Using direct numerical simulations (DNS), we investigate the structure and energetics of breaking internal waves on slopes. We employ a Navier–Stokes code in an idealized three-dimensional domain ...where an internal solitary wave of depression impinges upon a sloping bottom. Seven cases with varying initial wave amplitude and bathymetric slope, but constant wave Reynolds number
$\mathit{Re}_{w}$
are considered. Volume-integrated values of dissipation and irreversible mixing are related to the density and velocity structure of the wave throughout the breaking process. The majority of dissipation (63 %) occurs along the no-slip bottom boundary. Most of the remaining dissipation (35 %) and nearly all irreversible mixing occurs in the interior after breaking, when density overturns are present at the interface. Breaking introduces three-dimensionality to the flow field that is driven by the lateral breakdown of density overturns and the lobe–cleft instability typical of gravity currents. The resulting longitudinal rolls (streamwise vorticity) increase dissipation by roughly 8 % and decrease irreversible mixing by roughly 20 % when compared with a similar two-dimensional simulation. The bulk mixing efficiency is shown to increase for larger and smaller values of the internal Iribarren number
${\it\xi}$
, with a minimum for intermediate values of
${\it\xi}$
and a peak near
${\it\xi}=0.8$
for plunging breakers. This trend is explained by the degree of two-dimensionality in the flow, and agrees with previous results in the literature after accounting for Reynolds number effects. Local turbulence quantities are also calculated at ‘virtual moorings’, and a location upslope of the breakpoint but downslope of the intersection of the pycnocline and the bottom is shown to provide a signal that is most representative of the volume-integrated dissipation and mixing results.
We study the effects of Archimedes number $Ar$ and volume fraction $\phi$ in three-dimensional, high concentration and monodispersed particle suspensions. Simulations were conducted using the ...immersed boundary method with direct forcing for triply periodic cases and with $Ar = 21 - 23\,600$ and $\phi = 0.22 - 0.43$. We find that cluster formation is strongly dependent on the Archimedes number but weakly dependent on the volume fraction for concentrated suspensions. Particles in low $Ar$ cases are characterized by less frequent but long-lived clusters, resulting in higher hindered settling, while high $Ar$ cases consist of more frequent but short-lived clusters, leading to reduced hindered settling. By quantifying the effects of collisions on the hydrodynamic fluctuations, we show that the lifespan of clusters for the low $Ar$ cases is longer because particles are subject to appreciable wake interactions without collisions. On the other hand, clusters for high $Ar$ cases are broken before being subject to appreciable wake interactions due to frequent collisions, leading to a shorter cluster lifespan. The results imply that there exists an $Ar$ for particles in fluidized bed reactors that can reduce short circuiting due to clustering and enhance performance by maximizing flow–particle interactions. This result is consistent with existing reactor studies demonstrating that optimal particle diameters and $Ar$ values correspond to cases with short-lived clusters, although more thorough experimental studies are needed.
We study the effects of fluid–particle and particle–particle interactions in a three-dimensional monodispersed reactor with unstable fluidization. Simulations were conducted using the immersed ...boundary method for particle Reynolds numbers of 20–70 with an Archimedes number of 23 600. Two different flow regimes were identified as a function of the particle Reynolds number. For low particle Reynolds numbers ($20 < Re_p < 40$), the porosity is relatively low and the particle dynamics are dominated by interparticle collisions that produce anisotropic particle velocity fluctuations. The relative importance of hydrodynamic effects increases with increasing particle Reynolds number, leading to a minimized anisotropy in the particle velocity fluctuations at an intermediate particle Reynolds number. For high particle Reynolds numbers ($Re_p > 40$), the particle dynamics are dominated by hydrodynamic effects, leading to decreasing and more anisotropic particle velocity fluctuations. A sharp increase in the anisotropy occurs when the particle Reynolds number increases from 40 to 50, corresponding to a transition from a regime in which collision and hydrodynamic effects are equally important (regime 1) to a hydrodynamic-dominated regime (regime 2). The results imply an optimum particle Reynolds number of roughly 40 for the investigated Archimedes number of 23 600 at which mixing in the reactor is expected to peak, which is consistent with reactor studies showing peak performance at a similar particle Reynolds number and with a similar Archimedes number. Results also show that maximum effective collisions are attained at intermediate particle Reynolds number. Future work is required to relate optimum particle Reynolds number to Archimedes number.
We use the results of a direct numerical simulation (DNS) with a particle-tracking model to investigate three-dimensional transport by breaking internal gravity waves on slopes. Onshore transport ...occurs within an upslope surge of dense fluid after breaking. Offshore transport occurs due to an intrusion of mixed fluid that propagates offshore and resembles an intermediate nepheloid layer (INL). Entrainment of particles into the INL is related to irreversible mixing of the density field during wave breaking. Maximum onshore and offshore transport are calculated as a function of initial particle position, and can be of the order of the initial wave length scale for particles initialized within the breaking region. An effective cross-shore dispersion coefficient is also calculated, and is roughly three orders of magnitude larger than the molecular diffusivity within the breaking region. Particles are transported laterally due to turbulence that develops during wave breaking, and this lateral spreading is quantified with a lateral turbulent diffusivity. Lateral turbulent diffusivity values calculated using particles are elevated by more than one order of magnitude above the molecular diffusivity, and are shown to agree well with turbulent diffusivities estimated using a generic length scale turbulence closure model. Based on a favourable comparison of DNS results with those of a similar two-dimensional case, we use two-dimensional simulations to extend our cross-shore transport results to additional wave amplitude and bathymetric slope conditions.
This paper summarizes the findings of a workshop convened in the United States in 2018 to discuss methods in coastal and estuarine modeling and to propose key areas of research and development needed ...to improve their accuracy and reliability. The focus of this paper is on physical processes, and we provide an overview of the current state-of-the-art based on presentations and discussions at the meeting, which revolved around the four primary themes of parameterizations, numerical methods, in-situ and remote-sensing measurements, and high-performance computing. A primary outcome of the workshop was agreement on the need to reduce subjectivity and improve reproducibility in modeling of physical processes in the coastal ocean. Reduction of subjectivity can be accomplished through development of standards for benchmarks, grid generation, and validation, and reproducibility can be improved through development of standards for input/output, coupling and model nesting, and reporting. Subjectivity can also be reduced through more engagement with the applied mathematics and computer science communities to develop methods for robust parameter estimation and uncertainty quantification. Such engagement could be encouraged through more collaboration between the forward and inverse modeling communities and integration of more applied math and computer science into oceanography curricula. Another outcome of the workshop was agreement on the need to develop high-resolution models that scale on advanced HPC systems to resolve, rather than parameterize, processes with horizontal scales that range between the depth and the internal Rossby deformation scale. Unsurprisingly, more research is needed on parameterizations of processes at scales smaller than the depth, including parameterizations for drag (including bottom roughness, bedforms, vegetation and corals), wave breaking, and air–sea interactions under strong wind conditions. Other topics that require significantly more work to better parameterize include nearshore wave modeling, sediment transport modeling, and morphodynamics. Finally, it was agreed that coastal models should be considered as key infrastructure needed to support research, just like laboratory facilities, field instrumentation, and research vessels. This will require a shift in the way proposals related to coastal ocean modeling are reviewed and funded.
•Standards are needed for I/O, benchmarks, coupling/nesting, grids, and validation.•Methods for robust parameter estimation and uncertainty quantification are needed.•Models should resolve scales between the depth and the Rossby deformation scale.•Models for bottom drag, wave breaking, and air–sea interactions should be improved.•Improved sediment transport, nearshore circulation, morphodynamics models are needed.
Most commonly used models for turbulent mixing in the ocean rely on a background stratification against which turbulence must work to stir the fluid. While this background stratification is typically ...well defined in idealized numerical models, it is more difficult to capture in observations. Here, a potential discrepancy in ocean mixing estimates due to the chosen calculation of the background stratification is explored using direct numerical simulation data of breaking internal waves on slopes. Two different methods for computing the buoyancy frequency
$N$
, one based on a three-dimensionally sorted density field (often used in numerical models) and the other based on locally sorted vertical density profiles (often used in the field), are used to quantify the effect of
$N$
on turbulence quantities. It is shown that how
$N$
is calculated changes not only the flux Richardson number
$R_{f}$
, which is often used to parameterize turbulent mixing, but also the turbulence activity number or the Gibson number
$Gi$
, leading to potential errors in estimates of the mixing efficiency using
$Gi$
-based parameterizations.
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
$k\unicodeSTIX{x1D6FF}$
, where
$k$
is the horizontal wavenumber and
$\unicodeSTIX{x1D6FF}$
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
$k\unicodeSTIX{x1D6FF}$
. The bulk turbulent mixing efficiency ranges from 0.25 to 0.37 and is maximized when
$k\unicodeSTIX{x1D6FF}\approx 1$
. In order to connect local and bulk mixing efficiency measures, the variation in the bulk turbulent mixing efficiency with
$k\unicodeSTIX{x1D6FF}$
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.
A number of studies have illustrated the utility of environmental DNA (eDNA) for detecting marine vertebrates. However, little is known about the fate and transport of eDNA in the ocean, thus ...limiting the ability to interpret eDNA measurements. In the present study, we explore how fate and transport processes affect oceanic eDNA in Monterey Bay, California, USA (MB). Regional ocean modeling predictions of advection and mixing are used for an approximately 10,000 km2 area in and around MB to simulate the transport of eDNA. These predictions along with realistic settling rates and first-order decay rate constants are applied as inputs into a particle tracking model to investigate the displacement and spread of eDNA from its release location. We found that eDNA can be transported on the order of tens of kilometers in a few days and that horizontal advection, decay, and settling have greater impacts on the displacement of eDNA in the ocean than mixing. The eDNA particle tracking model was applied to identify possible origin locations of eDNA measured in MB using a quantitative PCR assay for Northern anchovy (Engraulis mordax). We found that eDNA likely originated from within 40 km and south of the sampling site if it had been shed approximately 4 days prior to sampling.
► Ratio of numerical to physical dispersion for ocean models is
Γ
=
Kλ
2. ► Ocean models thus require
λ
<
O(1) or Δ
x
<
h
1. ► When condition is not satisfied, numerical dispersion overwhelms ...physical dispersion. ► Satisfying this condition is a significant additional resolution requirement.
Many large-scale simulations of internal waves are computed with ocean models solving the primitive (hydrostatic) equations. Under certain circumstances, however, internal waves can represent a dynamical balance between nonlinearity and nonhydrostasy (dispersion), and thus may require computationally expensive nonhydrostatic simulations to be well-resolved. Most discretizations of the primitive equations are second-order accurate, inducing numerical dispersion generated from odd-order terms in the truncation error (3rd-order derivatives and higher). This numerical dispersion mimics physical dispersion due to nonhydrostasy. In this paper, we determine the numerical dispersion coefficient associated with common discretizations of the primitive equations. We compare this coefficient to the physical dispersion coefficient from the Boussinesq equations or KdV equation. The results show that, to lowest order, the ratio of numerical to physical dispersion is
Γ
=
Kλ
2, where
K is an
O(1) constant dependent on the discretization of the governing equations and
λ is the grid leptic ratio,
λ
≡
Δ
x/
h
1, where Δ
x is the horizontal grid spacing and
h
1 is the depth of the internal interface. In addition to deriving this relationship, we verify that it indeed holds in a nonhydrostatic ocean model (SUNTANS). To ensure relative dominance of physical over numerical effects, simulations require
Γ
≪
1. Based on this condition, the horizontal grid spacing required for proper resolution of nonhydrostatic effects is
λ
<
O(1) or Δ
x
<
h
1. When this condition is not satisfied, numerical dispersion overwhelms physical dispersion, and modeled internal waves exist with a dynamical balance between nonlinearity and numerical dispersion. Satisfaction of this condition may be a significant additional resolution requirement beyond the current state-of-the-art in ocean modeling.
Internal gravity waves, the subsurface analogue of the familiar surface gravity waves that break on beaches, are ubiquitous in the ocean. Because of their strong vertical and horizontal currents, and ...the turbulent mixing caused by their breaking, they affect a panoply of ocean processes, such as the supply of nutrients for photosynthesis, sediment and pollutant transport and acoustic transmission; they also pose hazards for man-made structures in the ocean. Generated primarily by the wind and the tides, internal waves can travel thousands of kilometres from their sources before breaking, making it challenging to observe them and to include them in numerical climate models, which are sensitive to their effects. For over a decade, studies have targeted the South China Sea, where the oceans' most powerful known internal waves are generated in the Luzon Strait and steepen dramatically as they propagate west. Confusion has persisted regarding their mechanism of generation, variability and energy budget, however, owing to the lack of in situ data from the Luzon Strait, where extreme flow conditions make measurements difficult. Here we use new observations and numerical models to (1) show that the waves begin as sinusoidal disturbances rather than arising from sharp hydraulic phenomena, (2) reveal the existence of >200-metre-high breaking internal waves in the region of generation that give rise to turbulence levels >10,000 times that in the open ocean, (3) determine that the Kuroshio western boundary current noticeably refracts the internal wave field emanating from the Luzon Strait, and (4) demonstrate a factor-of-two agreement between modelled and observed energy fluxes, which allows us to produce an observationally supported energy budget of the region. Together, these findings give a cradle-to-grave picture of internal waves on a basin scale, which will support further improvements of their representation in numerical climate predictions.
Celotno besedilo
Dostopno za:
DOBA, IJS, IZUM, KILJ, KISLJ, NUK, PILJ, PNG, SAZU, SBMB, SIK, UILJ, UKNU, UL, UM, UPUK
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