address the question: does stratified shear instability, occurring in localized patches on the upper flank of the tropospheric westerly jet, significantly contribute to midlatitude mesospheric gravity wave drag in summer? The single-event estimates of vertical momentum flux derived here are combined with observed statistics of stratified shear instability occurring in the lower stratosphere. This gives an estimate of the average mesospheric vertical momentum flux in summer arising from the nonlinear gravity wave forcing mechanism considered here. The estimate indicates that gravity waves forced by stratified shear instability may account for a significant fraction of mesospheric gravity wave drag in summer.

Effect of Splitter Plate on Generation Mechanism of Aeolian Tones.

This paper describes the effect of the splitter plate on the generation mechanism of the aeolian tones and the suppression effect of the splitter plate length on the aerodynamic sound radiated from the circular cylinder in an uniform flow. The experiment using a low noise wind tunenl has been carried out. As a result, the following conclusions were obtained. (1) The splitter plate suppresses the aerodynamic sound in case of 0 6, and amplifies in case of 2∼3<L/D<6. Where L is the splitter plate length and D is the diameter of the circular cylinder. (2) It is clarified by consideration based on experimental results that the expression L/D=(1/St)·(Uc/U) is necessary condition for generation of self-sustained tones and its mechanism is to make highly two dimensionality of the unstable separated shear layer due to the pressure fluctuation based on the vortex impinging on the trailing edge of the splitter plate.

NONLINEAR CONVECTIVE HEAT TRANSFER IN A TRANSITIONAL PLASMA PLUMEb

ABSTRACT: In the paper the results of experimental investigation of wave‐like heat transfer events taking place in the core of transitional plasma plumes are presented and discussed. In order to amplify the dynamic events governing them the arc heater operating conditions were chosen in such a manner that the strong feedback in the plasma column predominated during the nonlinear phase of the transition process. This enabled us to state, that in the events studied the crucial role plays an unstable plume shear layer vortex system inducing the oscillations of the whole plasma column. And just the coupling of them with a mode of organ pipe acoustical oscillations in the arc chamber cavity results in self sustained oscillations of the column and in strong linkage between the thermal events taking place in the plume and the arc chamber cavity. However, the results gained allow us not only to grasp the mechanism of the heat transfer process in the plume core during the transition to turbulence but also provide a means for formulating a conceptual model (scenario) of its evolution. And on the basis of this piece of knowledge a theoretical approach based on the methods of the nonlinear dynamics theory is proposed.

Initiation of in-plane shear instability under slip-dependent friction

AbstractWe study the initiation of an unstable homogeneous elastodynamic inplane shear process under slip-weakening friction. We assume a linear dependency of the friction at the beginning of the slip, and we make an eigenvalue analysis in the time domain. We prove that two types of eigenvalue are possible. With the first type, the eigenvalues have a negative square and represent the wave part of the solution. With the second type, they have a positive square and lead to the dominant part of the solution. We use a classical method based on the normalization of the dominant eigenfunctions in order to give the analytical expression of the dominant part of the solution. This analysis shows that the response of the dominant part will develop on a continuous but limited spectral domain. This limit depends on the weakening of the friction and a coefficient including the ratio of P-wave velocity to S-wave velocity. We also show that the exponential growth of the dominant part is directly linked to the weakening and the S-wave velocity. Using the expression of the dominant part, we give an estimation of the time of initiation for the crack to reach the steady propagation stage. We perform numerical tests with a finite-difference method and show very good agreement between the analytical dominant part of the solution and the complete numerical solution. Finally, in our case, where the initial stress is equal to the static admissible load, we study the crack propagation and observe that the crack tips travel asymptotically at P-wave velocity after a short time of apparent P supersonic velocity. The numerical results show that the linearized dynamic description is also valid ahead the crack tips in the propagation regime.

Connection between corner vortices and shear layer instability in flow past an ellipse

We investigate, by numerical simulation, the shear layer instability associated with the outer layer of a spiral vortex formed behind an impulsively started thin ellipse. The unstable free shear layer undergoes a secondary instability. We connect this instability with the dynamics of corner vortices adjacent to the tip of the ellipse by observing that the typical turnover time of the corner vortex matches the period of the unstable mode in the shear layer. We suggest that the corner vortex acts as a signal generator, and produces periodic perturbation which triggers the instability.

Flow-field and point velocity measurements in a barotropically unstable shear layer

A shear instability in a homogeneous rotating fluid is studied in a laboratory experiment. Geophysical situations where such shear layers play a role range from the breakdown of weather fronts to the atmospheres of the giant planets, as well as in the Earth's interior. Above a critical shear, the shear layer breaks up through an inertial instability, which is known as barotropic instability in Geophysical Fluid Dynamics. The flow then develops a string of vortices along the shear zone.This study used two complementary methods of measuring the flow, Laser Doppler Velocimetry and Particle Tracking Velocimetry. The respective merits of these two methods will be discussed, and how these techniques complement each other. It will become apparent that a combination of both methods is necessary to fully describe the flow structures and dynamics.

STROUHAL NUMBERS OF FLOW-EXCITED ACOUSTIC RESONANCE OF CLOSED SIDE BRANCHES

Flow-excited acoustic resonances of piping systems containing closed side-branches are often encountered in engineering applications. They are excited by the unstable shear layer which separates the mean flow in the main pipe from the stagnant fluid in the branch. The object of this paper is to develop a design chart that can be used to predict the critical flow velocities in the main pipe at which acoustic resonances are initiated. Model tests were carried out on three different configurations of side-branches (single, tandem, and coaxial branches). For each of these pipe configurations, the effects of the diameter ratio, the distance from an upstream elbow and the acoustic damping are investigated in some detail. The test results are implemented into a design chart to predict the flow velocity at the onset of resonance as a function of the system operational and geometric parameters.

Instability in Parallel Flows Revisited

An example of an unstable inviscid plane parallel shear flow with classical boundary conditions is presented. The complete unstable spectrum is exhibited using techniques of continued fractions for the shear flow with profile U(y)=cos m y. For such flows spectral instability implies nonlinear instability. A three‐dimensional generalization is discussed.

VORTEX-BODY INTERACTIONS

▪ Abstract Interaction of a vortex, or combinations of them, with a cylinder, blade, or foil may involve both rapid distortion of the incident vorticity field and shedding of vorticity from the surface of the body. This review focuses on the underlying flow physics, with the aim of clarifying the origin of the induced loading. In the case of near or direct encounter of the incident vortex, the relation between three-dimensional features of the flow structure and the local loading poses interesting challenges for further research. With recently developed simulation and laboratory techniques, opportunities now exist to determine the instantaneous quantitative structure of these complex distortions and to interpret them within a theoretical, vorticity-based framework. Effective control of vortex interactions appears to be attainable. It will be necessary, however, to develop creative strategies, distinct from those traditionally employed for control of unstable shear flows.

Phonon Instabilities in fcc and bcc Tungsten

The lattice dynamics of bcc and fcc W is studied as a function of pressure using the density-functional linear-response theory. At high pressures and $T\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0$ K, bcc W has a higher enthalpy than the fcc and hcp phases and it develops phonon softening anomalies related to this thermodynamic instability; however, it remains dynamically stable. In contrast, the widely unstable shear modes of fcc W at zero pressure (when ${H}_{\mathrm{W}}^{\mathrm{fcc}}g{H}_{\mathrm{W}}^{\mathrm{bcc}}$) stabilize with increasing pressure before ${H}_{\mathrm{W}}^{\mathrm{fcc}}l{H}_{\mathrm{W}}^{\mathrm{bcc}}$. Hence the thermodynamic and dynamic instabilities are uncorrelated.

Initiation of antiplane shear instability under slip dependent friction

We study the initiation of an unstable antiplane elastodynamic shear process under slip‐weakening friction. We give an analytical expression of the slip that we intrepret using an eigenvalue analysis. Considering only the part of the solution associated with positive eigenvalues, we define a “dominant part” characterized by an exponential growth with time. An explicit formula is given for the dominant part that controls the development of the instability after the application of an initial perturbation on the surface or inside the elastic body. It shows that in response to a small initial perturbation the instability will develop in a limited spectral domain. The limiting wavenumber (or reciprocal critical length) is a function of the parameters of the friction law and the elastic properties. The part of the solution associated with negative eigenvalues (the “wave part”) becomes rapidly negligible when the instability develops. We found that in the initiation phase the displacement field in the elastic body has a simple exponential dependence on the coordinate perpendicular to the fault. Using the expression of the dominant part, we estimate the duration of the initiation phase. We show the accuracy of the theoretical analysis by comparison with numerical tests computed with an independent technique. Finally, we show how the initiation phase determines the evolution toward the dynamic rupture propagation. We introduce the critical patch length in a natural way. The transition between the initiation and the propagation stages is characterized by an apparent supersonic velocity of the rupture front.

Observations of unstable atmospheric shear layers in the lower E region in the post‐midnight auroral oval

Observations of the neutral wind profiles in the post‐midnight sector of the auroral oval show the development of a narrow jet near 110–120 km altitude during disturbed conditions. The shears on the bottom side of the jet are highly unstable with Richardson numbers near or below the critical value of 0.25. The unstable shears imply that turbulence and, consequently, the eddy diffusivity will be enhanced in that part of the atmosphere.

Effects of Unstable Thermal Stratification and Mean Shear on Chemical Reaction and Turbulent Mixing in Grid-Generated Turbulence.

The effects of unstable thermal stratification and mean shear on chemical reaction and turbulent mixing were experimentally investigated in a liquid mixing-layer downstream of turbulence generating grids with and without a rapid chemical reaction. Experiments were carried out in both an unsheared unstably-stratified flow and a sheared unstratified flow. Instantaneous velocity and concentration were simultaneously measured using a two-component laser Doppler velocimeter (LDV) and a laser-induced fluorescence (LIF) technique. From these turbulence signals, turbulence quantities such as intensities and power spectra of velocity fluctuations, turbulent mass fluxes and the Reynolds stress were estimated. Furthermore, the total amount of reaction product was estimated from the transverse concentration profiles of chemical product. The results show that the turbulent mixing is enhanced at both large-and small-scales by buoyancy under unstably-stratified conditions and that the chemical reaction is also promoted. The mean shear acts to enhance the turbulent mixing mainly at large scales but the chemical reaction rate is not so large compared to the unstably stratified case. The unstable stratification is a good tool to attain the unsheared mixing since the shearing stress acting on the fluid is much weaker in an unstably-stratified flow than in a sheared unstratified flow.

Energy transport enhancements in a transitional thermal plasma plume

The evolution of heat and mass transfer in the initial region of a transitional plasma plume is investigated and discussed. The results show that these transport processes are controlled and limited by the plume shear layer instability. This process of laminar-turbulent transition is consecutively controlled by the plume core shear layer instability, by the "jet mode" induced by unstable shear layer, and by resonance in the jet and arc chamber. These three processes are manifested in three events. Between the first and second phase, there is a maximum of average enthalpy. The other two thresholds occur at maximum and minimum stagnation heat flux from the plume core. It seems that these processes also influence the thermal energy production in the arc chamber cavity.

Generation and structure of Rossby vortices in rotating fluids.

The formation of zonal flows and vortices in the generalized Charney-Hasegawa-Mima equation is studied. We focus on the regime when the size of structures is comparable to or larger than the deformation (Rossby) radius. Numerical simulations show the formation of anticyclonic vortices in unstable shear flows and ringlike vortices with quiescent cores and vorticity concentrated in a ring. Physical mechanisms that lead to these phenomena and their relevance to turbulence in planetary atmospheres are discussed.

Dynamic Excitation of Internal Gravity Waves in the Equatorial Oceans

Abstract It is proposed that shear instability of the upper flank of the equatorial undercurrent may generate, under a broad range of conditions, downward propagating internal gravity waves (IGW) of large amplitude. The generation mechanism is shown to require only that the background stratification is weak where the shear is large (i.e., in the mixing region) and that the stratification is sufficiently large in the far field (i.e., near the thermocline). In a series of studies, the generation of IGW from unstable shear flows is examined. Linear theory is used to predict under what circumstances the generation of IGW may be large, and fully nonlinear simulations restricted to two dimensions are employed to provide estimates of the degree of vertical mixing and of the vertical transport of horizontal momentum by IGW. In particular, the simulations demonstrate that, when large amplitude IGW are generated by shear instability, the mean flow itself is significantly decelerated in the mixing region. The moment...

A Numerical Method for the Incompressible Navier-Stokes Equations Based on an Approximate Projection

In this method we present a fractional step discretization of the time-dependent incompressible Navier–Stokes equations. The method is based on a projection formulation in which we first solve diffusion–cnvection equations to predict intermediate velocities, which are then projected onto the space of divergence-free vector fields. Our treatment of the diffusion-convection step uses a specialized second-order upwind method for differencing the nonlinear convective terms that provides a robust treatment of these terms at a high Reynolds number. In contrast to conventional projection-type discretization that impose a discrete form of the divergence-free constraint, we only approximately impose the constraint; i.e., the velocity field we compute is not exactly divergence-free. The approximate projection is computed using a conventional discretization of the Laplacian and the resulting linear system is solved using conventional multigrid methods. Numerical examples are presented to validate the second-order convergence of the method for Euler, finite Reynolds number, and Stokes flow. A second example illustrating the behavior of the algorithm on an unstable shear layer is also presented.

Structures of dynamically unstable shear flows and their implications for shallow internal gravity waves part II: Nonlinear response

The nonlinear response of a dynamically unstable shear flow with critical level to an initial temperature anomaly is investigated using a nonlinear numerical model. Both nonconstant and constant shear profiles of the basic flow are considered. Effects of the solid lower boundary on the dynamically unstable, nonlinear flow are also studied. It is found that in a dynamically unstable, linear flow with a hyperbolic tangent wind profile, the updraft is tilted upshear. The result in consistent with that of a linear stability model (LC). The upshear tilt can be explained by the Orr mechanism (1907) and the energy argument proposed by LC. In a dynamically unstable, nonlinear flow, the updrafts produced by a sinusoidal initial temperature perturbation are stronger in the lower layer and are more compact and located further apart compared to the corresponding linear flow. In addition, the perturbed wave energy is slightly smaller than the linear case. It is found that the growth rate is smaller during the early stage and much larger during the later stage. For a localized initial temperature perturbation in a dynamically unstable flow, a stronger updraft with two compensated downdrafts are produced. Gravity waves are produced in a dynamically stable flow with both a hyperbolic tangent wind profile and a linear wind profile. For a linear shear flow with Richardson number less than 1/4, the disturbance grows in the early stage and then decays algebraically at later times, similar to that found in other linear theoretical studies. The influence of the solid lower boundary is to suppress the shear instability in a nonlinear flow with a hyperbolic tangent wind profile ofRi<1/4.

Simulation of Alfven-wave-resonant-particle interaction

New numerical simulations are presented on the self-consistent dynamics of energetic particles and a set of unstable discrete shear Alfven modes in a. tokamak. The code developed for these simulations has been previously tested in simulations of the bump-on-tail instability model. The code has a Hamiltonian structure for the mode-particle coupling, with the superimposed wave damping, particle source and classical relaxation processes. In the alpha-particle-Alfven-wave problem, we observe a transition from a single mode saturation to mode overlap and global quasi-linear diffusion, which is qualitatively similar to that observed in the bump-on-tail model. A considerable enhancement in the wave energy due to the resonance overlap is demonstrated. The effect of global diffusion on the energetic particle losses is also demonstrated