Interactions of Gravity Waves Generated by a Moving Source With the Shelf: Laboratory Experiment

Rapidly moving storm crossing the shelf from shallow water to deep water can generate tsunami-like waves which can cause local flooding and damage to docks when the waves hit the coast. We report on laboratory experiments to examine the reflection of waves generated by a moving disturbance from the shelf. Experiments are performed in a two-layer fluid consisting of a layer of oil based ferrofluid lying on top of a layer of water with step bottom. The disturbance is generated by a permanent magnet moving above the surface of ferrofluid. Digital images of the flow are analyzed to obtain the evolution of the wave field. The experimental flows demonstrate two distinct regimes, namely subcritical when the speed of the magnet is less than the phase speed of the wave, and supercritical when the speed of the magnet is greater than the phase speed of the wave. In subcritical regime the disturbance is localized and its size is determined by the spatial extent of the forcing. In supercritical regime the waves form two beams extending at “Mach angle” with respect to the direction of motion. Oblique wave incident on the shelf can experience total reflection if the angle between the wave front and the shelf is greater than a critical value.

Wave Kinematics Computed With the Nonlinear Schro¨dinger Method for Deep Water

Journal of Offshore Mechanics and Arctic Engineering ◽

10.1115/1.2830077 ◽

1999 ◽

Vol 121 (2) ◽

pp. 126-130 ◽

Cited By ~ 3

Author(s):

K. Trulsen

Keyword(s):

Time Series ◽

Gravity Waves ◽

Deep Water ◽

Water Wave ◽

Surface Displacement ◽

Horizontal Position ◽

Two Dimensional ◽

Limited Bandwidth ◽

Wave Kinematics ◽

The nonlinear Schro¨dinger method for water wave kinematics under two-dimensional irregular deepwater gravity waves is developed. Its application is illustrated for computation of the velocity and acceleration fields from the time-series of the surface displacement measured at a fixed horizontal position. The method is based on the assumption that the waves have small steepness and limited bandwidth.

The interaction of deep-water gravity waves and an annular current: linear theory

10.1017/s0022112093000722 ◽

1993 ◽

Vol 248 ◽

pp. 153-172 ◽

Cited By ~ 8

Author(s):

Marius Gerber

Keyword(s):

Linear Theory ◽

Gravity Waves ◽

Deep Water ◽

Large Scale ◽

Ray Theory ◽

Velocity Parameter ◽

Dimensional Parameters ◽

The Waves ◽

Angle Parameter

The interaction of linear, steady, axisymmetric deep-water gravity waves with preexisting large-scale annular currents has been investigated. Waves originating inside the annulus as well as waves approaching the annulus from the outside were studied. Exact linear ray solutions were obtained and involve two non-dimensional parameters, a radius-angle parameter and a velocity parameter. For opposing currents the linear solutions also allow the derivation of radii at which the waves are blocked, reflected at a linear caustic or stopped by the current. Various examples of rays interacting with an annular current are presented to illustrate aspects of the solutions obtained. In particular, the behaviour of the ray solutions at blocking, reflection and stopping is investigated. Linear ray theory is shown to fail at caustics and caustic solutions are briefly discussed.

Evidence for tropospheric wind shear excitation of high-phase-speed gravity waves reaching the mesosphere using the ray-tracing technique

Atmospheric Chemistry and Physics ◽

10.5194/acp-15-2709-2015 ◽

2015 ◽

Vol 15 (5) ◽

pp. 2709-2721 ◽

Cited By ~ 24

Author(s):

M. Pramitha ◽

M. Venkat Ratnam ◽

A. Taori ◽

B. V. Krishna Murthy ◽

D. Pallamraju ◽

...

Keyword(s):

Ray Tracing ◽

Gravity Waves ◽

High Frequency ◽

Phase Speed ◽

Horizontal Wind ◽

Climatological Model ◽

Background Temperature ◽

The Waves ◽

High Phase ◽

Mf Radar

Abstract. Sources and propagation characteristics of high-frequency gravity waves observed in the mesosphere using airglow emissions from Gadanki (13.5° N, 79.2° E) and Hyderabad (17.5° N, 78.5° E) are investigated using reverse ray tracing. Wave amplitudes are also traced back, including both radiative and diffusive damping. The ray tracing is performed using background temperature and wind data obtained from the MSISE-90 and HWM-07 models, respectively. For the Gadanki region, the suitability of these models is tested. Further, a climatological model of the background atmosphere for the Gadanki region has been developed using nearly 30 years of observations available from a variety of ground-based (MST radar, radiosondes, MF radar) and rocket- and satellite-borne measurements. ERA-Interim products are utilized for constructing background parameters corresponding to the meteorological conditions of the observations. With the reverse ray-tracing method, the source locations for nine wave events could be identified to be in the upper troposphere, whereas for five other events the waves terminated in the mesosphere itself. Uncertainty in locating the terminal points of wave events in the horizontal direction is estimated to be within 50–100 km and 150–300 km for Gadanki and Hyderabad wave events, respectively. This uncertainty arises mainly due to non-consideration of the day-to-day variability in the tidal amplitudes. Prevailing conditions at the terminal points for each of the 14 events are provided. As no convection in and around the terminal points is noticed, convection is unlikely to be the source. Interestingly, large (~9 m s−1km−1) vertical shears in the horizontal wind are noticed near the ray terminal points (at 10–12 km altitude) and are thus identified to be the source for generating the observed high-phase-speed, high-frequency gravity waves.

Refraction of gravity waves by weak current gradients

10.1017/s0022112001005237 ◽

2001 ◽

Vol 442 ◽

pp. 157-159 ◽

Cited By ~ 17

Author(s):

KRISTIAN B. DYSTHE

Keyword(s):

Surface Waves ◽

Group Velocity ◽

Gravity Waves ◽

Deep Water ◽

Current Velocity ◽

Water Surface ◽

Simple Formula ◽

Vertical Component ◽

Weak Current ◽

When deep water surface waves cross an area with variable current, refraction takes place. If the group velocity of the waves is much larger than the current velocity we show that the curvature of a ray, χ, is given by the simple formula χ = ζ/vg. Here ζ is the vertical component of the current vorticity and vg is the group velocity.

Laboratory experiments and a non-harmonic theory for topographic Rossby waves over a linearly sloping bottom on the f-plane

10.1017/s0022112009992862 ◽

2010 ◽

Vol 645 ◽

pp. 479-496 ◽

Cited By ~ 7

Author(s):

YAIR COHEN ◽

NATHAN PALDOR ◽

JOËL SOMMERIA

Keyword(s):

Eigenvalue Problem ◽

Laboratory Experiments ◽

Numerical Solutions ◽

Order Approximation ◽

Low Frequency ◽

Phase Speed ◽

Wave Trapping ◽

The Cross ◽

The Waves ◽

Sloping Bottom

Low-frequency waves that develop in a shallow layer of fluid, contained in a channel with linearly slopping bottom and rotating with uniform angular speed are investigated theoretically and experimentally. Exact numerical solutions of the eigenvalue problem, obtained from the linearized shallow water equations on the f-plane, show that the waves are trapped near the channel's shallow wall and propagate along it with the shallow side on their right in the Northern hemisphere. The phase speed of the waves is slower compared with that of the harmonic theory in which bottom slope is treated inconsistently. A first-order approximation of the cross-channel dependence of the coefficient in the eigenvalue equation yields an approximation of the cross-channel velocity eigenfunction as an Airy function, which, for sufficiently wide channels, yields an explicit expression for the wave's dispersion relation. The analytic solutions of the eigenvalue problem agree with the numerical solutions in both the wave trapping and the reduced phase speed. For narrow channels, our theory yields an estimate of the channel width below which the harmonic theory provides a more accurate approximation. Laboratory experiments were conducted on a 13 m diameter turntable at LEGI-Coriolis (France) into which a linearly sloping bottom of 10 % incline was installed. A wavemaker generated waves of known frequency at one end of the turntable and the wavenumbers of these waves were measured at the opposite end using a particle imaging velocimetry technique. The experimental results regarding the phase speed and the radial structure of the amplitude are in very good agreement with our theoretical non-harmonic predictions, which support the present modification of the harmonic theory in wide channels.

Cyclic gravity waves in deep water

The Journal of the Australian Mathematical Society Series B Applied Mathematics ◽

10.1017/s033427000000388x ◽

1983 ◽

Vol 25 (1) ◽

pp. 2-15 ◽

Cited By ~ 1

Author(s):

P. J. Bryant

Keyword(s):

Wave Height ◽

Gravity Waves ◽

Deep Water ◽

Fourier Transforms ◽

Surface Displacement ◽

Surface Boundary ◽

Surface Boundary Conditions ◽

Method Of Solution ◽

Nonlinear Surface ◽

AbstractNumerical evidence is presented for the existence of unsteady periodic gravity waves of large height in deep water whose shape changes cyclically as they propagate. It is found that, for a given wavelength and maximum wave height, cyclic waves with a range of cyclic periods exist, with a steady wave of permanent shape being an extreme member of the range. The method of solution, using Fourier transforms of the nonlinear surface boundary conditions, determines the irrotational velocity field in the water and the water surface displacement as functions of space and time, from which properties of the waves are demonstrated. In particular, it is shown that cyclic waves are closer to the point of wave breaking than are steady permanent waves of the same wave height and wavelength.

Investigation of sources of gravity waves observed in the Brazilian Equatorial region on 08 April 2005

10.5194/angeo-2019-81 ◽

2019 ◽

Author(s):

Oluwakemi Dare-Idowu ◽

Igo Paulino ◽

Cosme A. O. B. Figueiredo ◽

Amauri F. Medeiros ◽

Ricardo A. Buriti ◽

...

Keyword(s):

Ray Tracing ◽

Gravity Waves ◽

Spectral Characteristics ◽

Phase Speed ◽

Radar Data ◽

Equatorial Region ◽

Inter Tropical Convergence Zone ◽

Wind Profiles ◽

Ray Path ◽

Abstract. On 08 April 2005, a strong gravity wave activity (more than 3 hours) was observed in São João do Cariri (7.4° S, 36.5° W). These waves propagated to the southeast and presented different spectral characteristics (wavelength, period and phase speed). Using OH airglow images, the parameters of 5 observed gravity waves were calculated; the wavelengths ranged from ~ 90 to 150 km, the periods from ~ 26 to 67 min and the phase speeds from 32 to 71 m/s. A reserve ray-tracing analysis was performed to investigate the likely sources of these waves. The ray-tracing database was composed of temperature profiles from NRLMSISE-00 model and SABER measurements and wind profiles from HWM-14 model and meteor radar data. According to the ray path, the likely source of these gravity waves was the Inter Tropical Convergence Zone with intense convective processes taking place in the northern part of the observatory. Also, the observed preferential propagation direction of the waves to the southeast could be explained using blocking diagrams, i.e., due to the wind filtering process.

Mesospheric gravity waves observed near equatorial and low–middle latitude stations: wave characteristics and reverse ray tracing results

Annales Geophysicae ◽

10.5194/angeo-24-3229-2006 ◽

2006 ◽

Vol 24 (12) ◽

pp. 3229-3240 ◽

Cited By ~ 19

Author(s):

C. M. Wrasse ◽

T. Nakamura ◽

H. Takahashi ◽

A. F. Medeiros ◽

M. J. Taylor ◽

...

Keyword(s):

Ray Tracing ◽

Gravity Wave ◽

Gravity Waves ◽

Source Region ◽

Phase Speed ◽

Middle Latitude ◽

Wave Source ◽

Middle Latitudes ◽

Summer Time ◽

Abstract. Gravity wave signatures were extracted from OH airglow observations using all-sky CCD imagers at four different stations: Cachoeira Paulista (CP) (22.7° S, 45° W) and São João do Cariri (7.4° S, 36.5° W), Brazil; Tanjungsari (TJS) (6.9° S, 107.9° E), Indonesia and Shigaraki (34.9° N, 136° E), Japan. The gravity wave parameters are used as an input in a reverse ray tracing model to study the gravity wave vertical propagation trajectory and to estimate the wave source region. Gravity waves observed near the equator showed a shorter period and a larger phase velocity than those waves observed at low-middle latitudes. The waves ray traced down into the troposphere showed the largest horizontal wavelength and phase speed. The ray tracing results also showed that at CP, Cariri and Shigaraki the majority of the ray paths stopped in the mesosphere due to the condition of m2<0, while at TJS most of the waves are traced back into the troposphere. In summer time, most of the back traced waves have their final position stopped in the mesosphere due to m2<0 or critical level interactions (|m|→∞), which suggests the presence of ducting waves and/or waves generated in-situ. In the troposphere, the possible gravity wave sources are related to meteorological front activities and cloud convections at CP, while at Cariri and TJS tropical cloud convections near the equator are the most probable gravity wave sources. The tropospheric jet stream and the orography are thought to be the major responsible sources for the waves observed at Shigaraki.

Planetary (Rossby) waves and inertia–gravity (Poincaré) waves in a barotropic ocean over a sphere

10.1017/jfm.2013.219 ◽

2013 ◽

Vol 726 ◽

pp. 123-136 ◽

Cited By ~ 13

Author(s):

Nathan Paldor ◽

Yair De-Leon ◽

Ofer Shamir

Keyword(s):

Gravity Waves ◽

Rossby Waves ◽

Phase Speed ◽

Mode Number ◽

Rotating Sphere ◽

Zonal Wavenumber ◽

Speed Of Gravity ◽

Meridional Mode ◽

Poincare Waves ◽

AbstractThe construction of approximate Schrödinger eigenvalue equations for planetary (Rossby) waves and for inertia–gravity (Poincaré) waves on an ocean-covered rotating sphere yields highly accurate estimates of the phase speeds and meridional variation of these waves. The results are applicable to fast rotating spheres such as Earth where the speed of barotropic gravity waves is smaller than twice the tangential speed on the equator of the rotating sphere. The implication of these new results is that the phase speed of Rossby waves in a barotropic ocean that covers an Earth-like planet is independent of the speed of gravity waves for sufficiently large zonal wavenumber and (meridional) mode number. For Poincaré waves our results demonstrate that the dispersion relation is linear, (so the waves are non-dispersive and the phase speed is independent of the wavenumber), except when the zonal wavenumber and the (meridional) mode number are both near 1.

Long Barotropic Waves Generated by a Storm Crossing Topography

Journal of Physical Oceanography ◽

10.1175/2007jpo3687.1 ◽

2007 ◽

Vol 37 (12) ◽

pp. 2809-2823 ◽

Cited By ~ 19

Author(s):

Ross Vennell

Keyword(s):

Continental Shelf ◽

Shallow Water ◽

Deep Water ◽

Fast Moving ◽

Passage Time ◽

Finite Width ◽

Translation Speed ◽

1D Model ◽

Moving Storm ◽

Abstract Storms crossing topography are shown to radiate long surface gravity waves. The waves are transients generated by changes in the depth-dependent amplitude of the atmospherically forced pressure wave beneath a storm. This generation mechanism for long waves, known as “meteorological tsunamis” or rissaga, does not appear to have been previously discussed. The transients have periods equal to the passage time of the storm, of order 30 min for small fast-moving storms. A 1D model is used to give the amplitudes of the transient waves generated by a small fast-moving storm crossing a topographic step on to a continental shelf and across a ridge. Large transients are generated by storms whose translation speed is subcritical in deep water and supercritical in shallow water, that is, faster than the shallow-water wave speed. Surprisingly, when the depth difference between the deep water and the continental shelf is large, a gentle transition from deep to shallow water over 10 storm widths only slightly reduces the amplitudes of the transients. The influence of a finite-width shelf on the enhancement of coastal storm surge is also discussed. A 2D numerical model illustrates the topographic transients generated by sub- and supercritical storms moving across a ridge. Topographic transients are suggested as a source of energy for seiches on shelves and within embayments. The energy may come from a storm crossing the adjacent continental slope and possibly from distant open-ocean storms crossing multiple ridges and seamounts.