Temporal Amplification Research Articles

Capillary instability of an annular liquid jet surrounding a solid cylinder

The capillary instability of an annular liquid jet surrounding a solid cylinder is presented. A general dispersion equation is derived based on the linear-perturbation technique. The instability as well as stability characteristics of that model are identified analytically and confirmed numerically. The model is unstable only to the axisymmetric perturbation whose wavelengths are longer than the circumference of the liquid jet, while it is stable to all other perturbations. The maximum temporal amplification values prevailing on such a model are fairly lower than those of the full liquid jet. The thicker the solid cylinder, whether it is regular or irregular, the larger is its stabilizing effect.

The stability of inviscid flows over passive compliant walls

The linear temporal stability of incompressible semi-bounded inviscid parallel flows over passive compliant walls is studied. It is shown that some of the well-known classical results for inviscid parallel flows with rigid boundaries can, in fact, be extended in modified form to passive compliant walls. These include a result of Rayleigh (1880) which shows that the real part of the phase velocity of a non-neutral disturbance must lie within the range of the velocity distribution; the semi-circle theorem of Howard (1961) and a result of Høiland (1953) which places a bound on the temporal amplification rates of unstable disturbances. The bounds on the phase velocity and the temporal amplification rates of unstable two-dimensional disturbances provide useful guides for numerical studies.The results are valid for a large class of passive compliant walls. This generality is achieved through a variational-Lagrangian formulation of the essential dynamics of wall motion. A general treatment of the marginal stability of thin shear flows over general passive compliant walls is given. It represents a generalization of the analysis given by Benjamin (1963) for membrane and plate surfaces. Sufficient conditions for the stability of thin shear flows over passive compliant walls are deduced. The applications of the stability criteria to simple cases of compliant wall are described to illustrate the use and the effectiveness of these criteria.

The structure of turbulent shear flow

A theoretical investigation is made of the mixing layer between two streams. The work is divided into four sections. The first involves the solution of the mean problem of laminar and turbulent mixing. The equations of motion are written in terms of a similarity variable. An eddy viscosity hypothesis is made to describe the shear stresses. The similarity equations for both laminar and turbulent problems are solved numerically by an iterative scheme. The second section examines the stability of the mixing layer. The Orr-Sommerfeld equation of hydrodynamic stability is solved numerically. Doth cases of spatial and temporal amplification are examined. The shear layer is shown to be unstable to both spatially and temporally growing disturbances at all Reynolds numbers. A correction is made for the divergence of the mean flow and leads to a value of critical Reynolds number of 12.3. The third section presents a model for the turbulent mixing layer. A set of partial differential equations describing the flow are obtained. A Fourier transform technique is employed to reduce this set to an ordinary differential equation for the fluctuating flow field. The homogeneous form of this equation is solved numerically. The resulting predictions of fluctuating velocity, pressure and their correlations are compared with measured values. The agreement is good in certain cases and this serves as a guide to components of the flow governed by non-linear processes. The final section examines the non-linear growth of the mixing layer through transition from laminar to turbulent flow. A set of integral momentum and energy equations are written in terms of a number of shape parameters of mean and fluctuating flow. The amplitude of disturbances is shown to grow rapidly and reach a limiting value. A sudden growth of the mixing layer thickness through transition is also predicted. Comparison is made with experimental results.