Optimal transient growth in thin-interface internal solitary waves

The dynamics of perturbations to large-amplitude Internal Solitary Waves (ISW) in two-layered flows with thin interfaces is analyzed by means of linear optimal transient growth methods. Optimal perturbations are computed through direct-adjoint iterations of the Navier-Stokes equations linearized around inviscid, steady ISWs obtained from the Dubreil-Jacotin-Long (DJL) equation. Optimal perturbations are found as a function of the ISW phase velocity $c$ (alternatively amplitude) for one representative stratification. These disturbances are found to be localized wave-like packets that originate just upstream of the ISW self-induced zone (for large enough $c$) of potentially unstable Richardson number, $Ri < 0.25$. They propagate through the base wave as coherent packets whose total energy gain increases rapidly with $c$. The optimal disturbances are also shown to be relevant to DJL solitary waves that have been modified by viscosity representative of laboratory experiments. The optimal disturbances are compared to the local WKB approximation for spatially growing Kelvin-Helmholtz (K-H) waves through the $Ri < 0.25$ zone. The WKB approach is able to capture properties (e.g., carrier frequency, wavenumber and energy gain) of the optimal disturbances except for an initial phase of non-normal growth due to the Orr mechanism. The non-normal growth can be a substantial portion of the total gain, especially for ISWs that are weakly unstable to K-H waves. The linear evolution of Gaussian packets of linear free waves with the same carrier frequency as the optimal disturbances is shown to result in less energy gain than found for either the optimal perturbations or the WKB approximation due to non-normal effects that cause absorption of disturbance energy into the leading face of the wave.Comment: 33 pages, 22 figure

Chandra Observation of the Radio Source / X-ray Gas Interaction in the Cooling Flow Cluster Abell 2052

We present a Chandra observation of Abell 2052, a cooling flow cluster with a central cD that hosts the complex radio source 3C 317. The data reveal ``holes'' in the X-ray emission that are coincident with the radio lobes. The holes are surrounded by bright ``shells'' of X-ray emission. The data are consistent with the radio source displacing and compressing, and at the same time being confined by, the X-ray gas. The compression of the X-ray shells appears to have been relatively gentle and, at most, slightly transonic. The pressure in the X-ray gas (the shells and surrounding cooler gas) is approximately an order of magnitude higher than the minimum pressure derived for the radio source, suggesting that an additional source of pressure is needed to support the radio plasma. The compression of the X-ray shells has speeded up the cooling of the shells, and optical emission line filaments are found coincident with the brightest regions of the shells.Comment: accepted for publication in ApJ Letters; for high-resolution color figures, see http://www.astro.virginia.edu/~elb6n/abell2052.htm

A model for large-amplitude internal solitary waves with trapped cores

© The Authors, 2010. This article is distributed under the terms of the Creative Commons Attribution 3.0 License. The definitive version was published in Nonlinear Processes in Geophysics 17 (2010): 303-318, doi:10.5194/npg-17-303-2010.Large-amplitude internal solitary waves in continuously stratified systems can be found by solution of the Dubreil-Jacotin-Long (DJL) equation. For finite ambient density gradients at the surface (bottom) for waves of depression (elevation) these solutions may develop recirculating cores for wave speeds above a critical value. As typically modeled, these recirculating cores contain densities outside the ambient range, may be statically unstable, and thus are physically questionable. To address these issues the problem for trapped-core solitary waves is reformulated. A finite core of homogeneous density and velocity, but unknown shape, is assumed. The core density is arbitrary, but generally set equal to the ambient density on the streamline bounding the core. The flow outside the core satisfies the DJL equation. The flow in the core is given by a vorticity-streamfunction relation that may be arbitrarily specified. For simplicity, the simplest choice of a stagnant, zero vorticity core in the frame of the wave is assumed. A pressure matching condition is imposed along the core boundary. Simultaneous numerical solution of the DJL equation and the core condition gives the exterior flow and the core shape. Numerical solutions of time-dependent non-hydrostatic equations initiated with the new stagnant-core DJL solutions show that for the ambient stratification considered, the waves are stable up to a critical amplitude above which shear instability destroys the initial wave. Steadily propagating trapped-core waves formed by lock-release initial conditions also agree well with the theoretical wave properties despite the presence of a "leaky" core region that contains vorticity of opposite sign from the ambient flow.This work is supported as part of the Office of Naval Research NLIWI and IWISE program grants N00014-06-1- 0798 and N00014-09-1-0227

A vortex-based model of velocity and shear stress in a partially vegetated shallow channel

Author Posting. © American Geophysical Union, 2008. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Water Resources Research 44 (2008): W01412, doi:10.1029/2006WR005651.This paper presents a method for predicting the distributions of velocity and shear stress in shallow channels with a boundary of emergent vegetation. Experiments in a laboratory channel with model vegetation show that the velocity profile exhibits a distinct two-layer structure, consisting of a rapidly varying shear layer across the vegetation interface and a more gradual boundary layer in the main channel. In addition, coherent vortices are observed which span both layers, and are the dominant contributors to lateral momentum fluxes. From these observations, we propose a model for the vortex-induced exchange and find expressions for the width of momentum penetration into the vegetation, the velocity and shear stress at the vegetation edge, and the width of the boundary layer in the main channel. These variables, along with a momentum balance in the main channel, comprise a modeling framework which accurately reproduces the observed velocity and shear stress distributions. The predictions for the velocity and shear stress can provide a basis for modeling flood conveyance, overbank sediment transport, and scalar residence time in the vegetated layer.This material is based upon work supported by the National Science Foundation under grant 0125056

Theories of developmental dyslexia: Insights from a multiple case study of dyslexic adults

A multiple case study was conducted in order to assess three leading theories of developmental dyslexia: the phonological, the magnocellular (auditory and visual) and the cerebellar theories. Sixteen dyslexic and 16 control university students were administered a full battery of psychometric, phonological, auditory, visual and cerebellar tests. Individual data reveal that all 16 dyslexics suffer from a phonological deficit, 10 from an auditory deficit, 4 from a motor deficit, and 2 from a visual magnocellular deficit. Results suggest that a phonological deficit can appear in the absence of any other sensory or motor disorder, and is sufficient to cause a literacy impairment, as demonstrated by 5 of the dyslexics. Auditory disorders, when present, aggravate the phonological deficit, hence the literacy impairment. However, auditory deficits cannot be characterised simply as rapid auditory processing problems, as would be predicted by the magnocellular theory. Nor are they restricted to speech. Contrary to the cerebellar theory, we find little support for the notion that motor impairments, when found, have a cerebellar origin, or reflect an automaticity deficit. Overall, the present data support the phonological theory of dyslexia, while acknowledging the presence of additional sensory and motor disorders in certain individuals

Shear instability and coherent structures in shallow flow adjacent to a porous layer

Author Posting. © Cambridge University Press, 2007. This article is posted here by permission of Cambridge University Press for personal use, not for redistribution. The definitive version was published in Journal of Fluid Mechanics 593 (2007): 1-32, doi:10.1017/S0022112007008415.Results are presented from an experimental study of shallow flow in a channel partially obstructed by an array of circular cylinders. The cylinder array is a model for emergent vegetation in an open channel, but also represents a simple sparse porous medium. A shear layer with regular vortex structures forms at the edge of the array, evolving downstream to an equilibrium width and vortex size. The vortices induce nearly periodic oscillations with a frequency that matches the most unstable linear mode for a parallel shear flow. The shear layer is asymmetric about the array interface and has a two-layer structure. An inner region of maximum shear near the interface contains a velocity inflection point and establishes the penetration of momentum into the array. An outer region, resembling a boundary layer, forms in the main channel, and establishes the scale of the vortices. The vortex structure, educed by conditional sampling, shows strong crossflows with sweeps from the main channel and ejections from the array, which create significant momentum and mass fluxes across the interface. The sweeps maintain the coherent structures by enhancing shear and energy production at the interface. A linear stability analysis is consistent with the experimental results and demonstrates that the instability is excited by the differential drag between the channel and the array.This material is based upon work supported by the National Science Foundation under Grant 0125056

Gravity currents and internal waves in a stratified fluid

Author Posting. © Cambridge University Press, 2008. This article is posted here by permission of Cambridge University Press for personal use, not for redistribution. The definitive version was published in Journal of Fluid Mechanics 616 (2008): 327-356, doi:10.1017/S0022112008003984.A steady theory is presented for gravity currents propagating with constant speed into a stratified fluid with a general density profile. Solution curves for front speed versus height have an energy-conserving upper bound (the conjugate state) and a lower bound marked by the onset of upstream influence. The conjugate state is the largest-amplitude nonlinear internal wave supported by the ambient stratification, and in the limit of weak stratification approaches Benjamin's energy-conserving gravity current solution. When the front speed becomes critical with respect to linear long waves generated above the current, steady solutions cannot be calculated, implying upstream influence. For non-uniform stratification, the critical long-wave speed exceeds the ambient long-wave speed, and the critical-Froude-number condition appropriate for uniform stratification must be generalized. The theoretical results demonstrate a clear connection between internal waves and gravity currents. The steady theory is also compared with non-hydrostatic numerical solutions of the full lock release initial-value problem. Some solutions resemble classic gravity currents with no upstream disturbance, but others show long internal waves propagating ahead of the gravity current. Wave generation generally occurs when the stratification and current speed are such that the steady gravity current theory fails. Thus the steady theory is consistent with the occurrence of either wave-generating or steady gravity solutions to the dam-break problem. When the available potential energy of the dam is large enough, the numerical simulations approach the energy-conserving conjugate state. Existing laboratory experiments for intrusions and gravity currents produced by full-depth lock exchange flows over a range of stratification profiles show excellent agreement with the conjugate state solutions.K. R. H. was supported by ONR grant N00014061079

Humanism in the Age of COVID-19: Renewing Focus on Communication and Compassion

The global COVID-19 pandemic has become one of the largest clinical and operational challenges faced by emergency medicine, and our EDs continue to see increased volumes of infected patients, many of whom are not only ill, but acutely aware and fearful of their circumstances and potential mortality. Given this, there may be no more important time to focus on staff-patient communication and expression of compassion.However, many of the techniques usually employed by emergency clinicians to provide comfort to patients and their families are made more challenging or impossible by the current circumstances. Geriatric ED patients, who are at increased risk of severe disease, are particularly vulnerable to the effects of isolation.Despite many challenges, emergency clinicians have at their disposal a myriad of tools that can still be used to express compassion and empathy to their patients. Placing emphasis on using these techniques to maximize humanism in the care of COVID-19 patients during this crisis has the potential to bring improvements to ED patient care well after this pandemic has passed