On the longitudinal optimal perturbations to inviscid plane shear flow: formal solution and asymptotic approximation

We study the longitudinal linear optimal perturbations (which maximize the energy gain up to a prescribed time $T$ ) to inviscid parallel shear flow, which present unbounded energy growth due to the lift-up mechanism. Using the phase invariance with respect to time, we show that for an arbitrary base flow profile and optimization time, the computation of the optimal longitudinal perturbation reduces to the resolution of a single one-dimensional eigenvalue problem valid for all times. The optimal perturbation and its amplification are then derived from the lowest eigenvalue and its associated eigenfunction, while the remainder of the infinite set of eigenfunctions provides an orthogonal base for decomposing the evolution of arbitrary perturbations. With this new formulation we obtain, asymptotically for large spanwise wavenumber ${k}_{z} ,$ a prediction of the optimal gain and the localization of inviscid optimal perturbations for the two main classes of parallel flows: free shear flow with an inflectional velocity profile, and wall-bounded flow with maximum shear at the wall. We show that the inviscid optimal perturbations are localized around the point of maximum shear in a region with a width scaling like ${ k}_{z}^{- 1/ 2}$ for free shear flow, and like ${ k}_{z}^{- 2/ 3}$ for wall-bounded shear flows. This new derivation uses the stationarity of the base flow to transform the optimization of initial conditions in phase space into the optimization of a temporal phase along each trajectory, and an optimization among all trajectories labelled by their intersection with a codimension-1 subspace. The optimization of the time phase directly imposes that the initial and final energy growth rates of the optimal perturbation should be equal. This result requires only time invariance of the base flow, and is therefore valid for any linear optimal perturbation problem with stationary base flo

Freeze-out volume in multifragmentation - dynamical simulations

Stochastic mean-field simulations for multifragmenting sources at the same excitation energy per nucleon have been performed. The freeze-out volume, a concept which needs to be precisely defined in this dynamical approach, was shown to increase as a function of three parameters: freeze-out instant, fragment multiplicity and system size.Comment: Submitted to Eur. Phys. J. A - march 200

Analysis of Boltzmann-Langevin Dynamics in Nuclear Matter

The Boltzmann-Langevin dynamics of harmonic modes in nuclear matter is analyzed within linear-response theory, both with an elementary treatment and by using the frequency-dependent response function. It is shown how the source terms agitating the modes can be obtained from the basic BL correlation kernel by a simple projection onto the associated dual basis states, which are proportional to the RPA amplitudes and can be expressed explicitly. The source terms for the correlated agitation of any two such modes can then be extracted directly, without consideration of the other modes. This facilitates the analysis of collective modes in unstable matter and makes it possible to asses the accuracy of an approximate projection technique employed previously.Comment: 13 latex pages, 4 PS figure

Absolute instability in axisymmetric wakes: Compressible and density variation effects

International audienceLesshafft & Huerre (Phys. Fluids, 2007; vol. 19, 024102) have recently studied the transition from convective to absolute instability in hot round jets, for which absolute instability is led by axisymmetric perturbations and enhanced when lowering the jet density. The present paper analyses similarly the counterpart problem of wake flows, and establishes that absolute instability is then led by a large-scale helical wake mode favoured when the wake is denser than the surrounding fluid. This generalizes to variable density and compressible wakes the results of Monkewitz (J. Fluid Mech. vol 192, 1988, p. 561). Furthermore, we show that in a particular range of density ratios, the large-scale helical wake mode can become absolutely unstable by increasing only the Mach number up to high subsonic values. This possibility of an absolute instability triggered by an increase of the Mach number is opposite to the behaviour previously described in shear flows such as plane mixing layers and axisymmetric jets. A physical interpretation based on the action of the baroclinic torque is proposed. An axisymmetric short-scale mode, similar to that observed in plane mixing layers, leads the transition in light wakes, but the corresponding configurations require large counterflow for the instability to be absolute. These results suggest that the low-frequency oscillation present in afterbody wakes may be due to a nonlinear global mode triggered by a local absolute instability, since the azimuthal wavenumber and absolute frequency of the helical wake mode agree qualitatively with observations. © 2008 Cambridge University Press

Spatial Holmboe instability

International audienceIn mixing-layers between two parallel streams of different densities, shear and gravity effects interplay; buoyancy acts as a restoring force and the Kelvin-Helmholtz mode is known to be stabilized by the stratification. If the density interface is sharp enough, two new instability modes, known as Holmboe modes, appear, propagating in opposite directions. This mechanism has been studied in the temporal instability framework. The present paper analyzes the associated spatial instability problem. It considers, in the Boussinesq approximation, two immiscible inviscid fluids with a piecewise linear broken-line velocity profile. We show how the classical scenario for transition between absolute and convective instability should be modified due to the presence of propagating waves. In the convective region, the spatial theory is relevant and the slowest propagating wave is shown to be the most spatially amplified, as suggested by intuition. Predictions of spatial linear theory are compared with mixing-layer [C.G. Koop and F.K. Browand, J. Fluid Mech. 93, 135 (1979)] and exchange flow [G. Pawlak and L. Armi, J. Fluid Mech. 376, 1 (1999)] experiments. The physical mechanism for Holmboe mode destabilization is analyzed via an asymptotic expansion that predicts the absolute instability domain at large Richardson number. © 2002 American Institute of Physics

Microscopic calculations of double and triple Giant Resonance excitation in heavy ion collisions

We perform microscopic calculations of the inelastic cross sections for the double and triple excitation of giant resonances induced by heavy ion probes within a semicalssical coupled channels formalism. The channels are defined as eigenstates of a bosonic quartic Hamiltonian constructed in terms of collective RPA phonons. Therefore, they are superpositions of several multiphonon states, also with different numbers of phonons and the spectrum is anharmonic. The inclusion of (n+1) phonon configurations affects the states whose main component is a n-phonon one and leads to an appreacible lowering of their energies. We check the effects of such further anharmonicities on the previous published results for the cross section for the double excitation of Giant Resonances. We find that the only effect is a shift of the peaks towards lower energies, the double GR cross section being not modified by the explicity inclusion of the three-phonon channels in the dynamical calculations. The latters give an important contribution to the cross section in the triple GR energy region which however is still smaller than the experimental available data. The inclusion of four phonon configurations in the structure calculations does not modify the results.Comment: Revtex4, to be published in PR