Spatial evolution of nonlinear acoustic mode instabilities on hypersonic boundary layers

The effects are considered of strong critical layer nonlinearity on the spatial evolution of an initially linear acoustic mode instability wave on a hypersonic flat plate boundary layer. The analysis shows that nonlinearity, which is initially confined to a thin critical layer, first becomes important when the amplitude of the pressure fluctuations become 0(1/M exp 4 In M exp 2), where M is the free stream Mach number. The flow outside the critical layer is still determined by linear dynamics and therefore takes the form of a linear instability wave, but with its amplitude completely determined by the flow within the critical layer. The latter flow is determined by a coupled set of nonlinear equations, which were solved numerically

Small-amplitude disturbances in turbomachine flows with swirl

A method is proposed for determining the response of the steady swirling potential flow past a blade row in an axial turbomachine to the most general type of 'nonacoustic' incident disturbance. The method is based on Goldstein's decomposition of the disturbance velocity and only requires solving a linear inhomogeneous wave equation. It is believed that numerical solutions to this wave equation can be obtained more efficiently and will be more accurate than corresponding solutions to the linearized compressible Euler equations

Nonlinear Instability of a Uni-directional Transversely Sheared Mean Flow

It is well known that the presence of a weak cross flow in an otherwise two-dimensional shear flow results in a spanwise variation in the mean streamwise velocity profile that can lead to an amplification of certain three-dimensional disturbances through a kind of resonant-interaction mechanism (Goldstein and Wundrow 1994). The spatial evolution of an initially linear, finite-growth-rate, instability wave in such a spanwise-varying shear flow is considered, The base flow, which is governed by the three-dimensional parabolized Navier-Stokes equations, is initiated by imposing a spanwise- periodic cross-flow velocity on an otherwise two-dimensional shear flow at some fixed streamwise location. The resulting mean-flow distortion initially grows with increasing streamwise distance, reaches a maximum and eventually decays through the action of viscosity. This decay, which coincides with the viscous spread of of the shear layer, means that the local growth rate of the instability wave will eventually decrease as the wave propagates downstream. Nonlinear effects can then become important within a thin spanwise-modulated critical layer once the local instability-wave amplitude and growth rate become sufficiently large and small, respectively. The amplitude equation that describes this stage of evolution is shown to be a generalization of the one obtained by Goldstein and Choi (1989) who considered the related problem of the interaction of two oblique modes in a two-dimensional shear layer

Interaction of Oblique Instability Waves with Weak Streamwise Vortices

This paper is concerned with the effect of a weak spanwise-variable mean-flow distortion on the growth of oblique instability waves in a Blasius boundary layer. The streamwise component of the distortion velocity initially grows linearly with increasing streamwise distance, reaches a maximum, and eventually decays through the action of viscosity. This decay occurs slowly and allows the distortion to destabilize the Blasius flow over a relatively large streamwise region. It is shown that even relatively weak distortions can cause certain oblique Rayleigh instability waves to grow much faster than the usual two-dimensional Tollmien-Schlichting waves that would be the dominant instability modes in the absence of the distortion. The oblique instability waves can then become large enough to interact nonlinearly within a common critical layer. It is shown that the resulting nonlinearity is weak and that the common amplitude of the interacting oblique waves is governed by the amplitude evolution equation derived in Goldstein & Choi (1989). The implications of these results for Klebanoff-type transition are discussed

Effect of Free Stream Turbulence and Other Vortical Disturbances on a Laminar Boundary Layer

This paper is concerned with the effect of free-stream turbulence on the pretransitional flat-plate boundary layer. It is assumed that either the turbulence Reynolds number or the downstream distance (or both) is small enough so that the flow can be linearized. The dominant disturbances in the boundary layer, which are of the Klebanoff type, are governed by the linearized unsteady boundary-region equations, i.e., the Navier Stokes equations with the streamwise derivatives neglected in the viscous and pressure-gradient terms. The turbulence is represented as a superposition of vortical free-stream Fourier modes, and the corresponding individual Fourier component solutions to the boundary-region equations are obtained numerically. The results are then superposed to compute the root mean square of the fluctuating streamwise velocity in the boundary layer produced by the actual free-stream turbulence. The calculated boundary-layer disturbances are in good quantitative agreement with the experimentally observed Klebanoff modes when strong low-frequency anisotropic effects are included in the free-stream turbulence spectrum. We discuss some additional effects that may need to be accounted for in order to obtain a complete description of the Klebanoff modes

A complex ray-tracing tool for high-frequency mean-field flow interaction effects in jets

This paper presents a complex ray-tracing tool for the calculation of high-frequency Green’s functions in 3D mean field jet flows. For a generic problem, the ray solution suffers from three main deficiencies: multiplicity of solutions, singularities at caustics, and the determining of complex solutions. The purpose of this paper is to generalize, combine and apply existing stationary media methods to moving media scenarios. Multiplicities are dealt with using an equivalent two-point boundary-value problem, whilst non-uniformities at caustics are corrected using diffraction catastrophes. Complex rays are found using a combination of imaginary perturbations, an assumption of caustic stability, and analytic continuation of the receiver curve. To demonstrate this method, the ray tool is compared against a high-frequency modal solution of Lilley’s equation for an off-axis point source. This solution is representative of high-frequency source positions in real jets and is rich in caustic structures. A full utilization of the ray tool is shown to provide excellent results<br/

Nonlinear description of transversal motion in a laminar boundary layer with streaks

The nonlinear streamwise growth of a spanwise periodic array of steady streaks in a flat plate boundary layer is numerically computed using the well known Reduced Navier-Stokes formulation. It is found that the flow configuration changes substantially when the amplitude of the streaks grows and the nonlinear effects come into play. The transversal motion (in the wall normal-spanwise plane), which is normally not considered, becomes non-negligible in the nonlinear regime, and it strongly distorts the streamwise velocity profiles, which end up being quite different from those predicted by the linear theory. We analyze in detail the resulting flow patterns for the nonlinearly saturated streaks, and compare them with available experimental results

The Effect of Diet and Opponent Size on Aggressive Interactions Involving Caribbean Crazy Ants (Nylanderia fulva)

Biotic interactions are often important in the establishment and spread of invasive species. In particular, competition between introduced and native species can strongly influence the distribution and spread of exotic species and in some cases competition among introduced species can be important. The Caribbean crazy ant, Nylanderia fulva, was recently introduced to the Gulf Coast of Texas, and appears to be spreading inland. It has been hypothesized that competition with the red imported fire ant, Solenopsis invicta, may be an important factor in the spread of crazy ants. We investigated the potential of interspecific competition among these two introduced ants by measuring interspecific aggression between Caribbean crazy ant workers and workers of Solenopsis invicta. Specifically, we examined the effect of body size and diet on individual-level aggressive interactions among crazy ant workers and fire ants. We found that differences in diet did not alter interactions between crazy ant workers from different nests, but carbohydrate level did play an important role in antagonistic interactions with fire ants: crazy ants on low sugar diets were more aggressive and less likely to be killed in aggressive encounters with fire ants. We found that large fire ants engaged in fewer fights with crazy ants than small fire ants, but fire ant size affected neither fire ant nor crazy ant mortality. Overall, crazy ants experienced higher mortality than fire ants after aggressive encounters. Our findings suggest that fire ant workers might outcompete crazy ant workers on an individual level, providing some biotic resistance to crazy ant range expansion. However, this resistance may be overcome by crazy ants that have a restricted sugar intake, which may occur when crazy ants are excluded from resources by fire ants

Facilitation and Competition among Invasive Plants: A Field Experiment with Alligatorweed and Water Hyacinth

Ecosystems that are heavily invaded by an exotic species often contain abundant populations of other invasive species. This may reflect shared responses to a common factor, but may also reflect positive interactions among these exotic species. Armand Bayou (Pasadena, TX) is one such ecosystem where multiple species of invasive aquatic plants are common. We used this system to investigate whether presence of one exotic species made subsequent invasions by other exotic species more likely, less likely, or if it had no effect. We performed an experiment in which we selectively removed exotic rooted and/or floating aquatic plant species and tracked subsequent colonization and growth of native and invasive species. This allowed us to quantify how presence or absence of one plant functional group influenced the likelihood of successful invasion by members of the other functional group. We found that presence of alligatorweed (rooted plant) decreased establishment of new water hyacinth (free-floating plant) patches but increased growth of hyacinth in established patches, with an overall net positive effect on success of water hyacinth. Water hyacinth presence had no effect on establishment of alligatorweed but decreased growth of existing alligatorweed patches, with an overall net negative effect on success of alligatorweed. Moreover, observational data showed positive correlations between hyacinth and alligatorweed with hyacinth, on average, more abundant. The negative effect of hyacinth on alligatorweed growth implies competition, not strong mutual facilitation (invasional meltdown), is occurring in this system. Removal of hyacinth may increase alligatorweed invasion through release from competition. However, removal of alligatorweed may have more complex effects on hyacinth patch dynamics because there were strong opposing effects on establishment versus growth. The mix of positive and negative interactions between floating and rooted aquatic plants may influence local population dynamics of each group and thus overall invasion pressure in this watershed