Polymer transport in random flow

The dynamics of polymers in a random smooth flow is investigated in the framework of the Hookean dumbbell model. The analytical expression of the time-dependent probability density function of polymer elongation is derived explicitly for a Gaussian, rapidly changing flow. When polymers are in the coiled state the pdf reaches a stationary state characterized by power-law tails both for small and large arguments compared to the equilibrium length. The characteristic relaxation time is computed as a function of the Weissenberg number. In the stretched state the pdf is unstationary and exhibits multiscaling. Numerical simulations for the two-dimensional Navier-Stokes flow confirm the relevance of theoretical results obtained for the delta-correlated model.Comment: 28 pages, 6 figure

Mean flow stability analysis of oscillating jet experiments

Linear stability analysis is applied to the mean flow of an oscillating round jet with the aim to investigate the robustness and accuracy of mean flow stability wave models. The jet's axisymmetric mode is excited at the nozzle lip through a sinusoidal modulation of the flow rate at amplitudes ranging from 0.1 % to 100 %. The instantaneous flow field is measured via particle image velocimetry and decomposed into a mean and periodic part utilizing proper orthogonal decomposition. Local linear stability analysis is applied to the measured mean flow adopting a weakly nonparallel flow approach. The resulting global perturbation field is carefully compared to the measurements in terms of spatial growth rate, phase velocity, and phase and amplitude distribution. It is shown that the stability wave model accurately predicts the excited flow oscillations during their entire growth phase and during a large part of their decay phase. The stability wave model applies over a wide range of forcing amplitudes, showing no pronounced sensitivity to the strength of nonlinear saturation. The upstream displacement of the neutral point and the successive reduction of gain with increasing forcing amplitude is very well captured by the stability wave model. At very strong forcing (>40%), the flow becomes essentially stable to the axisymmetric mode. For these extreme cases, the prediction deteriorates from the measurements due to an interaction of the forced wave with the geometric confinement of the nozzle. Moreover, the model fails far downstream in a region where energy is transferred from the oscillation back to the mean flow. This study supports previously conducted mean flow stability analysis of self-excited flow oscillations in the cylinder wake and in the vortex breakdown bubble and extends the methodology to externally forced convectively unstable flows.Comment: submitted to the Journal of Fluid Mechanic

Relaminarisation of Re_τ=100 channel flow with globally stabilising linear feedback control

The problems of nonlinearity and high dimension have so far prevented a complete solution of the control of turbulent flow. Addressing the problem of nonlinearity, we propose a flow control strategy which ensures that the energy of any perturbation to the target profile decays monotonically. The controller’s estimate of the flow state is similarly guaranteed to converge to the true value. We present a one-time off-line synthesis procedure, which generalises to accommodate more restrictive actuation and sensing arrangements, with conditions for existence for the controller given in this case. The control is tested in turbulent channel flow (Re_τ = 100) using full-domain sensing and actuation on the wall-normal velocity. Concentrated at the point of maximum inflection in the mean profile, the control directly counters the supply of turbulence energy arising from the interaction of the wall-normal perturbations with the flow shear. It is found that the control is only required for the larger-scale motions, specifically those above the scale of the mean streak spacing. Minimal control effort is required once laminar flow is achieved. The response of the near-wall flow is examined in detail, with particular emphasis on the pressure and wall-normal velocity fields, in the context of Landahl’s theory of sheared turbulence

Particle acceleration at ultrarelativistic shocks: an eigenfunction method

We extend the eigenfunction method of computing the power-law spectrum of particles accelerated at a relativistic shock fronts to apply to shocks of arbitrarily high Lorentz factor. In agreement with the findings of Monte-Carlo simulations, we find the index of the power-law distribution of accelerated particles which undergo isotropic diffusion in angle at an ultrarelativistic, unmagnetized shock is s=4.23 (where s=-d(ln f)/dp with f the Lorentz invariant phase-space density and p the momentum). This corresponds to a synchrotron index for uncooled electrons of a=0.62 (taking cooling into account a=1.12), where a=-d(ln F)/dn, F is the radiation flux and n the frequency. We also present an approximate analytic expression for the angular distribution of accelerated particles, which displays the effect of particle trapping by the shock: compared with the non-relativistic case the angular distribution is weighted more towards the plane of the shock and away from its normal. We investigate the sensitivity of our results to the transport properties of the particles and the presence of a magnetic field. Shocks in which the ratio of Poynting to kinetic energy flux upstream is not small are less compressive and lead to larger values of $s$.Comment: Minor additions on publicatio

Research on turbulence in plasma

The plasma turbulence research program at William and Mary is discussed. The search has been less for phenomena to explain than for nontrivial magnetohydrodynamic processes in the fully turbulent domain that can be understood. Two examples are used to illustrate this: (1) development of anisotropy in the presence of a strong do magnetic field; and (2) the decay of an MHD turbulent field to a dynamically aligned state with velocity field and magnetic fields parallel or antiparallel

Relaminarisation of Re_{\tau} = 100 channel flow with globally stabilising linear feedback control

The problems of nonlinearity and high dimension have so far prevented a complete solution of the control of turbulent flow. Addressing the problem of nonlinearity, we propose a flow control strategy which ensures that the energy of any perturbation to the target profile decays monotonically. The controller's estimate of the flow state is similarly guaranteed to converge to the true value. We present a one-time off-line synthesis procedure, which generalises to accommodate more restrictive actuation and sensing arrangements, with conditions for existence for the controller given in this case. The control is tested in turbulent channel flow ($Re_\tau=100$) using full-domain sensing and actuation on the wall-normal velocity. Concentrated at the point of maximum inflection in the mean profile, the control directly counters the supply of turbulence energy arising from the interaction of the wall-normal perturbations with the flow shear. It is found that the control is only required for the larger-scale motions, specifically those above the scale of the mean streak spacing. Minimal control effort is required once laminar flow is achieved. The response of the near-wall flow is examined in detail, with particular emphasis on the pressure and wall-normal velocity fields, in the context of Landahl's theory of sheared turbulence

Fluid flow dynamics under location uncertainty

We present a derivation of a stochastic model of Navier Stokes equations that relies on a decomposition of the velocity fields into a differentiable drift component and a time uncorrelated uncertainty random term. This type of decomposition is reminiscent in spirit to the classical Reynolds decomposition. However, the random velocity fluctuations considered here are not differentiable with respect to time, and they must be handled through stochastic calculus. The dynamics associated with the differentiable drift component is derived from a stochastic version of the Reynolds transport theorem. It includes in its general form an uncertainty dependent "subgrid" bulk formula that cannot be immediately related to the usual Boussinesq eddy viscosity assumption constructed from thermal molecular agitation analogy. This formulation, emerging from uncertainties on the fluid parcels location, explains with another viewpoint some subgrid eddy diffusion models currently used in computational fluid dynamics or in geophysical sciences and paves the way for new large-scales flow modelling. We finally describe an applications of our formalism to the derivation of stochastic versions of the Shallow water equations or to the definition of reduced order dynamical systems