Steady Radiating Gravity waves: An Exponential Asymptotics Approach
Name
42286_2023_Article_81.pdf
Size
812.09 KB
Format
Adobe PDF
Checksum (MD5)
7c5bfd0fc64e65e13830c591f3a4686a
Author(s)
Kataoka, Takeshi
Akylas, Triantaphyllos R.
Date Issued
January 15, 2024
Journal
Water Waves
Publisher
Springer International Publishing
Citation
Kataoka, T., Akylas, T.R. Steady Radiating Gravity waves: An Exponential Asymptotics Approach. Water Waves (2024).
Version
Final published version
Abstract
The radiation of steady surface gravity waves by a uniform stream
$$U_{0}$$
U
0
over locally confined (width
$$L$$
L
) smooth topography is analyzed based on potential flow theory. The linear solution to this classical problem is readily found by Fourier transforms, and the nonlinear response has been studied extensively by numerical methods. Here, an asymptotic analysis is made for subcritical flow
$$D/\lambda > 1$$
D
/
λ
>
1
in the low-Froude-number (
$$F^{2} \equiv \lambda /L \ll 1$$
F
2
≡
λ
/
L
≪
1
) limit, where
$$\lambda = U_{0}^{2} /g$$
λ
=
U
0
2
/
g
is the lengthscale of radiating gravity waves and
$$D$$
D
is the uniform water depth. In this regime, the downstream wave amplitude, although formally exponentially small with respect to
$$F$$
F
, is determined by a fully nonlinear mechanism even for small topography amplitude. It is argued that this mechanism controls the wave response for a broad range of flow conditions, in contrast to linear theory which has very limited validity.
MIT Department
Massachusetts Institute of Technology. Department of Mechanical Engineering
Terms of Use
Creative Commons Attribution
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1007/s42286-023-00081-z
