Mass transport under sea waves propagating over a rippled bed

1996 ◽  
Vol 314 ◽  
pp. 247-265 ◽  
Author(s):  
G. Vittori ◽  
P. Blondeaux
Keyword(s):  
Boundary Layer ◽  
Mass Transport ◽  
Outer Edge ◽  
Bottom Boundary Layer ◽  
Sea Waves ◽  
Bottom Boundary ◽  
Order Of Magnitude ◽  
Wave Slope ◽  
Rippled Bed ◽  
Sea Wave

Mass transport under a progressive sea wave propagating over a rippled bed is investigated. Wave amplitudes a* of the same order of magnitude as that of the boundary layer thickness δ* and of the ripple wavelength l* are considered. All the above quantities are assumed to be much smaller than the wavelength L* of the sea wave and much larger than the amplitude 2ε* of the ripples. The analysis is carried out up to the second order in the wave slope a*/L* and in the parameter ε*/δ* which is a measure of ripple steepness. Because of these assumptions, the slow damping of wave amplitude in the direction of wave propagation is taken into account. Attention is focused on the bottom boundary layer where an order (ε*/δ*)2 correction of the steady velocity components described by Longuet-Higgins (1953) is found. This correction persists at the outer edge of the bottom boundary layer and affects the solution in the entire water column.

scholarly journals Dissipation of Turbulent Kinetic Energy in the Oscillating Bottom Boundary Layer of a Large Shallow Lake

2020 ◽  
Vol 37 (3) ◽  
pp. 517-531 ◽  
Author(s):  
Aidin Jabbari ◽  
Leon Boegman ◽  
Reza Valipour ◽  
Danielle Wain ◽  
Damien Bouffard
Keyword(s):  
Boundary Layer ◽  
Kinetic Energy ◽  
Turbulent Kinetic Energy ◽  
Bottom Boundary Layer ◽  
Inertial Subrange ◽  
Order Structure ◽  
Inertial Method ◽  
Bottom Boundary ◽  
Law Of The Wall ◽  
Order Of Magnitude

AbstractMixing rates and biogeochemical fluxes are commonly estimated from the rate of dissipation of turbulent kinetic energy ε as measured with a single instrument and processing method. However, differences in measurements of ε between instruments/methods often vary by one order of magnitude. In an effort to identify error in computing ε, we have applied four common methods to data from the bottom boundary layer of Lake Erie. We applied the second-order structure function method (SFM) to velocity measurements from an acoustic Doppler current profiler, using both canonical and anisotropy-adjusted Kolmogorov constants, and compared the results with those computed from the law of the wall, Batchelor fitting to temperature gradient microstructure, and inertial subrange fitting to acoustic Doppler velocimeter data. The ε from anisotropy-adjusted constants in SFM increased by a factor of 6 or more at 0.2 m above the bed and showed a better agreement with microstructure and inertial method estimations. The maximum difference between SFM ε, computed using adjusted and canonical constants, and microstructure values was 25% and 50%, respectively. This difference was 30% and 55%, respectively, for those from inertial subrange fitting at times of high-intensity turbulence (Reynolds number at 1 m above the bed of more than 2 × 104). Comparison of the SFM ε to those from law of the wall was often poor, with errors as large as one order of magnitude. From the considerable improvement in ε estimates near the bed, anisotropy-adjusted Kolmogorov constants should be applied to compute dissipation in geophysical boundary layers.

Observational evidence of diapycnal upwelling in a bottom enhanced mixing environment

2020 ◽  
Author(s):  
Marcus Dengler ◽  
Martin Visbeck ◽  
Toste Tanhua ◽  
Jan Lüdke ◽  
Madelaine Freund
Keyword(s):  
Boundary Layer ◽  
Continental Slope ◽  
Center Of Mass ◽  
Mixing Layer ◽  
Observational Evidence ◽  
Bottom Boundary Layer ◽  
Turbulent Dissipation ◽  
Bottom Boundary ◽  
Order Of Magnitude ◽  
Upward Displacement

<p>In the framework of the Peruvian Oxygen minimum zone System Tracer Release Experiment (POSTRE) about 70 kg of trifluoromethyl sulfur pentafluoride (SF5CF3) was injected into the bottom boundary layer of the upper Peruvian continental slope at 250m depth in October 2015. Three different injection sites, at 10°45’S, 12°20’S and 14°S were selected. At the tracer release sites and due to tide-topography interaction, mixing above the upper continental slope of Peru was intensified. Turbulent dissipation rates increase by about an order of magnitude in lower 50 to 100m above the bottom. During previous tracer release experiments, where tracer was injected into the stratified mixing layer above the bottom boundary layer, a change of the center of mass toward higher densities resulted. Newer theories suggest that this diapycnal downwelling is balanced by a diapycnal upwelling within the bottom boundary layer. Indeed, during the tracer survey it was found that the density of tracer’s center of mass had decreased by 0.13 kg m<sup>-3</sup>. This corresponds to an upward displacement of 70-100m. Using microsctructure shear data from 8 cruises, we obtain a diapycnal velocity of about 0.5 m day<sup>-1</sup> within the bottom boundary layer. This suggests that on average, the tracer was trapped within the bottom boundary layer for a period between 1.5 and 3 month. Overall, our tracer study provides the first observational evidence of diapycnal upwelling occurring within the bottom boundary layer of a bottom enhanced mixing environment and supports recent ideas of a vigorous global overturning circulation.</p>

Mass transport in a turbulent boundary layer under a progressive water wave

1984 ◽  
Vol 146 ◽  
pp. 303-312 ◽  
Author(s):  
S. J. Jacobs
Keyword(s):  
Boundary Layer ◽  
Mass Transport ◽  
Water Wave ◽  
Approximate Solutions ◽  
Reynolds Numbers ◽  
Bottom Boundary Layer ◽  
Bottom Boundary ◽  
Transport Velocity ◽  
Mass Transport Velocity ◽  
Theoretical Results

The bottom boundary layer under a progressive water wave is studied using Saffman's turbulence model. Saffman's equations are analysed asymptotically for the case Re [Gt ] 1, where Re is a Reynolds number based on a characteristic magnitude of the orbital velocity and a characteristic orbital displacement. Approximate solutions for the mass-transport velocity at the edge of the boundary layer and for the bottom stress are obtained, and Taylor's formula for the rate of energy dissipation is verified. The theoretical results are found to agree well with observations for sufficiently large Reynolds numbers.

Mass transport in the bottom boundary layer of cnoidal waves

1976 ◽  
Vol 74 (3) ◽  
pp. 401-413 ◽  
Author(s):  
M. De St Q. Isaacson
Keyword(s):  
Boundary Layer ◽  
Mass Transport ◽  
Wave Theory ◽  
Bottom Boundary Layer ◽  
Inviscid Fluid ◽  
Viscous Boundary Layer ◽  
Cnoidal Waves ◽  
Bottom Boundary ◽  
Transport Velocity ◽  
Mass Transport Velocity

This study deals with the mass-transport velocity within the bottom boundary layer of cnoidal waves progressing over a smooth horizontal bed. Mass-transport velocity distributions through the boundary layer are derived and compared with that predicted by Longuet-Higgins (1953) for sinusoidal waves. The mass transport at the outer edge of the boundary layer is compared with various theoretical results for an inviscid fluid based on cnoidal wave theory and also with previous experimental results. The effect of the viscous boundary layer is to establish uniquely the bottom mass transport and this is appreciably greater than the somewhat arbitrary prediction for an inviscid fluid.

Sand ripples under sea waves. Part 4. Tile ripple formation

2001 ◽  
Vol 447 ◽  
pp. 227-246 ◽  
Author(s):  
P. C. ROOS ◽  
P. BLONDEAUX
Keyword(s):  
Boundary Layer ◽  
Three Dimensional ◽  
Resonant Interaction ◽  
Bottom Boundary Layer ◽  
Small Scale ◽  
Sea Waves ◽  
Nonlinear Stability Analysis ◽  
Sandy Bottom ◽  
Bottom Boundary ◽  
Ripple Formation

We investigate the formation of small-scale three-dimensional bedforms due to interactions of an erodible bed with a sea wave that obliquely approaches the coast, being partially reflected at the beach. In this case the trajectories of fluid particles at the top of the bottom boundary layer are ellipses in the horizontal plane, the axes of which depend on the angle of wave incidence and the distance from the shore. A weakly nonlinear stability analysis of an initially flat, cohesionless, sandy bottom is performed. We focus on the resonant interaction of three perturbation components. The results show that these elliptical forcing conditions are responsible for the formation of both brick-pattern ripples and tile ripples. In particular tile ripples are associated with a flow at the top of the bottom boundary layer which is near-circular (ellipticity close to one), whereas brick-pattern ripples are related to a unidirectional oscillatory flow (zero ellipticity).

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