skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.

Explore Research Products in the PAR
It may take a few hours for recently added research products to appear in PAR search results.


Title: Brief communication: A nonlinear self-similar solution to barotropic flow over varying topography
Beginning from the shallow water equations (SWEs), a nonlinear self-similar analytic solution is derived for barotropic flow over varying topography. We study conditions relevant to the ocean slope where the flow is dominated by Earth's rotation and topography. The solution is found to extend the topographic β-plume solution of Kuehl (2014) in two ways. (1) The solution is valid for intensifying jets. (2) The influence of nonlinear advection is included. The SWEs are scaled to the case of a topographically controlled jet, and then solved by introducing a similarity variable, η = cxnxyny. The nonlinear solution, valid for topographies h = h0 − αxy3, takes the form of the Lambert W-function for pseudo velocity. The linear solution, valid for topographies h = h0 − αxy−γ, takes the form of the error function for transport. Kuehl's results considered the case −1 ≤ γ < 1 which admits expanding jets, while the new result considers the case γ < −1 which admits intensifying jets and a nonlinear case with γ = −3.  more » « less
Award ID(s):
1823452
PAR ID:
10054378
Author(s) / Creator(s):
; ; ;
Date Published:
Journal Name:
Nonlinear Processes in Geophysics
Volume:
25
Issue:
1
ISSN:
1607-7946
Page Range / eLocation ID:
201 to 205
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. ; ; ; (, American Society of Mechanical Engineers)
    Abstract A newly developed nonlinear ultrasonic (NLU) technique called sideband band peak count-index (or SPC-I) measures the degree of nonlinearity associated with the inspected specimen – larger SPC-I values indicate higher nonlinearity. In various published papers, the SPC-I technique has shown its effectiveness and superiority in comparison to other techniques for nondestructive testing (NDT) and structural health monitoring (SHM) applications. In this work, the performance of SPC-I in non-homogeneous specimens having different topographies is investigated using peridynamics based periultrasound modeling. Three types of topographies – “X” topography, “Y” topography and “XY” topography are introduced by adding thin strips made up of a second material and thus converting the homogeneous plate into a heterogeneous structure. It is observed that “X” and “XY” topographies can help to hide the crack growth, thus making cracks undetectable to the nonlinear SPC-I based monitoring technique. In addition to the SPC-I technique, we investigate the applicability of the emerging method of topological acoustic sensing. This method monitors the changes in the geometric phase; a measure of the changes in linear or nonlinear wave’s spatial behavior during its propagation in plate structures having various topographies. The computed results show that the magnitudes of jumps in geometric phase change plots can be good indicators to distinguish cracks with different thicknesses although these cracks can remain hidden in some topographies during the single point inspection based on the nonlinear SPC-I based monitoring technique. 
    more » « less
  2. ; ; ; (, Ultrasonics)
    Some topographies in plate structures can hide cracks and make it difficult to monitor damage growth. This is because topographical features convert homogeneous structures to heterogeneous one and complicate the wave propagation through such structures. At certain points destructive interference between incident, reflected and transmitted elastic waves can make those points insensitive to the damage growth when adopting acoustics based structural health monitoring (SHM) techniques. A newly developed nonlinear ultrasonic (NLU) technique called sideband peak count – index (or SPC-I) has shown its effectiveness and superiority compared to other techniques for nondestructive testing (NDT) and SHM applications and is adopted in this work for monitoring damage growth in plate structures with topographical features. The performance of SPC-I technique in heterogeneous specimens having different topographies is investigated using nonlocal peridynamics based peri-ultrasound modeling. Three types of topographies – “X” topography, “Y” topography and “XY” topography are investigated. It is observed that “X” and “XY” topographies can help to hide the crack growth, thus making cracks undetectable when the SPC-I based monitoring technique is adopted. In addition to the SPC-I technique, we also investigate the effectiveness of an emerging sensing technique based on topological acoustic sensing. This method monitors the changes in the geometric phase; a measure of the changes in the acoustic wave’s spatial behavior. The computed results show that changes in the geometric phase can be exploited to monitor the damage growth in plate structures for all three topographies considered here. The significant changes in geometric phase can be related to the crack growth even when these cracks remain hidden for some topographies during the SPC-I based single point inspection. Sensitivities of both the SPC-I and the topological acoustic sensing techniques are also investigated for sensing the topographical changes in the plate structures. 
    more » « less
  3. ; ; ; ; ; ; ; ; ; ; et al (, EPJ Web of Conferences)
    Jentschel, M (Ed.)
    The nuclear structure of the98Zr nucleus was studied through theβ−decay of98Yg.s.at the TRIUMF-ISAC facility. The use of the 8π γ-ray spectrometer with its ancillary detectors SCEPTAR and PACES enabled γ-γ and γ-e−coincidence measurements as well as γ-γ angular correlations. The level spin assignments and transition mixing ratios obtained in this study were in good agreement with previous results. Furthermore, 12 previously unknown states in the low-energy region of98Zr were identified, including the 0+5and 0+6levels at 2418 and 2749 keV, respectively. The 2+and I=1 natures for multiple newly observed and previously known (but not firmly assigned) states have been established. Additionally, the previously assumed pureE2 character of the 2+2→ 2+1367.8-keV transition was confirmed. 
    more » « less
  4. ; ; ; (, Water Resources Research)
    Abstract The effective characterization of topographic surfaces is a central tenet of geomorphology. Differences in land surface properties reveal variations in structural controls and the nature and efficacy of Earth‐shaping processes. In this paper, we employ the Hölder exponents,α, characterizing the local scaling behavior of topography and commonly used in the study of the (multi)fractal properties of landscapes and show that the joint probability distribution of the area of the terrain with a given elevation andαcontains a wealth of information on topographic structure. The conditional distributions of the hypsometric integrals as a function ofα, that is,Ihyp|α, are shown to capture this structure. A multivariate analysis reveals three metrics that summarize these conditional distributions: Strahler's original hypsometric integral, the standard deviation of theIhyp|α, and the nature of any trend of theIhyp|αagainstα. An analysis of five digital elevation models (DEMs) from different regions of the United States shows that only one is truly described by the hypsometric integral (Mettman Ridge from central Oregon). In the other cases, the new metrics clearly discriminate between instances where topographic roughness is more clearly a function of elevation, as captured by the conditional variables. In a final example, we artificially sharpen the ridges and valleys of one DEM to show that while the hypsometric integral and standard deviation ofIhyp|αare invariant to the change, the trend ofIhyp|αagainstαcaptures the changes in topography. 
    more » « less
  5. ; ; (, Proteins: Structure, Function, and Bioinformatics)
    Abstract Structures at serine‐proline sites in proteins were analyzed using a combination of peptide synthesis with structural methods and bioinformatics analysis of the PDB. Dipeptides were synthesized with the proline derivative (2S,4S)‐(4‐iodophenyl)hydroxyproline [hyp(4‐I‐Ph)]. The crystal structure of Boc‐Ser‐hyp(4‐I‐Ph)‐OMe had two molecules in the unit cell. One molecule exhibitedcis‐proline and a type VIa2 β‐turn (BcisD). Thecis‐proline conformation was stabilized by a C–H/O interaction between Pro C–Hαand the Ser side‐chain oxygen. NMR data were consistent with stabilization ofcis‐proline by a C–H/O interaction in solution. The other crystallographically observed molecule hadtrans‐Pro and both residues in the PPII conformation. Two conformations were observed in the crystal structure of Ac‐Ser‐hyp(4‐I‐Ph)‐OMe, with Ser adopting PPII in one and the β conformation in the other, each with Pro in the δ conformation andtrans‐Pro. Structures at Ser‐Pro sequences were further examined via bioinformatics analysis of the PDB and via DFT calculations. Ser‐Pro versus Ala–Pro sequences were compared to identify bases for Ser stabilization of local structures. C–H/O interactions between the Ser side‐chain Oγand Pro C–Hαwere observed in 45% of structures with Ser‐cis‐Pro in the PDB, with nearly all Ser‐cis‐Pro structures adopting a type VI β‐turn. 53% of Ser‐trans‐Pro sequences exhibited main‐chain COi•••HNi+3or COi•••HNi+4hydrogen bonds, with Ser as theiresidue and Pro as thei + 1 residue. These structures were overwhelmingly either type I β‐turns or N‐terminal capping motifs on α‐helices or 310‐helices. These results indicate that Ser‐Pro sequences are particularly potent in favoring these structures. In each, Ser is in either the PPII or β conformation, with the Ser Oγcapable of engaging in a hydrogen bond with the amide N–H of thei + 2 (type I β‐turn or 310‐helix; Serχ1t) ori + 3 (α‐helix; Serχ1g+) residue. Non‐prolinecisamide bonds can also be stabilized by C–H/O interactions. 
    more » « less
  • Citation Formats
  • MLA
  • APA
  • Chicago
  • BibTeX
  • Save / Share this Record
  • Send to Email