Laboratory observations of mean flows under surface gravity waves

2007 ◽  
Vol 573 ◽  
pp. 131-147 ◽  
Author(s):  
S. G. MONISMITH ◽  
E. A. COWEN ◽  
H. M. NEPF ◽  
J. MAGNAUDET ◽  
L. THAIS
Keyword(s):  
Gravity Waves ◽  
Stokes Drift ◽  
Bottom Boundary Layer ◽  
Mean Velocity ◽  
Surface Gravity Waves ◽  
End Conditions ◽  
Different Types ◽  
Stokes Waves ◽  
Rotational Waves ◽  
Gerstner Waves

In this paper we present mean velocity distributions measured in several different wave flumes. The flows shown involve different types of mechanical wavemakers, channels of differing sizes, and two different end conditions. In all cases, when surface waves, nominally deep-water Stokes waves, are generated, counterflowing Eulerian flows appear that act to cancel locally, i.e. not in an integral sense, the mass transport associated with the Stokes drift. No existing theory of wave–current interactions explains this behaviour, although it is symptomatic of Gerstner waves, rotational waves that are exact solutions to the Euler equations. In shallow water (kH ≈ 1), this cancellation of the Stokes drift does not hold, suggesting that interactions between wave motions and the bottom boundary layer may also come into play.

Radiation of internal waves from groups of surface gravity waves

2017 ◽  
Vol 829 ◽  
pp. 280-303 ◽  
Author(s):  
S. Haney ◽  
W. R. Young
Keyword(s):  
Internal Waves ◽  
Energy Flux ◽  
Gravity Waves ◽  
Three Dimensions ◽  
Stokes Drift ◽  
Surface Gravity ◽  
Fourth Power ◽  
Buoyancy Frequency ◽  
Surface Gravity Waves ◽  
Short Period

Groups of surface gravity waves induce horizontally varying Stokes drift that drives convergence of water ahead of the group and divergence behind. The mass flux divergence associated with spatially variable Stokes drift pumps water downwards in front of the group and upwards in the rear. This ‘Stokes pumping’ creates a deep Eulerian return flow that sets the isopycnals below the wave group in motion and generates a trailing wake of internal gravity waves. We compute the energy flux from surface to internal waves by finding solutions of the wave-averaged Boussinesq equations in two and three dimensions forced by Stokes pumping at the surface. The two-dimensional (2-D) case is distinct from the 3-D case in that the stratification must be very strong, or the surface waves very slow for any internal wave (IW) radiation at all. On the other hand, in three dimensions, IW radiation always occurs, but with a larger energy flux as the stratification and surface wave (SW) amplitude increase or as the SW period is shorter. Specifically, the energy flux from SWs to IWs varies as the fourth power of the SW amplitude and of the buoyancy frequency, and is inversely proportional to the fifth power of the SW period. Using parameters typical of short period swell (e.g. 8 s SW period with 1 m amplitude) we find that the energy flux is small compared to both the total energy in a typical SW group and compared to the total IW energy. Therefore this coupling between SWs and IWs is not a significant sink of energy for the SWs nor a source for IWs. In an extreme case (e.g. 4 m amplitude 20 s period SWs) this coupling is a significant source of energy for IWs with frequency close to the buoyancy frequency.

Disruption of the bottom log layer in large-eddy simulations of full-depth Langmuir circulation

2012 ◽  
Vol 699 ◽  
pp. 79-93 ◽  
Author(s):  
A. E. Tejada-Martínez ◽  
C. E. Grosch ◽  
N. Sinha ◽  
C. Akan ◽  
G. Martinat
Keyword(s):  
Gravity Waves ◽  
Large Eddy Simulations ◽  
Stokes Drift ◽  
Navier Stokes ◽  
Wake Region ◽  
Langmuir Circulation ◽  
Mean Velocity ◽  
Wave Forcing ◽  
Large Eddy ◽  
Shear Current

AbstractWe report on disruption of the log layer in the resolved bottom boundary layer in large-eddy simulations (LES) of full-depth Langmuir circulation (LC) in a wind-driven shear current in neutrally-stratified shallow water. LC consists of parallel counter-rotating vortices that are aligned roughly in the direction of the wind and are generated by the interaction of the wind-driven shear with the Stokes drift velocity induced by surface gravity waves. The disruption is analysed in terms of mean velocity, budgets of turbulent kinetic energy (TKE) and budgets of TKE components. For example, in terms of mean velocity, the mixing due to LC induces a large wake region eroding the classical log-law profile within the range $90\lt { x}_{3}^{+ } \lt 200$. The dependence of this disruption on wind and wave forcing conditions is investigated. Results indicate that the amount of disruption is primarily determined by the wavelength of the surface waves generating LC. These results have important implications for turbulence parameterizations for Reynolds-averaged Navier–Stokes simulations of the coastal ocean.

A note on the divergence effect and the Lagrangian-mean surface elevation in periodic water waves

1988 ◽  
Vol 189 ◽  
pp. 235-242 ◽  
Author(s):  
M. E. Mcintyre
Keyword(s):  
Free Surface ◽  
Velocity Field ◽  
Gravity Waves ◽  
Water Waves ◽  
Wave Amplitude ◽  
Exact Expression ◽  
Mean Velocity ◽  
Surface Gravity Waves ◽  
Generalized Lagrangian ◽  
Divergence Effect

Longuet-Higgins’ exact expression for the increase in the Lagrangian-mean elevation of the free surface due to the presence of periodic, irrotational surface gravity waves is rederived from generalized Lagrangian-mean theory. The raising of the Lagrangian-mean surface as wave amplitude builds up illustrates the non-zero divergence of the Lagrangian-mean velocity field in an incompressible fluid.

scholarly journals Note on the velocity and related fields of steady irrotational two-dimensional surface gravity waves

2012 ◽  
Vol 370 (1964) ◽  
pp. 1572-1586 ◽  
Author(s):  
Didier Clamond
Keyword(s):  
Gravity Waves ◽  
Finite Amplitude ◽  
Numerical Results ◽  
Surface Gravity ◽  
Two Dimensional ◽  
Surface Gravity Waves ◽  
Stokes Waves ◽  
Irrotational Motion ◽  
Dimensional Surface

The velocity and other fields of steady two-dimensional surface gravity waves in irrotational motion are investigated numerically. Only symmetric waves with one crest per wavelength are considered, i.e. Stokes waves of finite amplitude, but not the highest waves, nor subharmonic and superharmonic bifurcations of Stokes waves. The numerical results are analysed, and several conjectures are made about the velocity and acceleration fields.

scholarly journals Observations and a Model of Undertow over the Inner Continental Shelf

2008 ◽  
Vol 38 (11) ◽  
pp. 2341-2357 ◽  
Author(s):  
Steven J. Lentz ◽  
Melanie Fewings ◽  
Peter Howd ◽  
Janet Fredericks ◽  
Kent Hathaway
Keyword(s):  
Gravity Waves ◽  
Vertical Structure ◽  
Surf Zone ◽  
Stokes Drift ◽  
Vertical Shear ◽  
Surface Gravity ◽  
Linear Wave ◽  
Surface Gravity Waves ◽  
Offshore Flow ◽  
Offshore Transport

Abstract Onshore volume transport (Stokes drift) due to surface gravity waves propagating toward the beach can result in a compensating Eulerian offshore flow in the surf zone referred to as undertow. Observed offshore flows indicate that wave-driven undertow extends well offshore of the surf zone, over the inner shelves of Martha’s Vineyard, Massachusetts, and North Carolina. Theoretical estimates of the wave-driven offshore transport from linear wave theory and observed wave characteristics account for 50% or more of the observed offshore transport variance in water depths between 5 and 12 m, and reproduce the observed dependence on wave height and water depth. During weak winds, wave-driven cross-shelf velocity profiles over the inner shelf have maximum offshore flow (1–6 cm s−1) and vertical shear near the surface and weak flow and shear in the lower half of the water column. The observed offshore flow profiles do not resemble the parabolic profiles with maximum flow at middepth observed within the surf zone. Instead, the vertical structure is similar to the Stokes drift velocity profile but with the opposite direction. This vertical structure is consistent with a dynamical balance between the Coriolis force associated with the offshore flow and an along-shelf “Hasselmann wave stress” due to the influence of the earth’s rotation on surface gravity waves. The close agreement between the observed and modeled profiles provides compelling evidence for the importance of the Hasselmann wave stress in forcing oceanic flows. Summer profiles are more vertically sheared than either winter profiles or model profiles, for reasons that remain unclear.

scholarly journals On the Lagrangian description of steady surface gravity waves

2007 ◽  
Vol 589 ◽  
pp. 433-454 ◽  
Author(s):  
DIDIER CLAMOND
Keyword(s):  
Gravity Waves ◽  
Order Approximation ◽  
Mathematical Formulation ◽  
Finite Depth ◽  
Stokes Drift ◽  
Surface Gravity ◽  
Lagrangian Description ◽  
Perturbation Scheme ◽  
Third Order ◽  
Surface Gravity Waves

This paper concerns the mathematical formulation of two-dimensional steady surface gravity waves in a Lagrangian description of motion. It is demonstrated first that classical second-order Lagrangian Stokes-like approximations do not exactly represent a steady wave motion in the presence of net mass transport (Stokes drift). A general mathematically correct formulation is then derived. This derivation leads naturally to a Lagrangian Stokes-like perturbation scheme that is uniformly valid for all time – in other words, without secular terms. This scheme is illustrated, both for irrotational waves, with seventh-order and third-order approximations in deep water and finite depth, respectively, and for rotational waves with a third-order approximation of the Gerstner-like wave on finite depth. It is also shown that the Lagrangian approximations are more accurate than their Eulerian counterparts of the same order.

On the skewness of sea-surface elevation

1986 ◽  
Vol 164 ◽  
pp. 487-497 ◽  
Author(s):  
M. A. Srokosz ◽  
M. S. Longuet-Higgins
Keyword(s):  
Gravity Waves ◽  
Simple Relation ◽  
Statistical Properties ◽  
Sea Surface ◽  
Surface Elevation ◽  
Statistical Measure ◽  
Constant Ratio ◽  
Surface Gravity Waves ◽  
Different Types ◽  
The Waves

Surface skewness is a statistical measure of the vertical asymmetry of the air-sea interface – exemplified by the sharp crests and rounded troughs of surface gravity waves. Some authors have proposed a constant ratio between surface skewness and the ‘significant slope’ of the waves. Here it is shown theoretically that no such simple relation is to be expected.Wave records are of at least two different types; Eulerian (as made with a fixed probe) or Lagrangian (as with a free-floating buoy). The corresponding statistical properties are examined. At first sight it might appear that the degree of skewness in corresponding records would be different. However it is shown that to lowest order the skewness is invariant; only the apparent mean level is different, at second order.

Sign in / Sign up

Export Citation Format

Share Document