scholarly journals Kinematics of fluid particles on the sea surface: Hamiltonian theory

2016 ◽  
Vol 801 ◽  
pp. 260-288 ◽  
Author(s):  
F. Fedele ◽  
C. Chandre ◽  
M. Farazmand

We derive the John–Sclavounos equations, describing the motion of a fluid particle on the sea surface, from first principles using Lagrangian and Hamiltonian formalisms applied to the motion of a frictionless particle constrained on an unsteady surface. This framework leads to a number of new insights into the particle kinematics. The main result is that vorticity generated on a stress-free surface vanishes at a wave crest when the horizontal particle velocity equals the crest propagation speed, which is the kinematic criterion for wave breaking. If this holds for the largest crest, then the symplectic two-form associated with the Hamiltonian dynamics reduces instantaneously to that associated with the motion of a particle in free flight, as if the surface did not exist. Further, exploiting the conservation of the Hamiltonian function for steady surfaces and travelling waves, we show that particle velocities remain bounded at all times, ruling out the possibility of the finite-time blowup of solutions.

2017 ◽  
Author(s):  
Yair De-Leon ◽  
Nathan Paldor

Abstract. Using 20 years of accurately calibrated, high resolution, observations of Sea Surface Height Anomalies (SSHA) by satellite ‎borne altimeters we show that in the Indian Ocean south of the Australian coast the low frequency variations of SSHA are ‎dominated by westward propagating, trapped, i.e. non-harmonic, planetary waves. Our results demonstrate that the ‎meridional-dependent amplitudes of the SSHA are large only within a few degrees of latitude next to the South-Australian ‎coast while farther in the ocean they are uniformly small. This meridional variation of the SSHA signal is typical of the ‎amplitude structure in the trapped wave theory. The westward propagation speed of the SSHA signals is analyzed by ‎employing three different methods of estimation. Each one of these methods yields speed estimates that can vary widely ‎between adjacent latitudes but the combination of at least two of the three methods yields much smoother variation. The ‎estimates obtained in this manner show that the observed phase speeds at different latitudes exceed the phase speeds of ‎harmonic Rossby (Planetary) waves by 140 % to 200 %. In contrast, the theory of trapped Rossby (Planetary) waves in a ‎domain bounded by a wall on its equatorward side yields phase speeds that approximate more closely the observed phase ‎speeds.‎


Ocean Science ◽  
2017 ◽  
Vol 13 (3) ◽  
pp. 483-494 ◽  
Author(s):  
Yair De-Leon ◽  
Nathan Paldor

Abstract. Using 20 years of accurately calibrated, high-resolution observations of sea surface height anomalies (SSHAs) by satellite borne altimeters, we show that in the Indian Ocean south of the Australian coast the low-frequency variations of SSHAs are dominated by westward propagating, trapped, i.e., non-harmonic, Rossby (Planetary) waves. Our results demonstrate that the meridional-dependent amplitudes of the SSHAs are large only within a few degrees of latitude next to the southern Australian coast while farther in the ocean they are uniformly small. This meridional variation of the SSHA signal is typical of the amplitude structure in the trapped wave theory. The westward propagation speed of the SSHA signal is analyzed by employing three different methods of estimation. Each one of these methods yields speed estimates that can vary widely between adjacent latitudes but the combination of at least two of the three methods yields much smoother variation. The estimates obtained in this manner show that the observed phase speeds at different latitudes exceed the phase speeds of harmonic Rossby (planetary) waves by 140 to 200 % (which was also reported in previous studies). In contrast, the theory of trapped Rossby (planetary) waves in a domain bounded by a wall on its equatorward side yields phase speeds that approximate more closely the observed phase speeds in the study area.


2014 ◽  
Vol 08 (03) ◽  
pp. 1440001 ◽  
Author(s):  
Chao An ◽  
Philip L.-F. Liu

In this paper, the time series of ocean water surface elevation, recorded by Deep-ocean Assessment and Recording of Tsunamis (DART) sensors in the Pacific Ocean, during three recent tsunami events — 2010 Chile tsunami, 2011 Tohoku tsunami, and 2012 Haida Gwaii tsunami — are analyzed. The characteristics of leading tsunami waves are examined in terms of their propagation speed, wave period and wave amplitude so as to determine the importance of wave nonlinearity and frequency dispersion. Using the estimated arrival time of leading waves at each DART station and the distance from each station to the epicenter of the corresponding earthquake, the averaged propagation speed of leading waves for each event is calculated. It is found that the wave propagation speed for 2010 Chile tsunami is roughly 190 m/s, and is slightly slower than that of 2011 Tohoku and 2012 Haida Gwaii tsunamis, 210 m/s for both events. Two time scales associated with the leading waves are introduced: the duration of leading wave crest and the leading wave period obtained from a wavelet analysis. The results show that the leading wave crest duration is roughly 15–20 min and the wave period is roughly 25–30 min at most of DART stations for all the three events. The wave nonlinearity and frequency dispersion parameters, being defined as the wave amplitude to water depth ratio and the square of water depth to wavelength ratio, respectively, are calculated for the leading waves. The parameter for wave nonlinearity is found to be smaller than 4.0 × 10-4, while the parameter for frequency dispersion is smaller than 0.02 at all stations for all the three events. Finally, the cumulative effects of nonlinearity and frequency dispersion for the leading waves are investigated. It is found that the distances between the epicenter and all DART stations in each event are much smaller than those required for the nonlinearity and/or frequency dispersive effects to become significant.


Author(s):  
Benedicte Brodtkorb ◽  
Arne Nestega˚rd ◽  
Atle Johansen

When an extreme wave crest hits the deck of a jacket-type structure, the kinematics in the wave beneath the deck is strongly influenced by the deck itself. The increased fluid particle velocities should be accounted for when assessing the load on obstructions located in a zone below the deck, i.e. on the upper part of the substructure and on under-deck attachments. Usually the wave-in-deck loads and substructure loads are calculated separately by two different analysis programs. The undisturbed velocity field is then applied to the substructure. In this study, we compare two methods, both based on CFD (Computational Fluid Dynamics), for calculating the increased substructure loads due to disturbed fluid particle velocities during extreme wave-in-deck events.


1997 ◽  
Vol 32 (2-3) ◽  
pp. 163-180 ◽  
Author(s):  
J. Bosboom ◽  
G. Klopman ◽  
J.A. Roelvink ◽  
J.A. Battjes

2021 ◽  
Author(s):  
Anne Vallette ◽  
François-Régis Martin-Lauzer

<p>The first version of the Litter -TEP (Thematic Exploitation Platform), which was developed by ARGANS Ltd on a grant of the Copernicus Marine Environment monitoring service (CMEMS), aimed at forecasting litter introduction by rivers and marine drift on the European North-Western Shelf (NWS) so as to help local coastal communities schedule beach cleansing and assess the potential origin of materials collected. It relies on the classic approximation that the pieces or patches of litter are passively transported like Lagrangian floats by currents, whether largescale, mesoscale, sub-mesoscale, Eckman, tides, Stokes drift, the elusive Langmuir circulation…</p><p>Yet, windage, i.e. the effect of wind on items with a freeboard, is often more critical than transport by currents. To stay in the ‘Lagrangian Particle Tracking’ framework, but correct the discrepancy between ground-truth and drift speed’s and direction’s forecast, windage has been grossly modelled in the Litter TEP as if we had an enhanced ocean surface layer drift which affects similarly all floating litter. Yet, neither ocean transport nor this modelling allows to reproduce the formation of litter rows. Hence the current study: coming back to the basics of classical mechanics (Newton-Euler equations for translations & rotations of rigid bodies) we have performed simulation of marine debris’ dynamics at the interface between i. the turbulent atmospheric surface layer (ASL) which is at the bottom of the atmospheric boundary layer (ABL), and ii. the wave breaking layer (WBL) which tops the wave-affected-surface-layer (WASL) within the turbulent ocean boundary layer (OBL), in maturing wave fields (wave age <1) in the open ocean, that are characterized by wind gusts, wave crest breaking and spray. The classic framework for the drift of flotsam, by which wind-induced drag force exerted on objects floating on the sea surface causes motion relative to ocean currents (i.e. leeway drift), and vice-versa, is obviously right; but that it reaches an equilibrium stationary state between the wind-induced drag force and current-induced one on the floating objects in a relatively short timescale proves wrong. In various situations a litter piece will constantly change its attitude and settings in the water, yet reaching a +/- time-invariant time state (but not time-independent) though chaotic. In short: if litter pieces “sail”, it is without Control & Command. The litter drift, i.e. motion from source to sink, might therefore be drastically different from usual views, temporarily by orders of magnitude, and on the long run by factors 2 to 3.</p><p>For a proper assessment of the behavior of litter pieces, one needs precise modelling of wind profiles above the waves in a non-equilibrium boundary layer (wind gusts above the wave crests and counter wind in the troughs), of wave breaking that creates shock dynamics (surf, immersion and/or flight), of sea spray that batters the litter pieces, and .</p><p>Our modelling applies to rigid bodies lighters, cans, wood…, and shall be extended to deformable bodies for algae, plastic bags…, as well as entangled debris that are +/- linked together. We look for partners to perform scaled physical experiments in tanks.</p>


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