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

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

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

Simulation of Drosophila Circadian Oscillations, Mutations, and Light Responses by a Model with VRI, PDP-1, and CLK

A model of Drosophila circadian rhythm generation was developed to represent feedback loops based on transcriptional regulation of per, Clk (dclock), Pdp-1, and vri (vrille). The model postulates that histone acetylation kinetics make transcriptional activation a nonlinear function of [CLK]. Such a nonlinearity is essential to simulate robust circadian oscillations of transcription in our model and in previous models. Simulations suggest two positive feedback loops involving Clk are not essential for oscillations, because oscillations of [PER] were preserved when Clk, vri, or Pdp-1 expression was fixed. Eliminating the negative feedback loop in which PER represses per expression abolished oscillations. Simulations of per or Clk null mutations and of vri, Clk, or Pdp-1 heterozygous null mutations altered model behavior in ways similar to experimental data. The model simulated a photic phase-response curve resembling experimental curves, and oscillations entrained to simulated light-dark cycles. The model makes experimental predictions, some of which could be tested in transgenic Drosophila.Comment: Accepted to Biophysical Journal, 1/16/04. Single PDF file, 7 figures at en

The multiple faces of self-assembled lipidic systems

Lipids, the building blocks of cells, common to every living organisms, have the propensity to self-assemble into well-defined structures over short and long-range spatial scales. The driving forces have their roots mainly in the hydrophobic effect and electrostatic interactions. Membranes in lamellar phase are ubiquitous in cellular compartments and can phase-separate upon mixing lipids in different liquid-crystalline states. Hexagonal phases and especially cubic phases can be synthesized and observed in vivo as well. Membrane often closes up into a vesicle whose shape is determined by the interplay of curvature, area difference elasticity and line tension energies, and can adopt the form of a sphere, a tube, a prolate, a starfish and many more. Complexes made of lipids and polyelectrolytes or inorganic materials exhibit a rich diversity of structural morphologies due to additional interactions which become increasingly hard to track without the aid of suitable computer models. From the plasma membrane of archaebacteria to gene delivery, self-assembled lipidic systems have left their mark in cell biology and nanobiotechnology; however, the underlying physics is yet to be fully unraveled

Sharing and community curation of mass spectrometry data with Global Natural Products Social Molecular Networking

The potential of the diverse chemistries present in natural products (NP) for biotechnology and medicine remains untapped because NP databases are not searchable with raw data and the NP community has no way to share data other than in published papers. Although mass spectrometry techniques are well-suited to high-throughput characterization of natural products, there is a pressing need for an infrastructure to enable sharing and curation of data. We present Global Natural Products Social molecular networking (GNPS, http://gnps.ucsd.edu), an open-access knowledge base for community wide organization and sharing of raw, processed or identified tandem mass (MS/MS) spectrometry data. In GNPS crowdsourced curation of freely available community-wide reference MS libraries will underpin improved annotations. Data-driven social-networking should facilitate identification of spectra and foster collaborations. We also introduce the concept of ‘living data’ through continuous reanalysis of deposited data

Senior Recitals

Senior recital presented at the UNT College of Music Voertman Hall in partial fulfillment of the Bachelor of Music (BM) degree