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94 records · Page 6

The Evolution of Finite Amplitude Wavetrains in Plane Channel Flow

We consider a viscous incompressible fluid flow driven between two parallel plates by a constant pressure gradient. The flow is at a finite Reynolds number, with an 0(l) disturbance in the form of a traveling wave. A phase equation approach is used to discuss the evolution of slowly varying fully nonlinear two dimensional wavetrains. We consider uniform wavetrains in detail, showing that the development of a wavenumber perturbation is governed by Burgers equation in most cases. The wavenumber perturbation theory, constructed using the phase equation approach for a uniform wavetrain, is shown to be distinct from an amplitude perturbation expansion about the periodic flow. In fact we show that the amplitude equation contains only linear terms and is simply the heat equation. We review, briefly, the well known dynamics of Burgers equation, which imply that both shock structures and finite time singularities of the wavenumber perturbation can occur with respect to the slow scales. Numerical computations have been performed to identify areas of the (wavenumber, Reynolds number, energy) neutral surface for which each of these possibilities can occur. We note that the evolution equations will breakdown under certain circumstances, in particular for a weakly nonlinear secondary flow. Finally we extend the theory to three dimensions and discuss the limit of a weak spanwise dependence for uniform wavetrains, showing that two functions are required to describe the evolution. These unknowns are a phase and a pressure function which satisfy a pair of linearly coupled partial differential equations. The results obtained from applying the same analysis to the fully three dimensional problem are included as an appendix.

Hewitt, R. E.↗

A New Formulation of Time Domain Boundary Integral Equation for Acoustic Wave Scattering in the Presence of a Uniform Mean Flow

It has been well-known that under the assumption of a constant uniform mean flow, the acoustic wave propagation equation can be formulated as a boundary integral equation, in both the time domain and the frequency domain. Compared with solving partial differential equations, numerical methods based on the boundary integral equation have the advantage of a reduced spatial dimension and, hence, requiring only a surface mesh. However, the constant uniform mean flow assumption, while convenient for formulating the integral equation, does not satisfy the solid wall boundary condition wherever the body surface is not aligned with the uniform mean flow. In this paper, we argue that the proper boundary condition for the acoustic wave should not have its normal velocity be zero everywhere on the solid surfaces, as has been applied in the literature. A careful study of the acoustic energy conservation equation is presented that shows such a boundary condition in fact leads to erroneous source or sink points on solid surfaces not aligned with the mean flow. A new solid wall boundary condition is proposed that conserves the acoustic energy and a new time domain boundary integral equation is derived. In addition to conserving the acoustic energy, another significant advantage of the new equation is that it is considerably simpler than previous formulations. In particular, tangential derivatives of the solution on the solid surfaces are no longer needed in the new formulation, which greatly simplifies numerical implementation. Furthermore, stabilization of the new integral equation by Burton-Miller type reformulation is presented. The stability of the new formulation is studied theoretically as well as numerically by an eigenvalue analysis. Numerical solutions are also presented that demonstrate the stability of the new formulation.

Hu, Fang↗

Introduction: Photons and Ground-Based

A Conference on Measurement Techniques for Solar and Space Physics was held on 20-24 April 2015 in Boulder, Colorado, at the National Center for Atmospheric Research Center Green Campus. The present volume collects together the conference papers for photons and ground-based categories. This gathering of over 200 scientists and instrumentalists was born out of the desire to collect in one place the latest experiment and instrument technologies required for advancement of scientific knowledge in the disciplines of solar and space physics. The two goals for this conference and the subsequent publication of its content are (a) to describe measurement techniques and technology development needed to advance high priority science in the fields of solar and space physics; and (b) to provide a survey or reference of techniques for in situ measurement and remote sensing of space plasmas. Towards this end, our goal has always been inspired by the two 1998 Geophysical Monographs (Nos. 102 and 103) entitled, "Measurement Techniques in Space Plasmas" (particles and fields) [Pfaff et al., 1998a, 1998b], which have served as a reference and resource for advanced students, engineers, and scientists who wish to learn the fundamentals of measurement techniques and technology in this field. Those monographs were the product of an American Geophysical Union Chapman Conference that took place in Santa Fe, NM, in 1995: "Measurement Techniques in Space Plasmas-What Works, What Doesn't." Two decades later, we believe that it is appropriate to revisit this subject, in light of recent advances in technology, research platforms, and analysis techniques. Moreover, we now include direct measurements of neutral gases in the upper atmosphere, optical imaging techniques, and remote observations in space and on the ground. Accordingly, the workshop was organized among four areas of measurement techniques: particles, fields, photons, and ground-based. This two-set volume is largely composed of the content of that workshop. Special attention is given to those techniques and technologies that demonstrate promise of significant advancement in measurements that will enable the highest priority science as described in the 2012 National Research Council Decadal Survey [Baker and Zurbuchen et al., 2013]. Additionally, a broad tutorial survey of the current technologies is provided to serve as reference material and as a basis from which advanced and innovative ideas can be discussed and pursued. Included are instrumentation and techniques to observe the solar environment from its interior to its outer atmosphere, the heliosphere out to the interstellar regions, in geospace, and other planetary magnetospheres and atmospheres. To make significant progress in priority science as expressed in the National Research Council solar and space physics decadal survey and recent NASA Heliophysics roadmaps, identification of enabling new measurement techniques and technologies to be developed is required. Also, it is valuable to the community and future scientists and engineers to have a complete survey of the techniques and technologies used by the practitioners of solar and space physics. As with the 1995 conference and subsequent 1998 publication, it is incumbent on the community to identify those measurements that are particularly challenging and still require new techniques to be identified and tested to enable the necessary accuracy and resolution of certain parameters to be achieved. The following is a partial list of the measurement technique categories that are featured in these special publications: Particles; Thermal plasma to MeV energetic particles, neutral gas properties including winds, density, temperature, and composition, and enhanced neutral atom imaging; Fields; DC electric and magnetic fields, plasma waves, and electron drift instruments from which the plasma velocity information provides a measure of the DC electric field; Photons; Instruments sensitive from the near-infrared to X-rays; Contributions of techniques and technology for optical design, optical components, sensors, material selection for cameras, telescopes, and spectrographs; Ground based; Remote sensing methods for solar and geospace activity and space weather. The focus includes solar observatories, all-sky cameras, lidars, and ionosphere thermosphere mesosphere observatory systems such as radars, ionosondes, GPS receivers, magnetometers, conjugate observations, and airborne campaigns. The present volume collects together the papers for photons and ground-based categories. The companion volume collects together the papers for particles and fields categories. It is recognized that there are measurement techniques that overlap among the four categories. For example, use of microchannel plate detectors is used in photon and particle measurement techniques or the observation of visible photons and magnetic fields in space and on the ground share common technologies. Therefore, the reader should consider the entire collection of papers as they seek to understand particular applications. We hope that these volumes will be as valuable as a reference for our community as the earlier 1998 volumes have been.

Spann, James↗

Consequences of Different Air-Sea Feedbacks on Ocean Using MITgcm and MERRA-2 Forcing: Implications for Coupled Data Assimilation Systems

Ocean surface flux estimates from atmospheric and oceanic reanalyses contain errors that compensate for inaccuracies in the respective atmosphere and ocean models used to generate these reanalyses. A conundrum for climate studies is the discrepancy between surface fluxes that minimize model-data differences for an atmosphere-only model vs surface fluxes that minimize model-data differences for an ocean model. As a first step towards a consistent coupled ocean-atmosphere data-assimilation (DA) system, we compare surface net heat flux from a state-of-the-art atmospheric reanalysis, the Modern-Era Retrospective analysis for Research and Applications, Version 2 (MERRA-2), to net heat flux from a state-of-the-art ocean state estimate, the Estimating the Circulation and Climate of the Ocean Version 4 (ECCO-v4). The possible impacts of the MERRA-2 and ECCO-v4 air-sea net heat flux difference in a coupled DA system were assessed using a set of experiments designed to imitate different “flavors” of a coupled DA system in an ocean-only setup. This was done by forcing the ECCO-v4 underlying ocean model - the Massachusetts Institute of Technology general circulation model (MITgcm) - with different sets of MERRA-2 fields and utilizing different forcing methods. By doing so we were able to turn off different air-sea feedbacks which, in a coupled DA setup, are partially muted by the constraining observations. The set of experiments, therefore, represents a range of active feedbacks in different “flavors” of coupled data-assimilation systems. For the period 1992–2011, MERRA-2 net heat flux has a global mean difference of -4.9 Wm(exp -2) relative to ECCO-v4. When MERRA-2 surface fields are used to force MITgcm, imbalances in the energy and the hydrological cycles of MERRA-2, which are directly related to the fact that MERRA-2 was created without an interactive ocean, propagate to the ocean. The experiment in which MITgcm is forced with MERRA-2 fluxes (MERRA-2-flux experiment) results in a 2.5°C global mean Sea Surface Temperature (SST) cooling, a 1m reduction in global mean sea level, and other drastic changes in the large scale ocean circulation relative to those resulting when the MITgcm is forced with the optimized ECCO-v4 net heat flux (the ECCO-v4 experiment itself). When MITgcm is forced with MERRA-2 state variables (MERRA-2-state experiment), the SST is somewhat restored to the observed SST, but the errors are shifted to the water cycle, resulting in a global mean sea level increase of 2.7 m. To further explore the pros and cons of these two approaches, we introduce a new intermediate forcing method in which the ocean is forced with turbulent fluxes but has a long wave feedback. This method, unlike MERRA-2 state, preserves the MERRA-2 water and salinity cycles, and it reduces the SST error compared to the MERRA-2-flux experiment, but the SST is not as good as that in the MERRA-2-state experiment. Our results have implications for ocean-model forcing recipes and clearly reveal the undesirable consequences of limiting the feedbacks in either these types of experiments or in coupled DA.

Ehud Strobach↗