Laurent Jacquin

Spectral approach to non-isotropic turbulence subjected to rotation

The non-isotropic effects of solid-body rotation on homogeneous turbulence are investigated in this paper. A spectral formalism using eigenmodes introduces the spectral Coriolis effects more easily and leads to simpler expressions for the integral quadratic terms which come mostly from classical two-point closures. The analysis is then applied to a specific eddy damped quasi-normal Markovian model, which includes the inertial waves regime in the evaluation of triple correlations. This procedure allows for a departure from isotropy by external rotation effects. When started with rigorously isotropic initial data, the various trends observed on the Reynolds stresses and the integral lengthscales remain in accordance with the results from direct simulations; moreover they reflect a very specific spectral angular distribution. Such an angular dependence allows a drain of spectral energy from the parallel to the normal wave vectors (with respect to the rotation axis), and thus appears consistent with a trend toward two-dimensionality.

Homogeneous turbulence in the presence of rotation

Turbulence in solid-body rotation is generated by a flow of air passing through a rotating cylinder containing a dense honeycomb structure and a turbulence-producing grid. The velocity field is probed downstream of this device by hot-wire probes. Using the statistical quantities characterising the fluctuating field, it is shown that the rotation affects mainly the components normal to the rotation axis and that these effects are triggered when the Rossby numbers, constructed from macroscopic turbulent quantities, are less than unity. These results are discussed in the framework of other experimental results on the subject. A theoretical interpretation, chiefly based on spectral analysis is proposed to explain the trends of the observations.

Sensitivity analysis and passive control of cylinder flow

A general theoretical formalism is developed to assess how base-flow modifications may alter the stability properties of flows studied in a global approach of linear stability theory. It also comprises a systematic approach to the passive control of globally unstable flows by the use of small control devices. This formalism is based on a sensitivity analysis of any global eigenvalue to base-flow modifications. The base-flow modifications investigated are either arbitrary or specific ones induced by a steady force. This leads to a definition of the so-called sensitivity to base-flow modifications and sensitivity to a steady force. These sensitivity analyses are applied to the unstable global modes responsible for the onset of vortex shedding in the wake of a cylinder for Reynolds numbers in the range 47 Re 80. First, it is demonstrated how the sensitivity to arbitrary base-flow modifications may be used to identify regions and properties of the base flow that contribute to the onset of vortex shedding. Secondly, the sensitivity to a steady force determines the regions of the flow where a steady force acting on the base flow stabilizes the unstable global modes. Upon modelling the presence of a control device by a steady force acting on the base flow, these predictions are then extensively compared with the experimental results of Strykowski & Sreenivasan (J. Fluid Mech., vol. 218, 1990, p. 71). A physical interpretation of the suppression of vortex shedding by use of a control cylinder is proposed in the light of the sensitivity analysis.

The mixing layer over a deep cavity at high-subsonic speed

The flow over a cavity at a Mach number 0.8 is considered. The cavity is deep with an aspect ratio (length over depth) L / D = 0.42. This deep cavity flow exhibits several features that makes it different from shallower cavities. It is subjected to very regular self-sustained oscillations with a highly two-dimensional and periodic organization of the mixing layer over the cavity. This is revealed by means of a high-speed schlieren technique. Analysis of pressure signals shows that the first tone mode is the strongest, the others being close to harmonics. This departs from shallower cavity flows where the tones are usually predicted well by the standard Rossiter’s model. A two-component laser-Doppler velocimetry system is also used to characterize the phase-averaged properties of the flow. It is shown that the formation of coherent vortices in the region close to the boundary layer separation has some resemblance to the ‘collective interaction mechanism’ introduced by Ho & Huang (1982) to describe mixing layers subjected to strong sub-harmonic forcing. Otherwise, the conditional statistics show close similarities with those found in classical forced mixing layers except for the production of random perturbations, which reaches a maximum in the structure centres, not in the hyperbolic regions with which turbulence production is usually associated. An attempt is made to relate this difference to the elliptic instability that may be observed here thanks to the particularly well-organized nature of the flow.

Optimal perturbations in a four-vortex aircraft wake in counter-rotating configuration

We consider the instability of two vortex pairs in a counter-rotating configuration. Such configurations model vortex wakes observed behind aircraft with inboard vortices produced at the inboard flap edges and at the tips of the horizontal tail. The instability potential is characterized by an optimal perturbation analysis. This extends the analysis of Fabre & Jacquin which was restricted to particular stationary configurations, and that of Crouch which considered co-rotating configurations. A complete mapping of the optimal perturbations is presented. The optimal perturbations grow faster than the Crow instability. However, they correspond to short-wavelength perturbations mainly affecting the weaker inboard vortices. A possible strategy which consists of forcing a long wavelength is then investigated. Application of both the optimal and the long-wave optimal perturbations to reduction of vortex wake danger is discussed

Kelvin waves and the singular modes of the Lamb–Oseen vortex

Columnar vortices are known to support a family of waves initially discovered by Lord Kelvin (1880) in the case of the Rankine vortex model. This paper presents an exhaustive cartography of the eigenmodes of a more realistic vortex model, the Lamb–Oseen vortex. Some modes are Kelvin waves related to those existing in the Rankine vortex, while some others are singular damped modes with a completely different nature. Several families are identified and are successively described. For each family, the underlying physical mechanism is explained, and the effect of viscosity is detailed. In the axisymmetric case (with azimuthal wavenumber

Stability analysis and large-eddy simulation of rotating turbulence with organized eddies

m\,{=}\,0

Turbulence amplification by a shock wave and rapid distortion theory

), all modes are Kelvin waves and weakly affected by viscosity. For helical modes (

Stability of a four-vortex aircraft wake model

m\,{=}\,1

Viscous instabilities in trailing vortices at large swirl numbers

), four families are identified. The first family, denoted D, corresponds to a particular wave called the displacement wave. The modes of the second family, denoted C, are cograde waves, except in the long-wave range where they become centre modes and are strongly affected by viscosity. The modes of the third family, denoted V, are retrograde, singular modes which are always strongly damped and do not exist in the inviscid limit. The modes of the last family, denoted L, are regular, counter-rotating waves for short wavelengths, but they become singular damped modes for long wavelengths. In an intermediate range of wavelengths between these two limits, they display a particular structure, with both a wave-like profile within the vortex core and a spiral structure at its periphery. This kind of mode is called a critical layer wave, and its significance is explained from both a physical and a mathematical point of view. Double-helix modes (