Stability of algebraically unstable dispersive flows

2016 ◽  
Vol 1 (7) ◽  
Author(s):  
Kristina R. King ◽  
Steven J. Weinstein ◽  
Paula M. Zaretzky ◽  
Michael Cromer ◽  
Nathaniel S. Barlow
Keyword(s):  
Dispersive Flows

Criteria for Dispersive Flows

1966 ◽  
Vol 32 (1-2) ◽  
pp. 89-93 ◽  
Author(s):  
Nam P. Bhatia
Keyword(s):  
Dispersive Flows

scholarly journals On the stability of waves in classically neutral flows

2020 ◽  
Vol 85 (2) ◽  
pp. 309-340
Author(s):  
Colin Huber ◽  
Meaghan Hoitt ◽  
Nathaniel S Barlow ◽  
Nicole Hill ◽  
Kimberlee Keithley ◽  
...  
Keyword(s):  
Stability Boundary ◽  
Fractional Power ◽  
Single Mode ◽  
Fourier Integral ◽  
Linear Stability Theory ◽  
System Response ◽  
Neutral Stability ◽  
Complex Frequency ◽  
The Stability ◽  
Dispersive Flows

Abstract This paper reports a breakdown in linear stability theory under conditions of neutral stability that is deduced by an examination of exponential modes of the form $h\approx{{e}^{i(kx-\omega t)}}$, where $h$ is a response to a disturbance, $k$ is a real wavenumber and $\omega (k)$ is a wavelength-dependent complex frequency. In a previous paper, King et al. (2016, Stability of algebraically unstable dispersive flows. Phys. Rev. Fluids, 1, 073604) demonstrates that when Im$[\omega (k)]=0$ for all $k$, it is possible for a system response to grow or damp algebraically as $h\approx{{t}^{s}}$ where $s$ is a fractional power. The growth is deduced through an asymptotic analysis of the Fourier integral that inherently invokes the superposition of an infinite number of modes. In this paper, the more typical case associated with the transition from stability to instability is examined in which Im$[\omega (k)]=0$ for a single mode (i.e. for one value of $k$) at neutral stability. Two partial differential equation systems are examined, one that has been constructed to elucidate key features of the stability threshold, and a second that models the well-studied problem of rectilinear Newtonian flow down an inclined plane. In both cases, algebraic growth/decay is deduced at the neutral stability boundary, and the propagation features of the responses are examined.

scholarly journals Generalized Mean Apparent Propagator MRI to Measure and Image Advective and Dispersive Flows in Medicine and Biology

2019 ◽  
Vol 38 (1) ◽  
pp. 11-20 ◽  
Author(s):  
Dan Benjamini ◽  
Michal E. Komlosh ◽  
Nathan H. Williamson ◽  
Peter J. Basser
Keyword(s):  
Generalized Mean ◽  
Dispersive Flows
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