Local versus volume-integrated turbulence and mixing in breaking internal waves on slopes

2017 ◽  
Vol 815 ◽  
pp. 169-198 ◽  
Author(s):  
Robert S. Arthur ◽  
Jeffrey R. Koseff ◽  
Oliver B. Fringer
Keyword(s):  
Froude Number ◽  
Internal Waves ◽  
Turbulent Mixing ◽  
Wave Breaking ◽  
Mixing Efficiency ◽  
Breaking Wave ◽  
Incoming Wave ◽  
Turbulent Dissipation ◽  
Efficiency Measures ◽  
Wave Properties

Using direct numerical simulations (DNS), we explore local and volume-integrated measures of turbulence and mixing in breaking internal waves on slopes. We consider eight breaking wave cases with a range of normalized pycnocline thicknesses $k\unicode[STIX]{x1D6FF}$, where $k$ is the horizontal wavenumber and $\unicode[STIX]{x1D6FF}$ is the pycnocline thickness, but with similar incoming wave properties. The energetics of wave breaking is quantified in terms of local turbulent dissipation and irreversible mixing using the method of Scotti & White (J. Fluid Mech., vol. 740, 2014, pp. 114–135). Local turbulent mixing efficiencies are calculated using the irreversible flux Richardson number $R_{f}^{\ast }$ and are found to be a function of the turbulent Froude number $Fr_{k}$. Volume-integrated measures of the turbulent mixing efficiency during wave breaking are also made, and are found to be functions of $k\unicode[STIX]{x1D6FF}$. The bulk turbulent mixing efficiency ranges from 0.25 to 0.37 and is maximized when $k\unicode[STIX]{x1D6FF}\approx 1$. In order to connect local and bulk mixing efficiency measures, the variation in the bulk turbulent mixing efficiency with $k\unicode[STIX]{x1D6FF}$ is related to the turbulent Froude number at which the maximum total mixing occurs over the course of the breaking event, $Fr_{k}^{max}$. We find that physically, $Fr_{k}^{max}$ is controlled by the vertical length scale of billows at the interface during wave breaking.

scholarly journals Scattering of Low-Mode Internal Waves at Finite Isolated Topography

2014 ◽  
Vol 44 (1) ◽  
pp. 359-383 ◽  
Author(s):  
Sonya Legg
Keyword(s):  
Internal Wave ◽  
Froude Number ◽  
Internal Waves ◽  
Wave Breaking ◽  
Internal Tides ◽  
Relative Height ◽  
Incoming Wave ◽  
Topographic Slope ◽  
Height Increase ◽  
Incoming Energy

Abstract A series of two-dimensional numerical simulations examine the breaking of first-mode internal waves at isolated ridges, independently varying the relative height of the topography compared to the depth of the ocean h0/H0; the relative steepness of the topographic slope compared to the slope of the internal wave group velocity γ; and the Froude number of the incoming internal wave Fr0. The fraction of the incoming wave energy, which is reflected back toward deep water, transmitted beyond the ridge, and lost to dissipation and mixing, is diagnosed from the simulations. For critical slopes, with γ = 1, the fraction of incoming energy lost at the slope scales approximately like h0/H0, independent of the incoming wave Froude number. For subcritical slopes, with γ < 1, waves break and lose a substantial proportion of their energy if the maximum Froude number, estimated as Frmax = Fr0/(1 − h0/H0)2, exceeds a critical value, found empirically to be about 0.3. The dissipation at subcritical slopes therefore increases as both incoming wave Froude number and topographic height increase. At critical slopes, the dissipation is enhanced along the slope facing the incoming wave. In contrast, at subcritical slopes, dissipation is small until the wave amplitude is sufficiently enhanced by the shoaling topography to exceed the critical Froude number; then large dissipation extends all the way to the surface. The results are shown to generalize to variable stratification and different topographies, including axisymmetric seamounts. The regimes for low-mode internal wave breaking at isolated critical and subcritical topography identified by these simulations provide guidance for the parameterization of the mixing due to radiated internal tides.

Turbulent mixing in a shear-free stably stratified two-layer fluid

1998 ◽  
Vol 354 ◽  
pp. 175-208 ◽  
Author(s):  
DAVID A. BRIGGS ◽  
JOEL H. FERZIGER ◽  
JEFFREY R. KOSEFF ◽  
STEPHEN G. MONISMITH
Keyword(s):  
Kinetic Energy ◽  
Froude Number ◽  
Internal Waves ◽  
Mixed Layer ◽  
Turbulent Mixing ◽  
Large Scale ◽  
Source Region ◽  
Buoyancy Flux ◽  
Mixing Efficiency ◽  
Principal Mechanism

Direct numerical simulation is used to examine turbulent mixing in a shear-free stably stratified fluid. Energy is continuously supplied to a small region to maintain a well-developed kinetic energy profile, as in an oscillating grid flow (Briggs et al. 1996; Hopfinger & Toly 1976; Nokes 1988). A microscale Reynolds number of 60 is maintained in the source region. The turbulence forms a well-mixed layer which diffuses from the source into the quiescent fluid below. Turbulence transport at the interface causes the mixed layer to grow under weakly stratified conditions. When the stratification is strong, large-scale turbulent transport is inactive and pressure transport becomes the principal mechanism for the growth of the turbulence layer. Down-gradient buoyancy flux is present in the large scales; however, far from the source, weak counter-gradient fluxes appear in the medium to small scales. The production of internal waves and counter-gradient fluxes rapidly reduces the mixing when the turbulent Froude number is lower than unity. When the stratification is weak, the turbulence is strong enough to break up the density interface and transport fluid parcels of different density over large vertical distances. As the stratification intensifies, turbulent eddies flatten against the interface creating anisotropy and internal waves. The dominant entrainment mechanism is then scouring. Mixing efficiency, defined as the ratio of buoyancy flux to available kinetic energy, exhibits a similar dependence on Froude number to other stratified flows (Holt et al. 1992; Lienhard & Van Atta 1990). However, using the anisotropy of the turbulence to define an alternative mixing efficiency and Froude number improves the correlation and allows local scaling.

Models of energy loss from internal waves breaking in the ocean

2017 ◽  
Vol 836 ◽  
pp. 72-116 ◽  
Author(s):  
S. A. Thorpe
Keyword(s):  
Exact Solution ◽  
Internal Wave ◽  
Internal Waves ◽  
Wave Breaking ◽  
Convective Instability ◽  
Helmholtz Instability ◽  
Turbulent Dissipation ◽  
The Waves ◽  
Data Representative ◽  
Made In

The supply of energy to the internal wave field in the ocean is, in total, sufficient to support the mixing required to maintain the stratification of the ocean, but can the required rates of turbulent dissipation in mid-water be sustained by breaking internal waves? It is assumed that turbulence occurs in regions where the field of motion can be represented by an exact solution of the equations that describe waves propagating through a uniformly stratified fluid and becoming unstable. Two instabilities leading to wave breaking are examined, convective instability and shear-induced Kelvin–Helmholtz instability. Models are constrained by data representative of the mid-water ocean. Calculations of turbulent dissipation are first made on the assumption that all the waves representing local breaking have the same steepness, $s$, and frequency, $\unicode[STIX]{x1D70E}$. For some ranges of $s$ and $\unicode[STIX]{x1D70E}$, breaking can support the required transfer of energy to turbulence. For convective instability this proves possible for sufficiently large $s$, typically exceeding 2.0, over a range of $\unicode[STIX]{x1D70E}$, while for shear-induced instability near-inertial waves are required. Relaxation of the constraint that the model waves all have the same $s$ and $\unicode[STIX]{x1D70E}$ requires new assumptions about the nature and consequences of wave breaking. Examples predict an overall dissipation consistent with the observed rates. Further observations are, however, required to test the validity of the assumptions made in the models and, in particular, to determine the nature and frequency of internal wave breaking in the mid-water ocean.

scholarly journals Turbulent Mixing and Exchange with Interior Waters on Sloping Boundaries

2012 ◽  
Vol 42 (6) ◽  
pp. 910-927 ◽  
Author(s):  
Eric Kunze ◽  
Chris MacKay ◽  
Erika E. McPhee-Shaw ◽  
Katie Morrice ◽  
James B. Girton ◽  
...  
Keyword(s):  
Turbulent Mixing ◽  
World Ocean ◽  
Mixing Efficiency ◽  
Turbulent Layer ◽  
Turbulent Dissipation ◽  
Eddy Diffusivities ◽  
Dissipation Rates ◽  
Mixing Dynamics ◽  
Order Of Magnitude ◽  
Internal Wave Generation

Abstract Microstructure measurements along the axes of Monterey and Soquel Submarine Canyons reveal 200–300-m-thick well-stratified turbulent near-bottom layers with average turbulent kinetic energy dissipation rates 〈ɛ〉 = 4 × 10−8 W kg−1 and eddy diffusivities K = 16 × 10−4 m2 s−1 (assuming mixing efficiency γ = 0.2) to at least thalweg depths of 1200 m. Turbulent dissipation rates are an order of magnitude lower in overlying waters, whereas buoyancy frequencies are only 25% higher. Well-mixed bottom boundary layer thicknesses hN are an order of magnitude thinner than the stratified turbulent layer (hN ≪ hɛ). Because well-stratified turbulent layers are commonly observed above slopes, arguments that mixing efficiency should be reduced on sloping boundaries do not hold in cases of energetic internal-wave generation or interaction with topography. An advective–diffusive balance is used to infer velocities and transports, predicting horizontal upslope flows of 10–50 m day−1. Extrapolating this estimate globally suggests that canyon turbulence may contribute 2–3 times as much diapycnal transport to the World Ocean as interior mixing. The upcanyon turbulence-driven transports are not uniform, and the resulting upslope convergences will drive exchange between the turbulent layer and more quiescent interior. Predicted density surfaces of detrainment and entrainment are consistent with observed isopycnals of intermediate nepheloid and clear layers. These data demonstrate that turbulent mixing dynamics on sloping topography are fundamentally 2D or 3D in the ocean, so they cannot be accurately described by 1D models.

scholarly journals Characteristics of Breaking Wave Forces on Piles over a Permeable Seabed

2021 ◽  
Vol 9 (5) ◽  
pp. 520
Author(s):  
Zhenyu Liu ◽  
Zhen Guo ◽  
Yuzhe Dou ◽  
Fanyu Zeng
Keyword(s):  
Wave Breaking ◽  
Stokes Equations ◽  
Slope Angle ◽  
Wave Force ◽  
Breaking Waves ◽  
Offshore Wind ◽  
Secondary Wave ◽  
Wave Forces ◽  
Breaking Wave ◽  
Breaking Wave Forces

Most offshore wind turbines are installed in shallow water and exposed to breaking waves. Previous numerical studies focusing on breaking wave forces generally ignored the seabed permeability. In this paper, a numerical model based on Volume-Averaged Reynolds Averaged Navier–Stokes equations (VARANS) is employed to reveal the process of a solitary wave interacting with a rigid pile over a permeable slope. Through applying the Forchheimer saturated drag equation, effects of seabed permeability on fluid motions are simulated. The reliability of the present model is verified by comparisons between experimentally obtained data and the numerical results. Further, 190 cases are simulated and the effects of different parameters on breaking wave forces on the pile are studied systematically. Results indicate that over a permeable seabed, the maximum breaking wave forces can occur not only when waves break just before the pile, but also when a “secondary wave wall” slams against the pile, after wave breaking. With the initial wave height increasing, breaking wave forces will increase, but the growth can decrease as the slope angle and permeability increase. For inclined piles around the wave breaking point, the maximum breaking wave force usually occurs with an inclination angle of α = −22.5° or 0°.

scholarly journals Assessment of Numerical Methods for Plunging Breaking Wave Predictions

2021 ◽  
Vol 9 (3) ◽  
pp. 264
Author(s):  
Shanti Bhushan ◽  
Oumnia El Fajri ◽  
Graham Hubbard ◽  
Bradley Chambers ◽  
Christopher Kees
Keyword(s):  
Solitary Wave ◽  
Wave Breaking ◽  
Large Scale ◽  
Turbulence Models ◽  
Navier Stokes ◽  
Wave Crest ◽  
Breaking Wave ◽  
Rans Turbulence Models ◽  
Run Up ◽  
Better Than

This study evaluates the capability of Navier–Stokes solvers in predicting forward and backward plunging breaking, including assessment of the effect of grid resolution, turbulence model, and VoF, CLSVoF interface models on predictions. For this purpose, 2D simulations are performed for four test cases: dam break, solitary wave run up on a slope, flow over a submerged bump, and solitary wave over a submerged rectangular obstacle. Plunging wave breaking involves high wave crest, plunger formation, and splash up, followed by second plunger, and chaotic water motions. Coarser grids reasonably predict the wave breaking features, but finer grids are required for accurate prediction of the splash up events. However, instabilities are triggered at the air–water interface (primarily for the air flow) on very fine grids, which induces surface peel-off or kinks and roll-up of the plunger tips. Reynolds averaged Navier–Stokes (RANS) turbulence models result in high eddy-viscosity in the air–water region which decays the fluid momentum and adversely affects the predictions. Both VoF and CLSVoF methods predict the large-scale plunging breaking characteristics well; however, they vary in the prediction of the finer details. The CLSVoF solver predicts the splash-up event and secondary plunger better than the VoF solver; however, the latter predicts the plunger shape better than the former for the solitary wave run-up on a slope case.

Entrainment and mixing in stratified shear flows

2001 ◽  
Vol 428 ◽  
pp. 349-386 ◽  
Author(s):  
E. J. STRANG ◽  
H. J. S. FERNANDO
Keyword(s):  
Internal Waves ◽  
Richardson Number ◽  
Transition Period ◽  
Lower Layer ◽  
Buoyancy Flux ◽  
Shear Instability ◽  
Mixing Efficiency ◽  
Buoyancy Frequency ◽  
Entrainment Rate ◽  
Turbulent Eddies

The results of a laboratory experiment designed to study turbulent entrainment at sheared density interfaces are described. A stratified shear layer, across which a velocity difference ΔU and buoyancy difference Δb is imposed, separates a lighter upper turbulent layer of depth D from a quiescent, deep lower layer which is either homogeneous (two-layer case) or linearly stratified with a buoyancy frequency N (linearly stratified case). In the parameter ranges investigated the flow is mainly determined by two parameters: the bulk Richardson number RiB = ΔbD/ΔU2 and the frequency ratio fN = ND=ΔU.When RiB > 1.5, there is a growing significance of buoyancy effects upon the entrainment process; it is observed that interfacial instabilities locally mix heavy and light fluid layers, and thus facilitate the less energetic mixed-layer turbulent eddies in scouring the interface and lifting partially mixed fluid. The nature of the instability is dependent on RiB, or a related parameter, the local gradient Richardson number Rig = N2L/ (∂u/∂z)2, where NL is the local buoyancy frequency, u is the local streamwise velocity and z is the vertical coordinate. The transition from the Kelvin–Helmholtz (K-H) instability dominated regime to a second shear instability, namely growing Hölmböe waves, occurs through a transitional regime 3.2 < RiB < 5.8. The K-H activity completely subsided beyond RiB ∼ 5 or Rig ∼ 1. The transition period 3.2 < RiB < 5 was characterized by the presence of both K-H billows and wave-like features, interacting with each other while breaking and causing intense mixing. The flux Richardson number Rif or the mixing efficiency peaked during this transition period, with a maximum of Rif ∼ 0.4 at RiB ∼ 5 or Rig ∼ 1. The interface at 5 < RiB < 5.8 was dominated by ‘asymmetric’ interfacial waves, which gradually transitioned to (symmetric) Hölmböe waves at RiB > 5:8.Laser-induced fluorescence measurements of both the interfacial buoyancy flux and the entrainment rate showed a large disparity (as large as 50%) between the two-layer and the linearly stratified cases in the range 1.5 < RiB < 5. In particular, the buoyancy flux (and the entrainment rate) was higher when internal waves were not permitted to propagate into the deep layer, in which case more energy was available for interfacial mixing. When the lower layer was linearly stratified, the internal waves appeared to be excited by an ‘interfacial swelling’ phenomenon, characterized by the recurrence of groups or packets of K-H billows, their degeneration into turbulence and subsequent mixing, interfacial thickening and scouring of the thickened interface by turbulent eddies.Estimation of the turbulent kinetic energy (TKE) budget in the interfacial zone for the two-layer case based on the parameter α, where α = (−B + ε)/P, indicated an approximate balance (α ∼ 1) between the shear production P, buoyancy flux B and the dissipation rate ε, except in the range RiB < 5 where K-H driven mixing was active.

Flow Geometry Effects on the Turbulent Mixing Efficiency

2006 ◽  
Vol 128 (4) ◽  
pp. 874-879 ◽  
Author(s):  
Roberto C. Aguirre ◽  
Jennifer C. Nathman ◽  
Haris C. Catrakis
Keyword(s):  
Shear Layer ◽  
Turbulent Mixing ◽  
Large Scale ◽  
Mixture Fraction ◽  
Mixing Efficiency ◽  
Developed Turbulence ◽  
Planar Shear ◽  
Flow Geometry ◽  
Schmidt Numbers ◽  
Geometry Effects

Flow geometry effects are examined on the turbulent mixing efficiency quantified as the mixture fraction. Two different flow geometries are compared at similar Reynolds numbers, Schmidt numbers, and growth rates, with fully developed turbulence conditions. The two geometries are the round jet and the single-stream planar shear layer. At the flow conditions examined, the jet exhibits an ensemble-averaged mixing efficiency which is approximately double the value for the shear layer. This substantial difference is explained fluid mechanically in terms of the distinct large-scale entrainment and mixing-initiation environments and is therefore directly due to flow geometry effects.

Detailed Study on Breaking Wave Interactions With a Jacket Structure Based on Experimental Investigations

2017 ◽  
Vol 140 (2) ◽  
Author(s):  
Jithin Jose ◽  
Olga Podrażka ◽  
Ove Tobias Gudmestad ◽  
Witold Cieślikiewicz
Keyword(s):  
Wind Turbines ◽  
Wave Breaking ◽  
Offshore Structures ◽  
Offshore Wind ◽  
Wave Forces ◽  
Breaking Wave ◽  
Offshore Wind Turbines ◽  
Wave Parameters ◽  
Wave Slamming ◽  
Breaking Wave Forces

Wave breaking is one of the major concerns for offshore structures installed in shallow waters. Impulsive breaking wave forces sometimes govern the design of such structures, particularly in areas with a sloping sea bottom. Most of the existing offshore wind turbines were installed in shallow water regions. Among fixed-type support structures for offshore wind turbines, jacket structures have become popular in recent times as the water depth for fixed offshore wind structures increases. However, there are many uncertainties in estimating breaking wave forces on a jacket structure, as only a limited number of past studies have estimated these forces. Present study is based on the WaveSlam experiment carried out in 2013, in which a jacket structure of 1:8 scale was tested for several breaking wave conditions. The total and local wave slamming forces are obtained from the experimental measured forces, using two different filtering methods. The total wave slamming forces are filtered from the measured forces using the empirical mode decomposition (EMD) method, and local slamming forces are obtained by the frequency response function (FRF) method. From these results, the peak slamming forces and slamming coefficients on the jacket members are estimated. The breaking wave forces are found to be dependent on various breaking wave parameters such as breaking wave height, wave period, wave front asymmetry, and wave-breaking positions. These wave parameters are estimated from the wave gauge measurements taken during the experiment. The dependency of the wave slamming forces on these estimated wave parameters is also investigated.

Study Based on FLUENT of Broken Internal Waves in Different Slope Angles

2014 ◽  
Vol 638-640 ◽  
pp. 1769-1777
Author(s):  
Zi Tong Yan ◽  
Liang Qiu Cheng ◽  
Feng Yi ◽  
Tai Zhong Chen ◽  
Han Sun ◽  
...  
Keyword(s):  
Internal Waves ◽  
Solitary Waves ◽  
Wave Breaking ◽  
Slope Angle ◽  
Ecological Environment ◽  
Internal Solitary Waves ◽  
Propagation Process ◽  
Numerical Wave Flume ◽  
Wave Flume ◽  
New Methods

Internal waves will break in the process of communication, the broken will make water in upper and lower mixing, which has significant influence on the hydrodynamic and layered characteristics of density stratification of the water. In order to reveal the propagation of internal solitary waves, a 3d numerical wave flume was built. The research of the propagation of internal solitary waves in the regular topography and broken on slopes was based on FLUENT. Comparing the fragmentation degree of different slope angle and researching the energy dissipation of the wave propagation process , which are supposed to successfully match the results with the experiment results, can provide new methods and means for the further study of internal wave breaking characteristics and the improvement of ecological environment of water bodies.

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