Maher Lagha

Laminar-turbulent boundary in plane Couette flow.

We apply the iterated edge-state tracking algorithm to study the boundary between laminar and turbulent dynamics in plane Couette flow at Re=400. Perturbations that are not strong enough to become fully turbulent or weak enough to relaminarize tend toward a hyperbolic coherent structure in state space, termed the edge state, which seems to be unique up to obvious continuous shift symmetries. The results reported here show that in cases where a fixed point has only one unstable direction, such as for the lower-branch solution in plane Couette flow, the iterated edge tracking algorithm converges to this state. They also show that the choice of initial state is not critical and that essentially arbitrary initial conditions can be used to find the edge state.

A numerical study of compressible turbulent boundary layers

Compressible turbulent boundary layers with free-stream Mach number ranging from 2.5 up to 20 are analyzed by means of direct numerical simulation of the Navier–Stokes equations. The fluid is assumed to be an ideal gas with constant specific heats. The simulation generates its inflow condition using the rescaling-recycling method. The main objective is to study the effect of Mach number on turbulence statistics and near-wall turbulence structures. The present study shows that supersonic/hypersonic boundary layers at zero pressure gradient exhibit close similarities to incompressible boundary layers and that the main turbulence statistics can be correctly described as variable-density extensions of incompressible results. The study also shows that the spanwise streak’s spacing of 100 wall units in the inner region y + 15 still holds for the considered high Mach numbers. The probability density function of the velocity dilatation shows significant variations as the Mach number is increased, but it can also be normalized by accounting for the variable-density effect. The compressible boundary layer also shows an additional similarity to the incompressible boundary layer in the sense that without the linear coupling term, near-wall turbulence cannot be sustained.

Modeling of plane Couette flow. I. Large scale flow around turbulent spots

Numerical simulations of a model of plane Couette flow focusing on its in-plane spatio-temporal properties are used to study the dynamics of turbulent spots. While the core of a spot is filled with small-scale velocity fluctuations, a large-scale flow extending far away and occupying the full gap between the driving plates is revealed upon filtering out small scales. It is characterized by streamwise inflow towards the spot and spanwise outflow from the spot, giving it a quadrupolar shape. A correction to the base flow is present within the spot in the form of a spanwise vortex with vorticity opposite in sign to that of the base flow. The Reynolds stresses are shown to be at the origin of this recirculation, whereas the quadrupolar shape of the in-plane flow results from the transport of this recirculation by the base flow that pumps it towards the spot in the streamwise direction and flushes it in the spanwise direction to insure mass conservation. These results shed light on earlier observations in plan...

Near-wall dynamics of compressible boundary layers

The coherent structures populating the inner-region of a compressible boundary layer with free-stream Mach number equal to 2.5 are analyzed by means of direct numerical simulations of the Navier–Stokes equations. This study shows similarity with the incompressible case in the sense that turbulence in the near-wall region can be sustained without fluctuations in the outer region, proving the existence of a local cycle within the near-wall region. The dynamics are further simplified by making use of the coherence of the inner region. The wall-normal velocity component in this region is split into two: one coherent part representing vortices spanning all the inner-region, and one incoherent part representing the background turbulence. By damping the latter part, the statistical features of the flow are only slightly influenced, showing that the coherent part is essential in determining the flow characteristics. Flow dynamics and turbulence structures within this coherent part are examined. It is shown that t...

Turbulent spots and waves in a model for plane Poiseuille flow

The structure of a turbulent spot in plane Poiseuille flow is investigated using a model derived from the Navier–Stokes equations through a Galerkin method. The mean profile of the streamwise velocity inside the turbulent spot has the characteristic flat profile of a turbulent Poiseuille flow. The waves developing at the wing tips of the spot have an asymmetric streamwise velocity with respect to the channel centerline, whereas their associated wall-normal velocity component is symmetric. On the outskirts of the spot, a large-scale flow occupying the full gap between the plates is observed. It is characterized by a streamwise inflow toward the spot and a spanwise outflow from the spot. A detailed comparison with the numerical simulations and the experiments in the literature shows that these results are in fair agreement with the main features of the transitional plane Poiseuille flow.

Modeling of plane Couette flow. II. On the spreading of a turbulent spot

In this paper, we study the spreading mechanism of turbulent spots in plane Couette flow, where fluid is sheared between two parallel plates moving in opposite directions. The analysis of the coherent structures on the border between the laminar and turbulent regions reveals the existence of many vortices with wall-normal axes occupying the full gap between the plates. The streamwise component of the velocity field of these vortices is the streaks. Due to their self-advection, these vortices move parallel to the plates. During their motions, they carry the other perturbation components such as the streamwise and spanwise vortices.

A comprehensible low-order model for wall turbulence dynamics

Streamwise vortices play an important role in the sustainment of wall turbulence. They are associated with regions with strong Reynolds shear stress production. In turbulent plane Couette flow at low Reynolds numbers, these streamwise vortices fill the whole gap between the plates. Using a low-order model obtained from the Navier-Stokes equations through a two-step Galerkin projection, the dynamics of these streamwise vortices is shown to be similar to the dynamics observed in the near-wall region of turbulent boundary layers [M. Lagha, J. Kim, J. D. Eldredge, and X. Zhong, “Near-wall dynamics of compressible boundary layer,” Phys. Fluids 23, 065109 (2011)]. A spanwise vortex filling the whole gap between the plates and with vorticity opposite in sign to that of the base flow, is tilted in the streamwise direction by the spanwise shear of the streaks. The resultant vortex has a crescent shape and its legs are two streamwise vortices. They regenerate the streaks by the lift-up effect. Through its ability t...