scholarly journals Langmuir circulations beneath growing or decaying surface waves

2002 ◽  
Vol 469 ◽  
pp. 317-342 ◽  
Author(s):  
W. R. C. PHILLIPS
Keyword(s):  
Growth Rate ◽  
Free Surface ◽  
Surface Waves ◽  
Wind Wave ◽  
Similarity Solutions ◽  
Base Flow ◽  
Wave Conditions ◽  
Langmuir Circulations ◽  
The Waves ◽  
Base Flows

The instability to longitudinal vortices of two-dimensional density-stratified temporally evolving wavy shear flow is considered. The problem is posited in the context of Langmuir circulations, LCs, beneath wind-driven surface waves and the instability mechanism is generalized Craik–Leibovich, either CLg or CL2. Of interest is the influence of non-stationary base flows on the instability according to linear theory. It is found that the instability is described by a family of similarity solutions and that the growth rate of the instability, in non-stationary base flows, is doubly exponential in time, although the growth rate reduces to exponential when the base flow is stationary. An example is given for weakly sheared wind-driven flow evolving in the presence of growing irrotational surface waves. Waves aligned both with the wind and counter to it are considered, as is the role of stratification. Antecedent to the example is an initial value problem posed by Leibovich & Paolucci (1981) for neutral waves in slowly evolving shear. Here, however, the waves and shear may grow (or decay) at rates comparable with the LCs. Furthermore the current here has two components: a wind-driven portion due to the wind stress applied at the free surface and a second due to the diffusion of momentum due to the wave-amplitude-squared free-surface stress condition. Using the case for neutral waves in non-stratified uniform shear for reference, it is found, in general, that growing waves are stabilizing while decaying waves are destabilizing to the formation of LCs, although the latter applies only for sufficiently large spanwise spacings and is subject to a globally stable lower bound. Decaying waves in the absence of wind can also be destabilizing to LCs. When the wind is counter to the waves, however, only decaying waves are unstable to LCs. Furthermore, while growing waves are stable to the formation of LCs in the presence of stable stratification, decaying waves are unstable in both aligned and opposed wind-wave conditions. Unstable stratification on the other hand, is destabilizing to LCs for all temporal waves in both aligned and opposed wind-wave conditions.

scholarly journals Mutual Interaction between Surface Waves and Langmuir Circulations Observed in Wave-Resolving Numerical Simulations

2020 ◽  
Vol 50 (8) ◽  
pp. 2323-2339
Author(s):  
Yasushi Fujiwara ◽  
Yutaka Yoshikawa
Keyword(s):  
Surface Waves ◽  
Friction Velocity ◽  
Phase Speed ◽  
Mutual Interaction ◽  
Stokes Drift ◽  
Horizontal Shear ◽  
Budget Analysis ◽  
Vorticity Budget ◽  
Langmuir Circulations ◽  
The Waves

AbstractWave-resolving simulations of monochromatic surface waves and Langmuir circulations (LCs) under an idealized condition are performed to investigate the dynamics of wave–current mutual interaction. When the Froude number (the ratio of the friction velocity of wind stress imposed at the surface and wave phase speed) is large, waves become refracted by the downwind jet associated with LCs and become amplitude modulated in the crosswind direction. In such cases, the simulations using the Craik–Leibovich (CL) equation with a prescribed horizontally uniform Stokes drift profile are found to underestimate the intensity of LCs. Vorticity budget analysis reveals that horizontal shear of Stokes drift induced by the wave modulation tilts the wind-driven vorticity to the downwind direction, intensifying the LCs that caused the waves to be modulated. Such an effect is not reproduced in the CL equation unless the Stokes drift of the waves modulated by LCs is prescribed. This intensification mechanism is similar to the CL1 mechanism in that the horizontal shear of the Stokes drift plays a key role, but it is more likely to occur because the shear in this interaction is automatically generated by the LCs whereas the shear in the CL1 mechanism is retained only when a particular phase relation between two crossing waves is kept locked for many periods.

Trapping modes in the theory of surface waves

1951 ◽  
Vol 47 (2) ◽  
pp. 347-358 ◽  
Author(s):  
F. Ursell
Keyword(s):  
Free Surface ◽  
Circular Cylinder ◽  
Total Energy ◽  
Surface Waves ◽  
Radiation Condition ◽  
Finite Width ◽  
Energy Trapping ◽  
Sloping Beach ◽  
The Waves

ABSTRACTIt is shown that a mass of fluid bounded by fixed surfaces and by a free surface of infinite extent may be capable of vibrating under gravity in a mode (called a trapping mode) containing finite total energy. Trapping modes appear to be peculiar to the theory of surface waves; it is known that there are no trapping modes in the theory of sound. Two trapping modes are constructed: (1) a mode on a sloping beach in a semi-infinite canal of finite width, (2) a mode near a submerged circular cylinder in an infinite canal of finite width. The existence of trapping modes shows that in general a radiation condition for the waves at infinity is insufficient for uniqueness.

scholarly journals Waves’ Numerical Dispersion and Damping due to Discrete Dispersion Relation

2014 ◽  
Author(s):  
Babak Ommani ◽  
Odd M. Faltinsen
Keyword(s):  
Free Surface ◽  
Dispersion Relation ◽  
Surface Waves ◽  
Boundary Integral ◽  
Panel Method ◽  
Numerical Dispersion ◽  
Finite Difference Schemes ◽  
Rankine Panel Method ◽  
Free Surface Waves ◽  
The Waves

In linear Rankine panel method, the discrete linear dispersion relation is solved on a discrete free-surface to capture the free-surface waves generated due to wave-body interactions. Discretization introduces numerical damping and dispersion, which depend on the discretization order and the chosen methods for differentiation in time and space. The numerical properties of a linear Rankine panel method, based on a direct boundary integral formulation, for capturing two and three dimensional free-surface waves were studied. Different discretization orders and differentiation methods were considered, focusing on the linear distribution and finite difference schemes. The possible sources for numerical instabilities were addressed. A series of cases with and without forward speed was selected, and numerical investigations are presented. For the waves in three dimensions, the influence of the panels’ aspect ratio and the waves’ angle were considered. It has been shown that using the cancellation effects of different differentiation schemes the accuracy of the numerical method could be improved.

scholarly journals A Wave-Resolving Simulation of Langmuir Circulations with a Nonhydrostatic Free-Surface Model: Comparison with Craik–Leibovich Theory and an Alternative Eulerian View of the Driving Mechanism

2018 ◽  
Vol 48 (8) ◽  
pp. 1691-1708 ◽  
Author(s):  
Yasushi Fujiwara ◽  
Yutaka Yoshikawa ◽  
Yoshimasa Matsumura
Keyword(s):  
Free Surface ◽  
Wave Motion ◽  
Phase Speed ◽  
Current Speed ◽  
Surface Model ◽  
Mean Flow ◽  
Langmuir Circulations ◽  
Wave Induced ◽  
The Waves ◽  
Present Simulation

AbstractThe present study performs a wave-resolving simulation of wind-driven currents under monochromatic surface gravity waves using the latest nonhydrostatic free-surface numerical model. Here, phase speed of the waves is set much greater than the current speed. Roll structures very similar to observed Langmuir circulations (LCs) appear in the simulation only when both waves and down-wave surface currents are present, demonstrating that the rolls are driven by the wave–current interaction. A vorticity analysis of simulated mean flow reveals that the rolls are driven by the torque associated with wave motion, which arises from a correlation between wave-induced vorticity fluctuation and the wave motion itself. Furthermore, it is confirmed that the wave-induced torque is very well represented by the curl of the vortex force (VF), that is, the vector product of mean vorticity and Stokes drift velocity. Therefore, it is concluded that the simulated rolls are LCs and that the wave effects are well represented by the VF expression in the present simulation. The present study further revisits the scaling assumptions made by previous studies that derived VF formulation and shows that there is disagreement among the previous studies regarding the applicability of VF formulation when the wave orbital velocity (proportional to the amplitude times the frequency) is much smaller than the mean flow velocity. The result from the present simulation shows that the VF expression is still valid even with such small wave amplitudes, as long as phase speed of the waves is much greater than the current speed.

Wind-induced growth of water waves

1982 ◽  
Vol 123 ◽  
pp. 425-442 ◽  
Author(s):  
H. Mitsuyasu ◽  
T. Honda
Keyword(s):  
Growth Rate ◽  
Water Waves ◽  
Friction Velocity ◽  
Wind Wave ◽  
Wind Waves ◽  
Pure Water ◽  
Wave Flume ◽  
Wind Speeds ◽  
Wind Profiles ◽  
The Waves

Spatial growth of mechanically generated water waves under the action of wind has been measured in a laboratory wind-wave flume both for pure water and for water containing a surfactant (sodium lauryl sulphate, concentration 2.6 × 10−2%). I n the latter case, no wind waves develop on the surface of the mechanically generated waves as well as on the still water surface for wind speeds up to U10≈ 15 m/s, where U10 is the wind velocity at the height Z = 10 m. Therefore we can study the wind-induced growth of monochromatic waves without the effects of co-existing short wind waves. The mechanically generated waves grew exponentially under the action of the wind, with fetch in both cases. The measured growth rate β for the pure water can be fitted by β/f = 0.34(U*/C)2 0.1 [lsime ] U*/C [lsime ] 1.0, where f is the frequency of the waves, C is the corresponding phase velocity, and U, is the friction velocity obtained from vertical wind profiles. The effect of the wave steepness H/L on the dimensionless growth rate β/f is not clear, but seems to be small. For water containing the surfactant, the measured growth rate is smaller than that for pure water, but the friction velocity of the wind is also small, and the above relation between β/f and U*/C holds approximately if the measured friction velocity U* is used for the relation.

Seismic waves in a wedge

1975 ◽  
Vol 65 (6) ◽  
pp. 1697-1719
Author(s):  
Z. Alterman ◽  
R. Nathaniel
Keyword(s):  
Free Surface ◽  
Surface Waves ◽  
Particle Motion ◽  
Seismic Waves ◽  
Wedge Angle ◽  
Compressional Wave ◽  
Elastic Wedge ◽  
Compressional Wave Velocity ◽  
Quarter Plane ◽  
The Waves

abstract The equations for elastic-wave propagation caused by an explosive point source are solved, by a finite difference scheme, for the case of an elastic wedge, with free boundary. Varying the wedge angle shows that the amplitude of the motion, at the corner, increases as the wedge angle is decreased. The results indicate that for wedges with angles varying from 0° to 180°, the amplitude decreases with decreasing β/α (shear- to compressional-wave velocity). The corner of the wedge generates surface waves and the elliptical particle motion in the waves is analyzed. The particle motion is elliptic and the major axes of the ellipses are inclined at half the wedge angle to the free surface. The surface wave travels to the corner from where it is “transmitted” and reflected. Surface waves are shifted by 180° - θ after transmission. For the case of a quarter plane, we get the same result as Alterman and Loewenthal (1970).

Capillary–gravity waves produced by a wavemaker

1991 ◽  
Vol 224 ◽  
pp. 217-226 ◽  
Author(s):  
L. M. Hocking ◽  
D. Mahdmina
Keyword(s):  
Surface Tension ◽  
Contact Angle ◽  
Free Surface ◽  
Surface Waves ◽  
Gravity Waves ◽  
Contact Line ◽  
Dynamic Properties ◽  
Transient Motion ◽  
Infinite Depth ◽  
The Waves

Surface waves in a channel can be produced by the horizontal motion of a plane wavemaker at one end of the channel. The amplitude and the frequency of the waves depend on both surface tension and gravity, as well as on the condition imposed at the contact line between the free surface and the wavemaker. Some of the previous work on the generation of capillary–gravity waves has been based on the unjustified assumption that the slope of the free surface at the contact line can be prescribed. A more acceptable condition is one that relates the slope to the motion of the contact line relative to the wavemaker; in this way the dynamic properties of the contact angle can be incorporated. The waves generated by a plane wavemaker in fluid of infinite depth and in fluid of a depth equal to that of the wavemaker are determined. An important reason for including surface tension is that in its absence the transient motion initiated by an impulsive start is singular; when surface tension is included this singularity is removed.

scholarly journals Future Changes in Wave Conditions at the German Baltic Sea Coast Based on a Hybrid Approach Using an Ensemble of Regional Climate Change Projections

Water ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 167
Author(s):  
Norman Dreier ◽  
Edgar Nehlsen ◽  
Peter Fröhle ◽  
Diana Rechid ◽  
Laurens M. Bouwer ◽  
...  
Keyword(s):  
21St Century ◽  
Wind Wave ◽  
Regional Climate ◽  
Hybrid Approach ◽  
Wave Modelling ◽  
Long Term Changes ◽  
Mean Wave Period ◽  
Wave Conditions ◽  
Sea Coast

In this study, the projected future long-term changes of the local wave conditions at the German Baltic Sea coast over the course of the 21st century are analyzed and assessed with special focus on model agreement, statistical significance and ranges/spread of the results. An ensemble of new regional climate model (RCM) simulations with the RCM REMO for three RCP forcing scenarios was used as input data. The outstanding feature of the simulations is that the data are available with a high horizontal resolution and at hourly timesteps which is a high temporal resolution and beneficial for the wind–wave modelling. A new data interface between RCM output data and wind–wave modelling has been developed. Suitable spatial aggregation methods of the RCM wind data have been tested and used to generate input for the calculation of waves at quasi deep-water conditions and at a mean water level with a hybrid approach that enables the fast compilation of future long-term time series of significant wave height, mean wave period and direction for an ensemble of RCM data. Changes of the average wind and wave conditions have been found, with a majority of the changes occurring for the RCP8.5 forcing scenario and at the end of the 21st century. At westerly wind-exposed locations mainly increasing values of the wind speed, significant wave height and mean wave period have been noted. In contrast, at easterly wind-exposed locations, decreasing values are predominant. Regarding the changes of the mean wind and wave directions, westerly directions becoming more frequent. Additional research is needed regarding the long-term changes of extreme wave events, e.g., the choice of a best-fit extreme value distribution function and the spatial aggregation method of the wind data.

scholarly journals Modification of Airflow Structure Due to Wave Breaking on a Submerged Topography

2021 ◽  
Author(s):  
Petter Vollestad ◽  
Atle Jensen
Keyword(s):  
Wind Wave ◽  
Separated Flow ◽  
Flow Region ◽  
Breaking Waves ◽  
Leeward Side ◽  
Geometrical Properties ◽  
Image Velocimetry ◽  
Wind Profiles ◽  
The Waves ◽  
Sheltered Area

AbstractExperimental results from a combined wind–wave tank are presented. Wind profiles and resulting wind–wave spectra are described, and an investigation of the airflow above breaking waves is presented. Monochromatic waves created by the wave maker are directed towards a submerged topography. This causes the waves to break at a predictable location, facilitating particle-image-velocimetry measurements of the airflow above steep breaking and non-breaking waves. We analyze how the breaking state modifies the airflow structure, and in particular the extent of the sheltered area on the leeward side of the waves. Results illustrate that while the geometrical properties of the waves greatly influence the airflow structure on the leeward side of the waves, the state of breaking (i.e., whether the waves are currently in a state of active breaking) is not observed to have a clear effect on the extent of the separated flow region, or on the velocity distribution within the sheltered region.

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