Nonparallel stability of three-dimensional compressible boundary layers. Part 1: Stability analysis

A compressible linear stability theory is presented for nonparallel three-dimensional boundary-layer flows, taking into account the normal velocity component as well as the streamwise and spanwise variations of the basic flow. The method of multiple scales is used to account for the nonparallelism of the basic flow, and equations are derived for the spatial evolution of the disturbance amplitude and wavenumber. The numerical procedure for obtaining the solution of the nonparallel problem is outlined

Spatial three-dimensional secondary instability compressible boundary-layer flows

Three-dimensional linear secondary instability theory is extended for compressible and high Mach number boundary layer flows. The small but finite amplitude compressible Tollmien-Schlichting wave effect on the growth of 3-D perturbations is investigated. The focus is on principal parametric resonance responsible for the strong growth of subharmonic in low disturbance environment. The effect of increasing Mach number on the onset, growth, the shape of eigenfunctions of the subharmonic is assessed, and the resulting vortical structure is examined

Secondary three-dimensional instability in compressible boundary layers

Three dimensional linear secondary instability theory is extended for compressible boundary layers on a flat plate in the presence of finite amplitude Tollmien-Schlichting waves. The focus is on principal parametric resonance responsible for strong growth of subharmonics in low disturbance environment

Effect of Suction on Controlling the Secondary Instability of Boundary Layers

The effect of suction on controlling the 3-D secondary instability is investigated for a boundary layer with pressure gradient in the presence of small but finite amplitude Tollmien-Schlichting wave. The focus is on principal parametric resonance responsible for strong growth of subharmonics in low disturbance environment. Calculations are presented for the effect of suction on the onset and amplification of the secondary instability in Blasius and Falkner-Skan flows, as well as its effect on controlling the production of the vortical structure

Foraging as an evidence accumulation process

A canonical foraging task is the patch-leaving problem, in which a forager must decide to leave a current resource in search for another. Theoretical work has derived optimal strategies for when to leave a patch, and experiments have tested for conditions where animals do or do not follow an optimal strategy. Nevertheless, models of patch-leaving decisions do not consider the imperfect and noisy sampling process through which an animal gathers information, and how this process is constrained by neurobiological mechanisms. In this theoretical study, we formulate an evidence accumulation model of patch-leaving decisions where the animal averages over noisy measurements to estimate the state of the current patch and the overall environment. Evidence accumulation models belong to the class of drift diffusion processes and have been used to model decision making in different contexts. We solve the model for conditions where foraging decisions are optimal and equivalent to the marginal value theorem, and perform simulations to analyze deviations from optimal when these conditions are not met. By adjusting the drift rate and decision threshold, the model can represent different strategies, for example an increment-decrement or counting strategy. These strategies yield identical decisions in the limiting case but differ in how patch residence times adapt when the foraging environment is uncertain. To account for sub-optimal decisions, we introduce an energy-dependent utility function that predicts longer than optimal patch residence times when food is plentiful. Our model provides a quantitative connection between ecological models of foraging behavior and evidence accumulation models of decision making. Moreover, it provides a theoretical framework for potential experiments which seek to identify neural circuits underlying patch leaving decisions

Mechanical Surface Waves Accompany Action Potential Propagation

Many studies have shown that a mechanical displacement of the axonal membrane accompanies the electrical pulse defining the Action Potential (AP). Despite a large and diverse body of experimental evidence, there is no theoretical consensus either for the physical basis of this mechanical wave nor its interdependence with the electrical signal. In this manuscript we present a model for these mechanical displacements as arising from the driving of surface wave modes in which potential energy is stored in elastic properties of the neuronal membrane and cytoskeleton while kinetic energy is carried by the axoplasmic fluid. In our model these surface waves are driven by the traveling wave of electrical depolarization that characterizes the AP, altering the compressive electrostatic forces across the membrane as it passes. This driving leads to co-propagating mechanical displacements, which we term Action Waves (AWs). Our model for these AWs allows us to predict, in terms of elastic constants, axon radius and axoplasmic density and viscosity, the shape of the AW that should accompany any traveling wave of voltage, including the AP predicted by the Hodgkin and Huxley (HH) equations. We show that our model makes predictions that are in agreement with results in experimental systems including the garfish olfactory nerve and the squid giant axon. We expect our model to serve as a framework for understanding the physical origins and possible functional roles of these AWs in neurobiology.Comment: 6 pages 3 figures + 2 page supplemen

Goertler instability in compressible boundary layers along curved surfaces with suction and cooling

The Goertler instability of the laminar compressible boundary layer flows along concave surfaces is investigated. The linearized disturbance equations for the three-dimensional, counter-rotating streamwise vortices in two-dimensional boundary layers are presented in an orthogonal curvilinear coordinate. The basic approximation of the disturbance equations, that includes the effect of the growth of the boundary layer, is considered and solved numerically. The effect of compressibility on critical stability limits, growth rates, and amplitude ratios of the vortices is evaluated for a range of Mach numbers for 0 to 5. The effect of wall cooling and suction of the boundary layer on the development of Goertler vortices is investigated for different Mach numbers

Nonparallel stability of two-dimensional nonuniformly heated boundary-layer flows

An analysis is presented for the linear stability of water boundary-layer flows over nonuniformly flat plates. Included in the analysis are disturbances due to velocity, pressure, temperatures, density, and transport properties as well as variations of the liquid properties with temperature. The method of multiple scales is used to account for the nonparallelism of the mean flow. In contrast with previous analyses, the nonsimilarity of the mean flow is taken into account. No analysis agrees, even qualitatively, with the experimental data when similar profiles are used. However, both the parallel and nonparallel results qualitatively agree with the experimental results of Strazisar and Reshotko when nonsimilar profiles are used