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"wave breaking"
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On the over-production of turbulence beneath surface waves in Reynolds-averaged Navier–Stokes models
In previous computational fluid dynamics studies of breaking waves, there has been a marked tendency to severely over-estimate turbulence levels, both pre- and post-breaking. This problem is most likely related to the previously described (though not sufficiently well recognized) conditional instability of widely used turbulence models when used to close Reynolds-averaged Navier–Stokes (RANS) equations in regions of nearly potential flow with finite strain, resulting in exponential growth of the turbulent kinetic energy and eddy viscosity. While this problem has been known for nearly 20 years, a suitable and fundamentally sound solution has yet to be developed. In this work it is demonstrated that virtually all commonly used two-equation turbulence closure models are unconditionally, rather than conditionally, unstable in such regions. A new formulation of the
$k$
–
$\\unicode[STIX]{x1D714}$
closure is developed which elegantly stabilizes the model in nearly potential flow regions, with modifications remaining passive in sheared flow regions, thus solving this long-standing problem. Computed results involving non-breaking waves demonstrate that the new stabilized closure enables nearly constant form wave propagation over long durations, avoiding the exponential growth of the eddy viscosity and inevitable wave decay exhibited by standard closures. Additional applications on breaking waves demonstrate that the new stabilized model avoids the unphysical generation of pre-breaking turbulence which widely plagues existing closures. The new model is demonstrated to be capable of predicting accurate pre- and post-breaking surface elevations, as well as turbulence and undertow velocity profiles, especially during transition from pre-breaking to the outer surf zone. Results in the inner surf zone are similar to standard closures. Similar methods for formally stabilizing other widely used closure models (
$k$
–
$\\unicode[STIX]{x1D714}$
and
$k$
–
$\\unicode[STIX]{x1D700}$
variants) are likewise developed, and it is recommended that these be utilized in future RANS simulations of surface waves. (In the above
$k$
is the turbulent kinetic energy density,
$\\unicode[STIX]{x1D714}$
is the specific dissipation rate, and
$\\unicode[STIX]{x1D700}$
is the dissipation.)
Journal Article
On a unified breaking onset threshold for gravity waves in deep and intermediate depth water
We revisit the classical but as yet unresolved problem of predicting the breaking onset of 2D and 3D irrotational gravity water waves. Based on a fully nonlinear 3D boundary element model, our numerical simulations investigate geometric, kinematic and energetic differences between maximally tall non-breaking waves and marginally breaking waves in focusing wave groups. Our study focuses initially on unidirectional domains with flat bottom topography and conditions ranging from deep to intermediate depth (depth to wavelength ratio from 1 to 0.2). Maximally tall non-breaking (maximally recurrent) waves are clearly separated from marginally breaking waves by their normalised energy fluxes localised near the crest tip region. The initial breaking instability occurs within a very compact region centred on the wave crest. On the surface, this reduces to the local ratio of the energy flux velocity (here the fluid velocity) to the crest point velocity for the tallest wave in the evolving group. This provides a robust threshold parameter for breaking onset for 2D wave packets propagating in uniform water depths from deep to intermediate. Further targeted study of representative cases of the most severe laterally focused 3D wave packets in deep and intermediate depth water shows that the threshold remains robust. These numerical findings for 2D and 3D cases are closely supported by our companion observational results. Warning of imminent breaking onset is detectable up to a fifth of a carrier wave period prior to a breaking event.
Journal Article
High-resolution direct simulation of deep water breaking waves: transition to turbulence, bubbles and droplets production
We present high-resolution three-dimensional (3-D) direct numerical simulations of breaking waves solving for the two-phase Navier–Stokes equations. We investigate the role of the Reynolds number (Re, wave inertia relative to viscous effects) and Bond number (Bo, wave scale over the capillary length) on the energy, bubble and droplet statistics of strong plunging breakers. We explore the asymptotic regimes at high Re and Bo, and compare with laboratory breaking waves. Energetically, the breaking wave transitions from laminar to 3-D turbulent flow on a time scale that depends on the turbulent Re up to a limiting value $Re_\\lambda \\sim 100$, consistent with the mixing transition in other canonical turbulent flows. We characterize the role of capillary effects on the impacting jet and ingested main cavity shape and subsequent fragmentation process, and extend the buoyant-energetic scaling from Deike et al. (J. Fluid Mech., vol. 801, 2016, pp. 91–129) to account for the cavity shape and its scale separation from the Hinze scale, $r_H$. We confirm two regimes in the bubble size distribution, $N(r/r_H)\\propto (r/r_H)^{-10/3}$ for $r>r_H$, and $\\propto (r/r_H)^{-3/2}$ for $r
Journal Article
Capillary effects on wave breaking
We investigate the influence of capillary effects on wave breaking through direct numerical simulations of the Navier–Stokes equations for a two-phase air–water flow. A parametric study in terms of the Bond number,
$\\mathit{Bo}$
, and the initial wave steepness,
${\\it\\epsilon}$
, is performed at a relatively high Reynolds number. The onset of wave breaking as a function of these two parameters is determined and a phase diagram in terms of
$({\\it\\epsilon},\\mathit{Bo})$
is presented that distinguishes between non-breaking gravity waves, parasitic capillaries on a gravity wave, spilling breakers and plunging breakers. At high Bond number, a critical steepness
${\\it\\epsilon}_{c}$
defines the onset of wave breaking. At low Bond number, the influence of surface tension is quantified through two boundaries separating, first gravity–capillary waves and breakers, and second spilling and plunging breakers; both boundaries scaling as
${\\it\\epsilon}\\sim (1+\\mathit{Bo})^{-1/3}$
. Finally the wave energy dissipation is estimated for each wave regime and the influence of steepness and surface tension effects on the total wave dissipation is discussed. The breaking parameter
$b$
is estimated and is found to be in good agreement with experimental results for breaking waves. Moreover, the enhanced dissipation by parasitic capillaries is consistent with the dissipation due to breaking waves.
Journal Article
Rapid Arctic Sea Ice Loss on the Synoptic Time Scale and Related Atmospheric Circulation Anomalies
Large sea ice loss on the synoptic time scale is examined in various subregions in the Arctic as well as at the pan-Arctic scale. It is found that the frequency of large daily sea ice loss (LDSIL) days is significantly correlated with the September sea ice extent over the Beaufort–Chukchi–Siberian Seas, the Laptev–Kara Seas, the central Arctic, and the all-Arctic regions, indicating a link between the synoptic sea ice variability and the interannual variability of the annual minimum sea ice extent. A composite analysis reveals dipoles of anomalous cyclones and anticyclones associated with LDSIL days. Different from the well-known Arctic dipole pattern, the east–west dipoles are found over the corresponding regions of LDSIL in the Arctic marginal seas and are associated with the increasing occurrence of Rossby wave breaking and atmospheric rivers. The anticyclones of the dipoles are persistent and quasi-stationary, reminiscent of blocking. The anomalous poleward flow between the cyclone and the anticyclone enhances the poleward transport of heat and water vapor in the lower troposphere. Although enhanced downward shortwave radiation, associated with reduced cloud fraction, is found in some regions, it is not collocated with the regions of LDSIL. In contrast, enhanced downward longwave radiation owing to increasing column water vapor shows good spatial correspondence with LDSIL, indicating the importance of atmospheric rivers in LDSIL events. Lead/lag composites with respect to the onset of LDSIL episodes reveal precursor wave trains spanning the midlatitudes. The wave trains have predominantly zonal energy propagation in the midlatitudes and do not show a clear link to tropical or subtropical forcing.
Journal Article
The Influence of the Madden–Julian Oscillation on Northern Hemisphere Winter Blocking
The persistent and quasi-stationary nature of atmospheric blocking is associated with long-lasting extreme weather conditions that influence much of the Northern Hemisphere during boreal winter. The Madden–Julian oscillation (MJO) has been previously shown to influence important factors for blocking, including Rossby wave breaking and the North Atlantic Oscillation (NAO). However, the extent to which the MJO influences blocking across the Northern Hemisphere is not yet fully understood.
Utilizing a two-dimensional blocking index, composites of North Pacific, North Atlantic, and European blocking are generated relative to MJO phase. In the west and central Pacific, all MJO phases demonstrate significant changes in blocking, particularly at high latitudes. A significant decrease in east Pacific and Atlantic blocking occurs following phase 3 of the MJO, characterized by enhanced convection over the tropical East Indian Ocean and suppressed convection in the west Pacific. The opposite-signed MJO heating during phase 7 is followed by a significant increase in east Pacific and Atlantic blocking. A significant decrease in European blocking follows MJO phase 4, with an increase after phase 6. The phase 6 European blocking is hypothesized to result from two preexisting conditions: 1) an anomalous anticyclone over the Atlantic and 2) a preceding negative Pacific–North American (PNA) pattern initialized and influenced by MJO heating.
Journal Article
Characteristics of Long-Duration Heavy Precipitation Events along the West Coast of the United States
Prolonged periods (e.g., several days or more) of heavy precipitation can result in sustained high-impact flooding. Herein, an investigation of long-duration heavy precipitation events (HPEs), defined as periods comprising ≥3 days with precipitation exceeding the climatological 95th percentile, is conducted for 1979–2019 for the U.S. West Coast, specifically Northern California. An objective flow-based categorization method is applied to identify principal large-scale flow patterns for the events. Four categories are identified and examined through composite analyses and case studies. Two of the categories are characterized by a strong zonal jet stream over the eastern North Pacific, while the other two are characterized by atmospheric blocking over the central North Pacific and the Bering Sea–Alaska region, respectively. The composites and case studies demonstrate that the flow patterns for the HPEs tend to remain in place for several days, maintaining strong baroclinicity and promoting occurrences of multiple cyclones in rapid succession near the West Coast. The successive cyclones result in persistent water vapor flux and forcing for ascent over Northern California, sustaining heavy precipitation. For the zonal jet patterns, cyclones affecting the West Coast tend to occur in the poleward jet exit region in association with cyclonic Rossby wave breaking. For the blocking patterns, cyclones tend to occur in association with anticyclonic Rossby wave breaking on the downstream flank of the block. For Bering Sea–Alaska blocking cases, cyclones can move into this region in conjunction with cyclonically breaking waves that extend into the eastern North Pacific from the upstream flank of the block.
Journal Article
Response of the Midlatitude Jets, and of Their Variability, to Increased Greenhouse Gases in the CMIP5 Models
This work documents how the midlatitude, eddy-driven jets respond to climate change using model output from phase 5 of the Coupled Model Intercomparison Project (CMIP5). The authors consider separately the North Atlantic, the North Pacific, and the Southern Hemisphere jets. The analysis is not limited to annual-mean changes in the latitude and speed of the jets, but also explores how the variability of each jet changes with increased greenhouse gases.
All jets are found to migrate poleward with climate change: the Southern Hemisphere jet shifts poleward by 2° of latitude between the historical period and the end of the twenty-first century in the representative concentration pathway 8.5 (RCP8.5) scenario, whereas both Northern Hemisphere jets shift by only 1°. In addition, the speed of the Southern Hemisphere jet is found to increase markedly (by 1.2 m s−1between 850 and 700 hPa), while the speed remains nearly constant for both jets in the Northern Hemisphere.
More importantly, it is found that the patterns of jet variability are a strong function of the jet position in all three sectors of the globe, and as the jets shift poleward the patterns of variability change. Specifically, for the Southern Hemisphere and the North Atlantic jets, the variability becomes less of a north–south wobbling and more of a pulsing (i.e., variation in jet speed). In contrast, for the North Pacific jet, the variability becomes less of a pulsing and more of a north–south wobbling. These different responses can be understood in terms of Rossby wave breaking, allowing the authors to explain most of the projected jet changes within a single dynamical framework.
Journal Article
Predicting the breaking strength of gravity water waves in deep and intermediate depth
We revisit the classical but as yet unresolved problem of predicting the strength of breaking 2-D and 3-D gravity water waves, as quantified by the amount of wave energy dissipated per breaking event. Following Duncan (J. Fluid Mech., vol. 126, 1983, pp. 507–520), the wave energy dissipation rate per unit length of breaking crest may be related to the fifth moment of the wave speed and the non-dimensional breaking strength parameter
$b$
. We use a finite-volume Navier–Stokes solver with large-eddy simulation resolution and volume-of-fluid surface reconstruction (Derakhti & Kirby, J. Fluid Mech., vol. 761, 2014a, pp. 464–506; J. Fluid Mech., vol. 790, 2016, pp. 553–581) to simulate nonlinear wave evolution, with a strong focus on breaking onset and postbreaking behaviour for representative cases of wave packets with breaking due to dispersive focusing and modulational instability. The present study uses these results to investigate the relationship between the breaking strength parameter
$b$
and the breaking onset parameter
$B$
proposed recently by Barthelemy et al. (J. Fluid Mech., vol. 841, 2018, pp. 463–488). The latter, formed from the local energy flux normalized by the local energy density and the local crest speed, simplifies, on the wave surface, to the ratio of fluid speed to crest speed. Following a wave crest, when
$B$
exceeds a generic threshold value at the wave crest (Barthelemy et al. 2018), breaking is imminent. We find a robust relationship between the breaking strength parameter
$b$
and the rate of change of breaking onset parameter
$\\text{d}B/\\text{d}t$
at the wave crest, as it transitions through the generic breaking onset threshold (
$B\\sim 0.85$
), scaled by the local period of the breaking wave. This result significantly refines previous efforts to express
$b$
in terms of a wave packet steepness parameter, which is difficult to define robustly and which does not provide a generically accurate forecast of the energy dissipated by breaking.
Journal Article
Reynolds stress turbulence modelling of surf zone breaking waves
Computational fluid dynamics is increasingly used to investigate the inherently complicated phenomenon of wave breaking. To date, however, no single model has proved capable of accurately simulating the breaking process across the entirety of the surf zone for both spilling and plunging breakers. The present study newly considers the Reynolds stress–$\\omega$ turbulence closure model for this purpose, where $\\omega$ is the specific dissipation rate. Novel stability analysis proves that, unlike two-equation closures (at least in their standard forms), the stress–$\\omega$ model is neutrally stable in the idealized potential flow region beneath surface waves. It thus naturally avoids unphysical exponential growth of turbulence prior to breaking, which has plagued numerous prior studies. The analysis is confirmed through simulation of a progressive surface wave train. The stress–$\\omega$ model is then applied to simulate a turbulent wave boundary layer, demonstrating superior accuracy relative to a two-equation model, especially during flow deceleration. Finally, the stress–$\\omega$ model is employed to simulate spilling and plunging breaking waves, with seemingly unprecedented accuracy. Specifically, the present work marks the first time that a single turbulence closure model collectively: (1) avoids turbulence over-production prior to breaking, (2) accurately predicts the breaking point, (3) provides reasonable evolution of turbulent normal stresses, while also (4) yielding accurate evolution of undertow velocity structure and magnitude across the surf zone, for both spilling and plunging cases. Differences in the predicted Reynolds shear stresses (hence flow resistance) are identified as key to the improved inner surf zone performance, relative to a state-of-the-art two-equation model.
Journal Article