Inviscid instability of a stably stratified compressible boundary layer on an inclined surface

2012 ◽  
Vol 694 ◽  
pp. 524-539 ◽  
Author(s):  
Julien Candelier ◽  
Stéphane Le Dizès ◽  
Christophe Millet
Keyword(s):  
Boundary Layer ◽  
Boundary Layer Flow ◽  
Acoustic Waves ◽  
Three Dimensional ◽  
Vertical Direction ◽  
Maximum Velocity ◽  
Shear Plane ◽  
Layer Flow ◽  
The Stability ◽  
Inclined Surface

AbstractThe three-dimensional stability of an inflection-free boundary layer flow of length scale$L$and maximum velocity${U}_{0} $in a stably stratified and compressible fluid of constant Brunt–Väisälä frequency$N$, sound speed${c}_{s} $and stratification length$H$is examined in an inviscid framework. The shear plane of the boundary layer is assumed to be inclined at an angle$\theta $with respect to the vertical direction of stratification. The stability analysis is performed using both numerical and theoretical methods for all the values of$\theta $and Froude number$F= {U}_{0} / (LN)$. When non-Boussinesq and compressible effects are negligible ($L/ H\ll 1$and${U}_{0} / {c}_{s} \ll 1$), the boundary layer flow is found to be unstable for any$F$as soon as$\theta \not = 0$. Compressible and non-Boussinesq effects are considered in the strongly stratified limit: they are shown to have no influence on the stability properties of an inclined boundary layer (when$F/ \sin \theta \ll 1$). In this limit, the instability is associated with the emission of internal-acoustic waves.

EXPERIMENTAL INVESTIGATION OF FLOW RESPONSE TO STATIONARY DISTURBANCE IN ROTATING-DISK FLOW

2019 ◽  
Vol XVI (2) ◽  
pp. 13-22
Author(s):  
Muhammad Ehtisham Siddiqui
Keyword(s):  
Boundary Layer ◽  
Boundary Layer Flow ◽  
Three Dimensional ◽  
Rotating Disk ◽  
Careful Analysis ◽  
Laboratory Frame ◽  
Transition To Turbulence ◽  
Turbulent Regime ◽  
Mean Velocity ◽  
Layer Flow

Three-dimensional boundary-layer flow is well known for its abrupt and sharp transition from laminar to turbulent regime. The presented study is a first attempt to achieve the target of delaying the natural transition to turbulence. The behaviour of two different shaped and sized stationary disturbances (in the laboratory frame) on the rotating-disk boundary layer flow is investigated. These disturbances are placed at dimensionless radial location (Rf = 340) which lies within the convectively unstable zone over a rotating-disk. Mean velocity profiles were measured using constant-temperature hot-wire anemometry. By careful analysis of experimental data, the instability of these disturbance wakes and its estimated orientation within the boundary-layer were investigated.

Global three-dimensional optimal disturbances in the Blasius boundary-layer flow using time-steppers

2010 ◽  
Vol 650 ◽  
pp. 181-214 ◽  
Author(s):  
ANTONIOS MONOKROUSOS ◽  
ESPEN ÅKERVIK ◽  
LUCA BRANDT ◽  
DAN S. HENNINGSON
Keyword(s):  
Boundary Layer ◽  
Boundary Layer Flow ◽  
Wave Packets ◽  
Three Dimensional ◽  
Computational Domain ◽  
Initial Condition ◽  
Oblique Wave ◽  
Layer Flow ◽  
Optimal Disturbances ◽  
Matrix Free

The global linear stability of the flat-plate boundary-layer flow to three-dimensional disturbances is studied by means of an optimization technique. We consider both the optimal initial condition leading to the largest growth at finite times and the optimal time-periodic forcing leading to the largest asymptotic response. Both optimization problems are solved using a Lagrange multiplier technique, where the objective function is the kinetic energy of the flow perturbations and the constraints involve the linearized Navier–Stokes equations. The approach proposed here is particularly suited to examine convectively unstable flows, where single global eigenmodes of the system do not capture the downstream growth of the disturbances. In addition, the use of matrix-free methods enables us to extend the present framework to any geometrical configuration. The optimal initial condition for spanwise wavelengths of the order of the boundary-layer thickness are finite-length streamwise vortices exploiting the lift-up mechanism to create streaks. For long spanwise wavelengths, it is the Orr mechanism combined with the amplification of oblique wave packets that is responsible for the disturbance growth. This mechanism is dominant for the long computational domain and thus for the relatively high Reynolds number considered here. Three-dimensional localized optimal initial conditions are also computed and the corresponding wave packets examined. For short optimization times, the optimal disturbances consist of streaky structures propagating and elongating in the downstream direction without significant spreading in the lateral direction. For long optimization times, we find the optimal disturbances with the largest energy amplification. These are wave packets of Tollmien–Schlichting waves with low streamwise propagation speed and faster spreading in the spanwise direction. The pseudo-spectrum of the system for real frequencies is also computed with matrix-free methods. The spatial structure of the optimal forcing is similar to that of the optimal initial condition, and the largest response to forcing is also associated with the Orr/oblique wave mechanism, however less so than in the case of the optimal initial condition. The lift-up mechanism is most efficient at zero frequency and degrades slowly for increasing frequencies. The response to localized upstream forcing is also discussed.

The stability of boundary-layer flow over single-and multi-layer viscoelastic walls

1988 ◽  
Vol 196 ◽  
pp. 359-408 ◽  
Author(s):  
K. S. Yeo
Keyword(s):  
Boundary Layer ◽  
Boundary Layer Flow ◽  
Single Layer ◽  
Viscous Sublayer ◽  
Rigid Base ◽  
Theoretical Treatment ◽  
Dynamical Condition ◽  
Compliant Walls ◽  
Layer Flow ◽  
The Stability

In this paper, we are concerned with the linear stability of zero pressure-gradient laminar boundary-layer flow over compliant walls which are composed of one or more layers of isotropic viscoelastic materials and backed by a rigid base. Wall compliance supports a whole host of new instabilities in addition to the Tollmien-Schlichting mode of instability, which originally exists even when the wall is rigid. The perturbations in the flow and the compliant wall are coupled at their common interface through the kinematic condition of velocity continuity and the dynamical condition of stress continuity. The disturbance modes in the flow are governed by the Orr-Sommerfeld equation using the locally-parallel flow assumption, and the response of the compliant layers is described using a displacement-stress formalism. The theoretical treatment provides a unified formulation of the stability eigenvalue problem that is applicable to compliant walls having any finite number of uniform layers; inclusive of viscous sublayer. The formulation is well suited to systematic numerical implementation. Results for single- and multi-layer walls are presented. Analyses of the eigenfunctions give an insight into some of the physics involved. Multi-layering gives a measure of control over the stability characteristics of compliant walls not available to single-layer walls. The present study provides evidence which suggests that substantial suppression of disturbance growth may be possible for suitably tailored compliant walls.

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