Toroidal, compression, and vortical dipole strengths in 144−154^{144-154}Sm: Skyrme-RPA exploration of deformation effect

A comparative analysis of toroidal, compressional and vortical dipole strengths in the spherical $^{144}$Sm and the deformed $^{154}$Sm is performed within the random-phase-approximation using a set of different Skyrme forces. Isoscalar (T=0), isovector (T=1), and electromagnetic excitation channels are considered. The role of the nuclear convection $j_{\text{con}}$ and magnetization $j_{\text{mag}}$ currents is inspected. It is shown that the deformation leads to an appreciable redistribution of the strengths and causes a spectacular deformation splitting (exceeding 5 MeV) of the isoscalar compressional mode. In $^{154}$Sm, the $\mu$=0 and $\mu$=1 branches of the mode form well separated resonances. When stepping from $^{144}$Sm to $^{154}$Sm, we observe an increase of the toroidal, compression and vortical contributions in the low-energy region (often called pygmy resonance). The strength in this region seems to be an overlap of various excitation modes. The energy centroids of the strengths depend significantly on the isoscalar effective mass $m_0$. Skyrme forces with a large $m_0$ (typically $m_0/m \approx 0.8 - 1$) seem to be more suitable for description of experimental data for the isoscalar giant dipole resonance.Comment: 13 pages, 10 figures, submitted to EJP

Flow structure in a model of aircraft trailing vortices

We consider a model of incompressible trailing vortices consisting of an array of counter-rotating structures in a doubly periodic domain, infinite in the vertical direction. The two-dimensional vortex array of Mallier and Maslowe is combined with an axial velocity profile chosen proportional to the initial axial vorticity to provide an initial condition for the vortex wake. This base flow is a weak solution of the steady Euler equations with three velocity components that are functions of two spatial coordinates, thus allowing its linear stability properties to be investigated. These are used to interpret several stages in the development of vortex structure observed in fully three-dimensional direct numerical simulation (DNS) at Reynolds numbers Gamma/(2pinu)=[script O](1000). For sufficiently high axial velocity, its effect can be seen, in that each vortex in the linear array first develops helical structures before undergoing a period of relaminarization. At later times the more slowly growing cooperative elliptical instabilities become apparent, but the helical structure persists and the observed vortical structures remain coherent for longer periods than in the absence of axial velocity. Using the stretched-vortex subgrid model, large-eddy simulation runs are performed at large Reynolds numbers and a mixing transition identified at about Re=1–2×10^4. Similar phenomena are observed in these simulations as are seen in the DNS

High-resolution simulations and modeling of reshocked single-mode Richtmyer-Meshkov instability: Comparison to experimental data and to amplitude growth model predictions

The reshocked single-mode Richtmyer-Meshkov instability is simulated in two spatial dimensions using the fifth- and ninth-order weighted essentially nonoscillatory shock-capturing method with uniform spatial resolution of 256 points per initial perturbation wavelength. The initial conditions and computational domain are modeled after the single-mode, Mach 1.21 air(acetone)/SF6 shock tube experiment of Collins and Jacobs [J. Fluid Mech. 464, 113 (2002)]. The simulation densities are shown to be in very good agreement with the corrected experimental planar laser-induced fluorescence images at selected times before reshock of the evolving interface. Analytical, semianalytical, and phenomenological linear and nonlinear, impulsive, perturbation, and potential flow models for single-mode Richtmyer-Meshkov unstable perturbation growth are summarized. The simulation amplitudes are shown to be in very good agreement with the experimental data and with the predictions of linear amplitude growth models for small times, and with those of nonlinear amplitude growth models at later times up to the time at which the driver-based expansion in the experiment (but not present in the simulations or models) expands the layer before reshock. The qualitative and quantitative differences between the fifth- and ninth-order simulation results are discussed. Using a local and global quantitative metric, the prediction of the Zhang and Sohn [Phys. Fluids 9, 1106 (1997)] nonlinear Padé model is shown to be in best overall agreement with the simulation amplitudes before reshock. The sensitivity of the amplitude growth model predictions to the initial growth rate from linear instability theory, the post-shock Atwood number and amplitude, and the velocity jump due to the passage of the shock through the interface is also investigated numerically

Strong interaction of a turbulent spot with a shock-induced separation bubble

Direct numerical simulations have been conducted to study the passage of a turbulent spot through a shock-induced separation bubble. Localized blowing is used to trip the boundary layer well upstream of the shock impingement, leading to mature turbulent spots at impingement, with a length comparable to the length of the separation zone. Interactions are simulated at free stream Mach numbers of two and four, for isothermal (hot) wall boundary conditions. The core of the spot is seen to tunnel through the separation bubble, leading to a transient reattachment of the flow. Recovery times are long due to the influence of the calmed region behind the spot. The propagation speed of the trailing interface of the spot decreases during the interaction and a substantial increase in the lateral spreading of the spot was observed. A conceptual model based on the growth of the lateral shear layer near the wingtips of the spot is used to explain the change in lateral growth rat

On the spectrum of a stretched spiral vortex

Corrections are found to the k^–5/3 spectrum of Lundgren [Phys. Fluids 25, 2193 (1982)] for a stretched spiral vortex model (a is the stretching strain rate and k the scalar wave number) of turbulent fine scales. These take the form of additional terms arising from the early time evolution, when the stretching of vortex lines is small. For the special case when the spiral takes the form of a rolled-up shear layer, it is shown that the composite spectrum is divergent, thus requiring the introduction of a finite early cutoff time tau1 in the time integral for the nonaxisymmetric contribution. The identity nuomega2 = 2nu[integral]0[infinity]k^2E(k)dk which gives the dissipation is then satisfied self-consistently. Direct numerical calculation of the energy spectrum from the approximate vorticity field for a special choice of spiral structure nevertheless indicates that the one-term k^–5/3-spectrum result is asymptotically valid in the inertial range provided atau1 is O(1) but that the numerically calculated dissipation spectrum appears to lie somewhere between an exp(–B1k2) and an exp(–B2k) form. It is also shown that the stretched, rolled-up shear-layer model predicts asymptotic shell-summed spectra of the energy dissipation and of the square of the vorticity, each asymptotically constant, with no power-law dependence, for k smaller than the Kolmogorov wave number.The corresponding one-dimensional spectra each show –log(k1) behavior for small k1. The extension of the model given by Pullin and Saffman [Phys. Fluids A 5, 126 (1993)] is reformulated by the introduction of a long-time cutoff in the vortex lifetime and an additional requirement that the vortex structures be approximately space filling. This gives a reduction in the number of model free-parameters but introduces a dependence of the calculated Kolmogorov constant and skewness on the ratio of the initial vortex radius to the equivalent Burgers-vortex radius. A scaling for this ratio in terms of the Taylor microscale Reynolds number is proposed in which the stretching strain is assumed to be provided by the large scales with spatial coherence limited to the maximum stretched length of the structures. Postdictions of the fourth-order flatness factor and of higher moments of the longitudinal velocity gradient statistics are compared with numerical simulation

Geometric phases for corotating elliptical vortex patches

We describe a geometric phase that arises when two elliptical vortex patches corotate. Using the Hamiltonian moment model of Melander, Zabusky, and Styczek [J. Fluid Mech. 167, 95–115 (1986)] we consider two corotating uniform elliptical patches evolving according to the second order truncated equations of the model. The phase is computed in the adiabatic setting of a slowly varying Hamiltonian as in the work of Hannay [J. Phys. A 18, 221–230 (1985)] and Berry [Proc. R. Soc. London, Ser. A 392, 45–57 (1984)]. We also discuss the geometry of the symplectic phase space of the model in the context of nonadiabatic phases. The adiabatic phase appears in the orientation angle of each patch—it is similiar in form and is calculated using a multiscale perturbation procedure as in the point vortex configuration of Newton [Physica D 79, 416–423 (1994)] and Shashikanth and Newton [J. Nonlinear Sci. 8, 183–214 (1998)], however, an extra factor due to the internal stucture of the patch is present. The final result depends on the initial orientation of the patches unlike the phases in the works of Hannay and Berry [J. Phys. A 18, 221–230 (1985)]; [Proc. R. Soc. London, Ser. A 392, 45–57 (1984)]. We then show that the adiabatic phase can be interpreted as the holonomy of a connection on the trivial principal fiber bundle pi:T2×S1-->S1, where T2 is identified with the product of the momentum level sets of two Kirchhoff vortex patches and S1 is diffeomorphic to the momentum level set of two point vortex motion. This two point vortex motion is the motion that the patch centroids approach in the adiabatic limit

The effect of Mach number on unstable disturbances in shock/boundary-layer interactions

The effect of Mach number on the growth of unstable disturbances in a boundary layer undergoing a strong interaction with an impinging oblique shock wave is studied by direct numerical simulation and linear stability theory (LST). To reduce the number of independent parameters, test cases are arranged so that both the interaction location Reynolds number (based on the distance from the plate leading edge to the shock impingement location for a corresponding inviscid flow) and the separation bubble length Reynolds number are held fixed. Small-amplitude disturbances are introduced via both white-noise and harmonic forcing and, after verification that the disturbances are convective in nature, linear growth rates are extracted from the simulations for comparison with parallel flow LST and solutions of the parabolized stability equations (PSE). At Mach 2.0, the oblique modes are dominant and consistent results are obtained from simulation and theory. At Mach 4.5 and Mach 6.85, the linear Navier-Stokes results show large reductions in disturbance energy at the point where the shock impinges on the top of the separated shear layer. The most unstable second mode has only weak growth over the bubble region, which instead shows significant growth of streamwise structures. The two higher Mach number cases are not well predicted by parallel flow LST, which gives frequencies and spanwise wave numbers that are significantly different from the simulations. The PSE approach leads to good qualitative predictions of the dominant frequency and wavenumber at Mach 2.0 and 4.5, but suffers from reduced accuracy in the region immediately after the shock impingement. Three-dimensional Navier-Stokes simulations are used to demonstrate that at finite amplitudes the flow structures undergo a nonlinear breakdown to turbulence. This breakdown is enhanced when the oblique-mode disturbances are supplemented with unstable Mack modes

Numerical simulation of viscous vortex rings

Vortex interactions and their role in turbulent flow are examined. The objectives are twofold. First, to use the existing axisymmetric code to study the annihilation process of colliding vortex rings and determine the relevance of this problem to similar 3-D phenomena. The second objective is to extend the code to three dimensions. The code under development is unique in that it can compute flows in a truly infinite domain (i.e., without periodic boundary conditions or approximations from truncating the domain). Because of this, the far field sound can be computed, and therefore, contribute to improved models of turbulence generated noise for this class of flows. Issues which can be addressed by the code include: effects of viscosity on mode selection in azimuthal breakdown of vortex rings (i.e., the Widnall instability); reconnection, the associated production of small scales, and the time scale of the process