Phys. Rev. D
 2016
DOI: 10.1103/physrevd.93.124060
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Scattering of gravity waves in subcritical flows over an obstacle

Scott Robertson
1
,
Florent Michel
2
,
Renaud Parentani
3

Abstract: We numerically study the scattering coefficients of linear water waves on stationary flows above a localized obstacle. We compare the scattering on trans-and subcritical flows, and then focus on the latter which have been used in recent analog gravity experiments. The main difference concerns the magnitude of the mode amplification: whereas transcritical flows display a large amplification (which is generally in good agreement with the Hawking prediction), this effect is heavily suppressed in subcritical flows… Show more

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Cited by 25 publications

(41 citation statements)
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“…We see that the general behavior of | β| 2 is linear in ω. This contrasts with the case of a transcritical flow, and agrees with the results of [16,18,35]. Before analyzing this behavior in more details, we construct the mode φ in u , schematically represented in Fig.…”
Section: General Resultssupporting
confidence: 83%
Exaggerated anticipatory anxiety is common in social anxiety disorder (SAD). Neuroimaging studies have revealed altered neural activity in response to social stimuli in SAD, but fewer studies have examined neural activity during anticipation of feared social stimuli in SAD. The current study examined the time course and magnitude of activity in threat processing brain regions during speech anticipation in socially anxious individuals and healthy controls (HC). Method Participants (SAD n = 58; HC n = 16) underwent functional magnetic resonance imaging (fMRI) during which they completed a 90s control anticipation task and 90s speech anticipation task.
show abstract
“…We see that the general behavior of | β| 2 is linear in ω. This contrasts with the case of a transcritical flow, and agrees with the results of [16,18,35]. Before analyzing this behavior in more details, we construct the mode φ in u , schematically represented in Fig.…”
Section: General Resultssupporting
confidence: 83%
Exaggerated anticipatory anxiety is common in social anxiety disorder (SAD). Neuroimaging studies have revealed altered neural activity in response to social stimuli in SAD, but fewer studies have examined neural activity during anticipation of feared social stimuli in SAD. The current study examined the time course and magnitude of activity in threat processing brain regions during speech anticipation in socially anxious individuals and healthy controls (HC). Method Participants (SAD n = 58; HC n = 16) underwent functional magnetic resonance imaging (fMRI) during which they completed a 90s control anticipation task and 90s speech anticipation task.
show abstract
“…[29] The problem studied can be further generalized for waves of arbitrary length taking into account the effect of dispersion. Similar works in this direction were published recently for relatively smooth current variation in the canal with the finite-length bottom obstacles [17,18]. It is worthwhile to notice that in the dispersive case for purely gravity waves there is always one wave of negative energy for which the flow is supercritical.…”
Section: Discussionsupporting
confidence: 74%
Exaggerated anticipatory anxiety is common in social anxiety disorder (SAD). Neuroimaging studies have revealed altered neural activity in response to social stimuli in SAD, but fewer studies have examined neural activity during anticipation of feared social stimuli in SAD. The current study examined the time course and magnitude of activity in threat processing brain regions during speech anticipation in socially anxious individuals and healthy controls (HC). Method Participants (SAD n = 58; HC n = 16) underwent functional magnetic resonance imaging (fMRI) during which they completed a 90s control anticipation task and 90s speech anticipation task.
show abstract
“…Clearly, the scattering coefficients do not diverge as the frequency cancels. Hence, the expected thermal spectrum for trans-critical flow is not observed, since the scattering coefficients vanish when the angular frequency goes to zero (in accordance with the numerical and theoretical predictions for subcritical flows [37][38][39][40][41][42][43]).…”
supporting
confidence: 83%
Exaggerated anticipatory anxiety is common in social anxiety disorder (SAD). Neuroimaging studies have revealed altered neural activity in response to social stimuli in SAD, but fewer studies have examined neural activity during anticipation of feared social stimuli in SAD. The current study examined the time course and magnitude of activity in threat processing brain regions during speech anticipation in socially anxious individuals and healthy controls (HC). Method Participants (SAD n = 58; HC n = 16) underwent functional magnetic resonance imaging (fMRI) during which they completed a 90s control anticipation task and 90s speech anticipation task.
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