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

2010 ◽  
Vol 645 ◽  
pp. 479-496 ◽  
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.

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

2003 ◽  
Author(s):  
Yakov Afanasyev ◽  
Vasily Korabel
Keyword(s):  
Gravity Waves ◽  
Deep Water ◽  
Laboratory Experiments ◽  
Phase Speed ◽  
Critical Value ◽  
Total Reflection ◽  
Supercritical Regime ◽  
Subcritical Regime ◽  
Moving Storm ◽  
The Waves

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.

Magnetoelastic Plane Waves in Infinite Rotating Media

1983 ◽  
Vol 50 (2) ◽  
pp. 283-287 ◽  
Author(s):  
S. K. Roy Choudhuri ◽  
L. Debnath
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Phase Velocity ◽  
Applied Magnetic Field ◽  
Plane Waves ◽  
Low Frequency ◽  
Phase Speed ◽  
Elastic Solid ◽  
Finite Conductivity ◽  
The Waves

A study is made of the propagation of magnetoelastic plane waves in an electrically conducting, infinite elastic solid permeated by a primary uniform magnetic field when the entire medium rotates with a constant angular velocity. A more general dispersion relation is obtained to investigate the effects of rotation and the external magnetic field on the phase velocity of the waves. This analysis reveals that when the applied magnetic field has both longitudinal and transverse components, the coupled magnetoelastic waves are dispersive and damped in an infinitely conducting medium in contrast to the nonrotating medium where the coupled waves are dispersive, but undamped. In the case of finite conductivity, the waves are dispersive and undamped in the absence of the applied magnetic field. At low frequency ω, the phase velocity of the waves varies as ω1/2 for finite conductivity, and is independent of the external magnetic field and rotation; while in the nonrotating case with low frequency (when the applied magnetic field has either longitudinal or transverse components) the phase speed is less than that in the rotating medium and is found to depend on the applied magnetic field. Also in both rotating and nonrotating cases, the phase velocity becomes very small for finitely conducting material with a very high magnetic permeability.

Finite-amplitude waves in inviscid shear flows

1982 ◽  
Vol 382 (1783) ◽  
pp. 389-410 ◽  
Keyword(s):  
Stream Function ◽  
Numerical Solutions ◽  
Phase Speed ◽  
Finite Amplitude ◽  
Weakly Nonlinear ◽  
Poisson Equations ◽  
Weakly Nonlinear Theory ◽  
Finite Difference Discretization ◽  
Finite Amplitude Waves ◽  
The Waves

This paper examines the existence and properties of steady finite-amplitude waves of cats-eye form superposed on a unidirectional inviscid, incompressible shear flow. The problem is formulated as the solution of nonlinear Poisson equations for the stream function with boundary conditions on the unknown edges of the cats-eyes. The dependence of vorticity on stream function is assumed outside the cats-eyes to be as in the undisturbed flow, and uniform unknown vorticity is assumed inside. It is argued on the basis of a finite difference discretization that the problem is determinate, and numerical solutions are obtained for Couette-Poiseuille channel flow. These are compared with the predictions of a weakly nonlinear theory based on the approach of Benney & Bergeron (1969) and Davis (1969). The phase speed of the waves is found to be linear in the wave amplitude.

Resonant interactions between topographic planetary waves in a continuously stratified fluid

1978 ◽  
Vol 84 (4) ◽  
pp. 769-793 ◽  
Author(s):  
Lawrence A. Mysak
Keyword(s):  
Low Frequency ◽  
Phase Speed ◽  
Stratified Fluid ◽  
Planetary Waves ◽  
Buoyancy Frequency ◽  
Frequency Wave ◽  
Resonant Interactions ◽  
Frequency Correction ◽  
Resonant Triads ◽  
The Waves

The resonant interactions between topographic planetary waves in a continuously stratified fluid are investigated theoretically. The interacting waves form a resonant triad and travel along a channel with a uniformly sloping bottom. The basic state stratification in the channel is characterized by a constant buoyancy frequency. The existence of solutions to the quadratic resonance conditions is established graphically. Each wave by itself is a bottom-intensified oscillation of the type discovered by Rhines (1970) except for the addition of a small positive frequency correction. This correction must be included to satisfy higher-order terms in the bottom boundary condition. For strong stratification (r2[Gt ]L2, wherer= internal deformation radius andL= channel width), the waves are strongly bottom-trapped and this frequency correction is negligible. For weak stratification (r2[Lt ]L2) the waves are barotropic and the frequency correction isO(δ), where δ = fractional change in depth across the channel. In many oceanic contexts, δ lies in the range 0·1-0·4 and therefore this correction can produce a significant change in the phase speed. The amplitudes of the waves in the triad obey the classical gyroscopic equations usually encountered in quadratic resonance problems. In particular, the amplitudes evolve on the slow time scale\[ t=O(1/f_0\delta^2), \]which for our scaling assumptions is alsoO(1/f0Ro), whereRois the Rossby number.The results are applied to the Norwegian continental slope region. It is shown that, in this vicinity, there may exist resonant triads consisting of two short, high-frequency waves (periods around 3-4 days) and one long, low-frequency wave (period around 9 days).

The role of the Pacific Decadal Oscillation and ocean-atmosphere interactions in driving United States heatwaves

2021 ◽  
Author(s):  
Sem Vijverberg ◽  
Dim Coumou
Keyword(s):  
Rossby Wave ◽  
Rossby Waves ◽  
Low Frequency ◽  
Causal Link ◽  
Causal Mechanism ◽  
Temperature Forecast ◽  
The Pacific ◽  
Ocean Atmosphere ◽  
The Waves

<p>Heatwaves can have devastating impact on society and reliable early warnings at several weeks lead time are needed. Heatwaves are often associated with quasi-stationary Rossby waves, which interact with sea surface temperature (SST). Previous studies showed that north-Pacific SST can provide long-lead predictability for eastern U.S. temperature, moderated by an atmospheric Rossby wave. The exact mechanisms, however, are not well understood. Here we analyze Rossby waves associated with heatwaves in western and eastern US. Causal inference analyses reveal that both waves are characterized by positive ocean-atmosphere feedbacks at synoptic timescales, amplifying the waves. However, this positive feedback on short timescales is not the causal mechanism that leads to a long-lead SST signal. Only the eastern US shows a long-lead causal link from SSTs to the Rossby wave. We show that the long-lead SST signal derives from low-frequency PDO variability, providing the source of eastern US temperature predictability. We use this improved physical understanding to identify more reliable long-lead predictions. When, at the onset of summer, the Pacific is in a pronounced PDO phase, the SST signal is expected to persist throughout summer. These summers are characterized by a stronger ocean-boundary forcing, thereby more than doubling the eastern US temperature forecast skill, providing a temporary window of enhanced predictability.</p>

scholarly journals Consistent Weighted Average Flux of Well-Balanced TVD-RK Discontinuous Galerkin Method for Shallow Water Flows

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Thida Pongsanguansin ◽  
Montri Maleewong ◽  
Khamron Mekchay
Keyword(s):  
Shallow Water ◽  
Discontinuous Galerkin ◽  
Numerical Solutions ◽  
Order Approximation ◽  
Weighted Average ◽  
Flat Bottom ◽  
Flux Function ◽  
Dg Method ◽  
Average Flux ◽  
Steady Solutions

A well-balanced scheme with total variation diminishing Runge-Kutta discontinuous Galerkin (TVD-RK DG) method for solving shallow water equations is presented. Generally, the flux function at cell interface in the TVD-RK DG scheme is approximated by using the Harten-Lax-van Leer (HLL) method. Here, we apply the weighted average flux (WAF) which is higher order approximation instead of using the HLL in the TVD-RK DG method. The consistency property is shown. The modified well-balanced technique for flux gradient and source terms under the WAF approximations is developed. The accuracy of numerical solutions is demonstrated by simulating dam-break flows with the flat bottom. The steady solutions with shock can be captured correctly without spurious oscillations near the shock front. This presents the other flux approximations in the TVD-RK DG method for shallow water simulations.

Low Frequency Noise Annoyance Assessment by Low Frequency Noise Rating (LFNR) Curves

1983 ◽  
Vol 2 (1) ◽  
pp. 20-28 ◽  
Author(s):  
N. Broner ◽  
H.G. Leventhall
Keyword(s):  
Laboratory Experiments ◽  
Low Frequency ◽  
Frequency Noise ◽  
Low Frequency Noise ◽  
Low Frequencies ◽  
Noise Annoyance

Over recent years, it has become apparent that low frequency noise annoyance is more widespread than originally believed. Annoyance has occurred where the emitted noise is unbalanced towards the low frequencies even though the dB(A) level has been low. Following laboratory experiments carried out as part of an investigation into low frequency annoyance, combined with field annoyance data, the Low Frequency Noise Rating (LFNR) curves are proposed for the assessment of low frequency noise annoyance complaints.

scholarly journals CLUSTER–STAFF search coil magnetometer calibration – comparisons with FGM

2014 ◽  
Vol 3 (2) ◽  
pp. 153-177 ◽  
Author(s):  
P. Robert ◽  
N. Cornilleau-Wehrlin ◽  
R. Piberne ◽  
Y. de Conchy ◽  
C. Lacombe ◽  
...  
Keyword(s):  
Transfer Functions ◽  
Low Frequency ◽  
Temporal Analysis ◽  
Fluxgate Magnetometer ◽  
Data Sets ◽  
Spectral Matrix ◽  
Spatio Temporal ◽  
Cross Calibration ◽  
The Waves ◽  
The Way

Abstract. The main part of the Cluster Spatio-Temporal Analysis of Field Fluctuations (STAFF) experiment consists of triaxial search coils allowing the measurements of the three magnetic components of the waves from 0.1 Hz up to 4 kHz. Two sets of data are produced, one by a module to filter and transmit the corresponding waveform up to either 10 or 180 Hz (STAFF-SC), and the second by the onboard Spectrum Analyser (STAFF-SA) to compute the elements of the spectral matrix for five components of the waves, 3 × B and 2 × E (from the EFW experiment), in the frequency range 8 Hz to 4 kHz. In order to understand the way the output signals of the search coils are calibrated, the transfer functions of the different parts of the instrument are described as well as the way to transform telemetry data into physical units across various coordinate systems from the spinning sensors to a fixed and known frame. The instrument sensitivity is discussed. Cross-calibration inside STAFF (SC and SA) is presented. Results of cross-calibration between the STAFF search coils and the Cluster Fluxgate Magnetometer (FGM) data are discussed. It is shown that these cross-calibrations lead to an agreement between both data sets at low frequency within a 2% error. By means of statistics done over 10 yr, it is shown that the functionalities and characteristics of both instruments have not changed during this period.

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