33 research outputs found
The role of long waves in the stability of the plane wake
This work is directed towards investigating the fate of three-dimensional
long perturbation waves in a plane incompressible wake. The analysis is posed
as an initial-value problem in space. More specifically, input is made at an
initial location in the downstream direction and then tracing the resulting
behavior further downstream subject to the restriction of finite kinetic
energy. This presentation follows the outline given by Criminale and Drazin
[Stud. in Applied Math. \textbf{83}, 123 (1990)] that describes the system in
terms of perturbation vorticity and velocity. The analysis is based on large
scale waves and expansions using multi scales and multi times for the partial
differential equations. The multiscaling is based on an approach where the
small parameter is linked to the perturbation property independently from the
flow control parameter. Solutions of the perturbative equations are determined
numerically after the introduction of a regular perturbation scheme
analytically deduced up to the second order. Numerically, the complete linear
system is also integrated. Since the results relevant to the complete problem
are in very good agreement with the results of the first order analysis, the
numerical solution at the second order was deemed not necessary. The use for an
arbitrary initial-value problem will be shown to contain a wealth of
information for the different transient behaviors associated to the symmetry,
angle of obliquity and spatial decay of the long waves. The amplification
factor of transversal perturbations never presents the trend - a growth
followed by a long damping - usually seen in waves with wavenumber of order one
or less. Asymptotical instability is always observed.Comment: accepted Physical Review E, March 201
Pressure and kinetic energy transport across the cavity mouth in resonating cavities
Basic properties of the incompressible fluid motion in a rectangular cavity located along one wall of a plane channel are considered. For Mach numbers of the order of 1 × 10−3 and using the incompressible formulation, we look for observable properties that can be associated with acoustic emission, which is normally observed in this kind of flow beyond a critical value of Reynolds number. The focus is put on the energy dynamics, in particular on the accumulation of energy in the cavity which takes place in the form of pressure and kinetic energy. By increasing the external forcing, we observe that the pressure flow into the cavity increases very rapidly, then peaks. However, the flow of kinetic energy, which is many orders of magnitude lower than that of the pressure, slowly but continuously grows. This leads to the pressure-kinetic energy flows ratio reaching an asymptotic state around the value 1000 for the channel bulk speed Reynolds number. It is interesting to note that beyond this threshold when the channel flow is highly unsteady—a sort of coarse turbulent flow—a sequence of high and low pressure spots is seen to depart from the downward cavity step in the statistically averaged field. The set of spots forms a steady spatial structure, a sort of damped standing wave stretching along the spanwise direction. The line joining the centers of the spots has an inclination similar to the normal to the fronts of density or pressure waves, which are observed to propagate from the downstream cavity edge in compressible cavity flows (at Mach numbers of 1 × 102 to 1 × 103, larger than those considered here). The wavelength of the standing wave is of the order of 1/8 the cavity depth and observed at the channel bulk Reynolds number, Re ∼ 2900. In this condition, the measure of the maximum pressure differences in the cavity field shows values of the order of 1 × 10−1 Pa.We interpret the presence of this sort of wave as the fingerprint of the noise emission spots which could be observed in simulations where the full compressible formulation is used. The flow is studied by means of a sequence of direct numerical simulations in the Reynolds number range 25-2900. This allows the study to span across the steady laminar regime up to a first coarse turbulent regime. These results are confirmed by the good agreement with a set of laboratory results obtained at a Reynolds number one order of magnitude larger in a different cavity geometry [M. Gharib and A. Roshko, J. Fluid Mech. 177, 501 (1987)]. This leaves room for a certain degree of qualitative universality to be associated with the present findings. DOI: 10.1103/PhysRevE.87.01301
Linear waves in sheared flows. Lower bound of the vorticity growth and propagation discontinuities in the parameters space
This study provides sufficient conditions for the temporal monotonic decay of
enstrophy for two-dimensional perturbations traveling in the incompressible,
viscous, plane Poiseuille and Couette flows. Extension of J. L. Synge's
procedure (1938) to the initial-value problem allowed us to find the region of
the wavenumber-Reynolds number map where the enstrophy of any initial
disturbance cannot grow. This region is wider than the kinetic energy's one. We
also show that the parameters space is split in two regions with clearly
distinct propagation and dispersion properties