scholarly journals Wave Emission From Bottom Vibrations in Subsurface Open-channel Shear Flow

Water Waves ◽  
2020 ◽  
Vol 2 (2) ◽  
pp. 415-432
Author(s):  
Peder A. Tyvand ◽  
Eivind B. Sveen
Keyword(s):  
Shear Flow ◽  
Open Channel ◽  
Surface Velocity ◽  
Wave Number ◽  
Wave Radiation ◽  
Radiation Problem ◽  
Upstream Direction ◽  
Wave Emission ◽  
Hydrostatic Limit ◽  
Radiation Conditions

Abstract The linearized water-wave radiation problem for a 2D oscillating bottom source in an inviscid shear flow with a free surface is investigated analytically. The fluid depth is constant. The velocity of the basic flow varies linearly with depth (uniform vorticity), with zero surface velocity. The far-field surface waves radiated out from the 2D source are calculated, based on Euler’s equation of motion with the application of radiation conditions. There are always two waves, one emitted in the upstream direction and the other in the downstream direction. The energy fluxes of these two waves are calculated. The hydrostatic limit of zero wave number is related to the theory of undular bores.

scholarly journals Oscillating line source in a shear flow with a free surface: critical layer-like contributions

2016 ◽  
Vol 798 ◽  
pp. 201-231 ◽  
Author(s):  
Simen Å. Ellingsen ◽  
Peder A. Tyvand
Keyword(s):  
Free Surface ◽  
Shear Flow ◽  
Line Source ◽  
Fluid Velocity ◽  
Wave Pattern ◽  
Critical Layer ◽  
Surface Velocity ◽  
Wave Radiation ◽  
Closed Curves ◽  
Surface Manifestation

The linearized water wave radiation problem for an oscillating submerged line source in an inviscid shear flow with a free surface is investigated analytically at finite, constant depth in the presence of a shear flow varying linearly with depth. The surface velocity is taken to be zero relative to the oscillating source, so that Doppler effects are absent. The radiated wave out from the source is calculated based on Euler’s equation of motion with the appropriate boundary and radiation conditions, and differs substantially from the solution obtained by assuming potential flow. To wit, an additional wave is found in the downstream direction in addition to the previously known dispersive wave solutions; this wave is non-dispersive and we show how it is the surface manifestation of a critical layer-like flow generated by the combination of shear and mass flux at the source, passively advected with the flow. As seen from a system moving at the fluid velocity at the source’s depth, streamlines form closed curves in a manner similar to Kelvin’s cat’s eye vortices. A resonant frequency exists at which the critical wave resonates with the downstream propagating wave, resulting in a downstream wave pattern diverging linearly in amplitude away from the source.

scholarly journals Waves from an oscillating point source with a free surface in the presence of a shear current

2016 ◽  
Vol 798 ◽  
pp. 232-255 ◽  
Author(s):  
Simen Å. Ellingsen ◽  
Peder A. Tyvand
Keyword(s):  
Free Surface ◽  
Shear Flow ◽  
Point Source ◽  
Wave Field ◽  
Froude Number ◽  
Critical Layer ◽  
Surface Velocity ◽  
Wave Radiation ◽  
Gravitational Acceleration ◽  
Regular Waves

We investigate analytically the linearised water wave radiation problem for an oscillating submerged point source in an inviscid shear flow with a free surface. A constant depth is taken into account and the shear flow increases linearly with depth. The surface velocity relative to the source is taken to be zero, so that Doppler effects are absent. We solve the linearised Euler equations to calculate the resulting wave field as well as its far-field asymptotics. For values of the Froude number $F^{2}={\it\omega}^{2}D/g$ (where ${\it\omega}$ is the oscillation frequency, $D$ is the submergence depth and $g$ is the gravitational acceleration) below a resonant value $F_{res}^{2}$, the wave field splits cleanly into separate contributions from regular dispersive propagating waves and non-dispersive ‘critical waves’ resulting from a critical layer-like street of flow structures directly downstream of the source. In the subresonant regime, the regular waves behave like sheared ring waves, while the critical layer wave forms a street with a constant width of order $D\sqrt{S/{\it\omega}}$ (where $S$ is the shear flow vorticity) and is convected downstream at the fluid velocity at the depth of the source. When the Froude number approaches its resonant value, the downstream critical and regular waves resonate, producing a train of waves of linearly increasing amplitude contained within a downstream wedge.

Surface velocity divergence in open-channel flows with strip roughness

2014 ◽  
pp. 71-79
Author(s):  
M Sanjou ◽  
T Okamoto ◽  
Y Tanaka ◽  
K Toda
Keyword(s):  
Open Channel ◽  
Channel Flows ◽  
Surface Velocity ◽  
Open Channel Flows

scholarly journals Slip heterogeneity, body-wave spectra, and directivity of earthquake ruptures

1994 ◽  
Vol 37 (6) ◽  
Author(s):  
P. Bernard ◽  
A. Herrero
Keyword(s):  
Rise Time ◽  
Green's Functions ◽  
Green’S Functions ◽  
Body Wave ◽  
Kinematic Model ◽  
Wave Number ◽  
Wave Radiation ◽  
Wave Spectra ◽  
Directivity Effect ◽  
Directivity Factor

We present a broadband kinematic model based on a self-similar k-square distribution of the coseismic slip, with an instantaneous rise-time and a constant rupture velocity. The phase of the slip spectrum at high wave number is random. This model generates an ?-squared body-wave radiation, and a particular directivity factor C2d scaling the amplitude of the body-wave spectra, where Cd is the standard directivity factor. Considering the source models with a propagating pulse and a finite rise-time, we assume that within the slipping band, the rupture has some random character, with small scale rupture in various directions. With such a model, the pulse cannot be resolved, and the directivity factor is still C2d at low frequency; at periods shorter than the rise-time, however, the directivity effect drops to much smaller rms values. This frequency dependent directivity effect, which is expected to be the strongest for sites located in the direction of rupture, was evidenced for the Landers 1992 earthquake, leading to a 2 to 3 s rise-time of the slip pulse. This kinematic model can be used with more refined theoretical Green's functions, including near-field terms and surface waves, or with empirical Green's functions, for generating realistic broadband records in the vicinity of moderate to large earthquakes, in a frequency range relevant for engineering applications (0 Hz to about 20 Hz).

Hamilton’s Principle, Lagrange’s Method, and Ship Motion Theory

1984 ◽  
Vol 28 (04) ◽  
pp. 229-237 ◽  
Author(s):  
Touvia Miloh
Keyword(s):  
Lagrangian Density ◽  
Transfer Functions ◽  
Equations Of Motion ◽  
Steady Motion ◽  
Harmonic Oscillation ◽  
Wave Radiation ◽  
Forward Speed ◽  
Forward Motion ◽  
Radiation Problem ◽  
Lagrange’S Method

Lagrange's equations of motion, describing the motion of several bodies on or below a free surface, are here derived from Hamilton's variational principle. The Lagrangian density is obtained by extending Luke's principle to the wave-radiation problem, and the hydrodynamical loads on the bodies are expressed in terms of the Lagrangian density and its derivatives with respect to the generalized coordinates of the bodies. First we consider a forced harmonic oscillation without a forward speed and then we discuss the case of the same oscillatory motion superimposed on arbitrary steady motion. In both cases we employ Lagrange's method to derive the transfer functions between the generalized forces and the amplitudes of the harmonic motions, in terms of added mass, damping, and the hydrostatic restoring coefficients. The case of a steady forward motion, for which the transfer function is already known, is obtained as a particular case of the general solution.

scholarly journals Galactic structure at meter wavelengths

1959 ◽  
Vol 9 ◽  
pp. 431-446 ◽  
Author(s):  
B. Y. Mills
Keyword(s):  
Fine Structure ◽  
Data Analysis ◽  
Milky Way ◽  
Wave Radiation ◽  
Galactic Emission ◽  
Radiation Distribution ◽  
Wave Emission ◽  
Observational Program ◽  
Cross Type ◽  
Astrophysical Significance

The study of meter-wave radiation from the Milky Way has been hampered, until recently, by the difficulty of obtaining sufficiently high resolution. Observations using interferometers had early indicated the probability of fine structure in the radiation distribution, but the interpretation of these observations was not unique. It was not until the Sydney 3.5-m cross-type radio telescope (beamwidth 50 minutes of arc) was put into operation in 1954 that it became possible to study the distribution of meter wave emission in detail. The observational program with this instrument, together with most of the data analysis relating to the galactic emission, has now been completed and some of the results have already been described [1, 2]. It seems appropriate at this time to give a rather detailed account of the results of this completed work and to discuss its astronomical and astrophysical significance.

The radiation and scattering of surface waves by vertical barriers

1974 ◽  
Vol 63 (4) ◽  
pp. 625-634 ◽  
Author(s):  
D. Porter
Keyword(s):  
Boundary Value Problem ◽  
Surface Waves ◽  
Incident Wave ◽  
Small Amplitude ◽  
Fluid Motion ◽  
Vertical Plane ◽  
Wave Radiation ◽  
Two Dimensional ◽  
Radiation Problem ◽  
Vertical Barriers

A train of small-amplitude surface waves is incident normally on an arbitrary arrangement of thin barriers lying in a vertical plane in deep water. Each barrier is allowed to make small rolling or swaying oscillations of the same frequency as that of the incident wave. The boundary-value problem for the consequent fluid motion, assumed two-dimensional, is solved exactly using a technique which enables the amplitudes of the scattered waves far from the barriers to be readily determined. Reference is made to the associated wave radiation problem and to the calculation of forces and moments on the barriers.

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