Hydrodynamic stability of inviscid rotating coaxial jets
Hydrodynamic stability of inviscid rotating coaxial jets
Leibovich, S.↗
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Sensitivity analysis of hydrodynamic stability operators
The eigenvalue sensitivity for hydrodynamic stability operators is investigated. Classical matrix perturbation techniques as well as the concept of epsilon-pseudoeigenvalues are applied to show that parts of the spectrum are highly sensitive to small perturbations. Applications are drawn from incompressible plane Couette, trailing line vortex flow and compressible Blasius boundary layer flow. Parametric studies indicate a monotonically increasing effect of the Reynolds number on the sensitivity. The phenomenon of eigenvalue sensitivity is due to the non-normality of the operators and their discrete matrix analogs and may be associated with large transient growth of the corresponding initial value problem.
Schmid, Peter J.↗
A study of eigenvalue sensitivity for hydrodynamic stability operators
The eigenvalue sensitivity for hydrodynamic stability operators is investigated. Classical matrix perturbation techniques as well as the concept of epsilon-pseudospectra are applied to show that parts of the spectrum are highly sensitive to small perturbations. Applications are drawn from incompressible plane Couette flow, trailing line vortex flow, and compressible Blasius boundary-layer flow. Parameter studies indicate a monotonically increasing effect of the Reynolds number on the sensitivity. The phenomenon of eigenvalue sensitivity is due to the nonnormality of the operators and their discrete matrix analogs and may be associated with large transient growth of the corresponding initial value problem.
Schmid, Peter J.↗
On the consistency of Reynolds stress turbulence closures with hydrodynamic stability theory
The consistency of second-order closure models with results from hydrodynamic stability theory is analyzed for the simplified case of homogeneous turbulence. In a recent study, Speziale, Gatski, and MacGiolla Mhuiris showed that second-order closures are capable of yielding results that are consistent with hydrodynamic stability theory for the case of homogeneous shear flow in a rotating frame. It is demonstrated in this paper that this success is due to the fact that the stability boundaries for rotating homogeneous shear flow are not dependent on the details of the spatial structure of the disturbances. For those instances where they are -- such as in the case of elliptical flows where the instability mechanism is more subtle -- the results are not so favorable. The origins and extent of this modeling problem are examined in detail along with a possible resolution based on rapid distortion theory (RDT) and its implications for turbulence modeling.
Speziale, Charles G.↗
Hydrodynamic stability and frames of reference
The dependence of criteria of hydrodynamic stability upon a frame of reference is discussed. It is demonstrated that these criteria are not frame indifferent.
Zak, M.↗
Hydrodynamic Stability of Multicomponent Droplet Gasification in Reduced Gravity
This investigation addresses the problem of hydrodynamic stability of a two-component droplet undergoing spherically-symmetrical gasification. The droplet components are assumed to have characteristic liquid species diffusion times that are large relative to characteristic droplet surface regression times. The problem is formulated as a linear stability analysis, with a goal of predicting when spherically-symmetric droplet gasification can be expected to be hydrodynamically unstable from surface-tension gradients acting along the surface of a droplet which result from perturbations. It is found that for the conditions assumed in this paper (quasisteady gas phase, no initial droplet temperature gradients, diffusion-dominated gasification), surface tension gradients do not play a role in the stability characteristics. In addition, all perturbations are predicted to decay such that droplets were hydrodynamically stable. Conditions are identified, however, that deserve more analysis as they may lead to hydrodynamic instabilities driven by capillary effects.
Aharon, I.↗
Hydrodynamic stability problem formulated by numerical solutions of the Navier-Stokes equations
The problem of hydrodynamic stability and the transition from laminar to turbulent flows are reformulated by seeking numerical solutions of the full, unapproximated Navier-Stokes equations. This method differs significantly from the well known Orr-Sommerfeld equation approach. The oncoming laminar flow is disturbed by forced, time dependent perturbations. The magnitudes of these perturbations are arbitrary. Then, the ensuing spatial and temporal development of the imposed perturbations on the basic flow is calculated by direct numerical solutions of the time dependent Navier-Stokes equations. One of the main advantages of this method is its ability to simulate nonlinear processes. As a specific application of this technique to SSME (Space Shuttle Main Engine) flow configurations, computer programs have been written for the two dimensional flow over a backward facing step. This numerical code will be tested for operational use as part of a continued research collaboration effort with the NASA/MSFC counterparts.
Hyun, J. M.↗
Laboratory Study of Magnetorotational Instability and Hydrodynamic Stability at Large Reynolds Numbers
Two plausible mechanisms have been proposed to explain rapid angular momentum transport during accretion processes in astrophysical disks: nonlinear hydrodynamic instabilities and magnetorotational instability (MRI). A laboratory experiment in a short Taylor-Couette flow geometry has been constructed in Princeton to study both mechanisms, with novel features for better controls of the boundary-driven secondary flows (Ekman circulation). Initial results on hydrodynamic stability have shown negligible angular momentum transport in Keplerian-like flows with Reynolds numbers approaching one million, casting strong doubt on the viability of nonlinear hydrodynamic instability as a source for accretion disk turbulence.
Ji, H.↗
Hydrodynamic Stability of Liquid-Propellant Combustion: Landau's Problem Revisited
Hydrodynamic, or Landau, instability in combustion is typically associated with the onset of wrinkling of a flame surface, corresponding to the formation of steady cellular structures as the stability threshold is crossed. As its name suggests, it stems from hydrodynamic effects connected with thermal expansion across the reaction region. In the context of liquid-propellant combustion, the classical models that originally predicted this phenomenon have been extended to include the important effects that arise from a dynamic dependence of the burning rate on the local pressure and temperature fields. Thus, the onset of Landau instability has now been shown to occur for sufficiently small negative values of the pressure sensitivity of the burning rate, significantly generalizing previous classical results for this problem that assumed a constant normal burning rate. It has also been shown that the onset of instability occurs for decreasing values of the disturbance wave number as the gravitational-acceleration parameter decreases. Consequently, in an appropriate weak-gravity limit, Landau instability becomes a long-wave phenomena associated with the formation of large cells on the liquid-propellant surface. Additionally, a pulsating form of hydrodynamic instability has been shown to occur as well, corresponding to the onset of temporal oscillations in the location of the liquid/gas interface. This instability occurs for sufficiently large negative values of the pressure sensitivity, and is enhanced by increasing values of the burning-rate temperature sensitivity. It is further shown that for sufficiently small values of this parameter, there exists a stable range of pressure sensitivities for steady, planar burning such that the classical cellular form of hydrodynamic instability and the more recent pulsating form of hydrodynamic instability can each occur as the corresponding stability threshold is crossed. For larger thermal sensitivities, however, the pulsating stability boundary evolves into a C-shaped curve in the (disturbance-wave number, pressure-sensitivity) plane, indicating loss of stability to pulsating perturbations for all sufficiently large disturbance wavelengths. It is thus concluded, based on characteristic parameter values that an equally likely form of hydrodynamic instability in liquid-propellant combustion is of a nonsteady, long-wave nature, distinct from the steady, cellular form originally predicted by Landau.
Margolis, S. B.↗
Hydrodynamic Stability And Frames Of Reference
Criteria of stability different in different sets of coordinates. Report discusses dependence of criteria of hydrodynamic instability upon frame of reference used to analyze motion of fluid.
Zak, Michail A.↗
Beryllium–tungsten graded density inner shells in double shell capsules for improved hydrodynamic stability
The outer surface of the high-Z inner shell in the double shell configuration of inertial confinement fusion experiments experiences Rayleigh–Taylor instability growth during the implosion process due to inverted density and pressure gradients between a highly compressed foam interstitial layer and the accelerating dense inner shell. Graded density layers have long been known to reduce instability growth rates. In this study, we employ high-fidelity radiation hydrodynamic simulations to demonstrate this improved stability when grading beryllium into tungsten. We first characterize the response to L-band preheat of these layers using a newly calibrated radiation drive. While graded layer capsules suffer reduced performance (here, measured as DD neutron yield from a CD foam fuel) in 1D simulations due to reduced kinetic energy coupling and reduced fuel compression, they suffer less of a performance drop when 2D instabilities are accounted for. With the improved stability of graded layers, we explore the performance of capsules with larger fuel radii and thinner shells as a preliminary study to find new designs in which graded layers produce the highest yields.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Coronal closed structures. IV - Hydrodynamical stability and response to heating perturbations
The response of magnetically confined atmospheres to perturbations in the temperature and density distribution, and the local heating rate by means of a one-dimensional time-dependent hydrodynamical code, which incorporates the full energy, momentum and mass conservation equations is studied. These studies extend the linear instability analysis of Habbal and Rosner (1979) into the finite-amplitude regime, and generalize the confined atmosphere models of Serio et al., to the time-dependent domain. The results show that closed coronal atmospheres are stable against finite-amplitude perturbations if the chromospheric response is taken into account; and observed correlated increases in coronal density and temperature can only be achieved under quiescent conditions by increasing the heat deposition rate relatively more in the chromosphere than in the corona.
Peres, G.↗
A new direction in hydrodynamic stability: Beyond eigenvalues
Fluid flows that are smooth at low speeds become unstable and then turbulent at higher speeds. This phenomenon has traditionally been investigated by linearizing the equations of flow and looking for unstable eigenvalues of the linearized problem, but the results agree poorly in many cases with experiments. Nevertheless, it has become clear in recent years that linear effects play a central role in hydrodynamic instability. A reconciliation of these findings with the traditional analysis can be obtained by considering the 'pseudospectra' of the linearized problem, which reveals that small perturbations to the smooth flow in the form of streamwise vortices may be amplified by factors on the order of 10(exp 5) by a linear mechanism, even though all the eigenmodes are stable. The same principles apply also to other problems in the mathematical sciences that involve non-orthogonal eigenfunctions.
Trefethen, Lloyd N.↗
The hydrodynamic stability of pipe flow semiannual status report, period ending 30 jun. 1968
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Dalton, C.↗
Hydrodynamic stability of viscoelastic fluids - Importance of fluid model, overstability, and form of disturbance.
A linearized stability analysis has been applied to a fluid flowing in a gravity field between horizontal planes in Couette flow under conditions such that the temperature of the bottom plane exceeds that of the top. It is shown that, under conditions likely to be encountered with polymer solutions, oscillatory instabilities will not be controlling. Criteria are offered for ascertaining when an analysis based upon a second-order fluid model may be expected to yield physically meaningful results. It is also shown that, for the fluid model considered, critical conditions for stability are not changed when disturbances which vary in the flow direction are substituted for those which are a function of the coordinate transverse to the flow.
Mcintire, L. V.↗
Hydrodynamic stability of jets produced by mass accreting systems
The existing model for pulsed X-ray emission from the source Hercules X-1 is reviewed. A necessary part of this model is a processing accretion disk which turns the source on and off with 35 day cycle. It is usually assumed that precession of the primary star in this binary system, Hz Hercules, slaves the disk to its precession rate. This model can account for the system behavior in a qualitative manner. Precession of Hz Hercules with 35 day period requires precession of the binary orbit. Pulse arrival times from Herc X-1 have been analyzed for orbital precession. The inclusion of precession does not significantly improve the results obtained assuming a non-precessing orbit. The fluid dynamical stability of extra-galactic jets and the possible consequences of Kelvin-Helmholtz instability at the jet surface external medium interface are considered.
Hardee, P. E.↗
Singularities of the Euler equation and hydrodynamic stability
Equations governing the motion of a specific class of singularities of the Euler equation in the extended complex spatial domain are derived. Under some assumptions, it is shown how this motion is dictated by the smooth part of the complex velocity at a singular point in the unphysical domain. These results are used to relate the motion of complex singularities to the stability of steady solutions of the Euler equation. A sufficient condition for instability is conjectured. Several examples are presented to demonstrate the efficacy of this sufficient condition which include the class of elliptical flows and the Kelvin-Stuart Cat's Eye.
Tanveer, S.↗
Efficient computation of spatial eigenvalues for hydrodynamic stability analysis
The simple procedure presented for spatial stability computations can substantially reduce the computational requirements of such analyses, as illustrated for the cases of both internal and external cases of compressible and incompressible flows, and both viscous and inviscid instability modes. Excellent estimates of spatial eigenvalues are obtained.
Khorrami, Mehdi R.↗