Bottom Boundary Layer Research Articles

Hydrodynamic force coefficients for spherical triangle shell fragments: Dependence on the aspect ratio and flatness

Euler–Lagrange simulations of particle-laden flow require hydrodynamic models of drag and lift forces for individual particles. Our goal is to develop models that can prescribe these forces for arbitrarily orientated shell objects. Here, we use computational fluid dynamics simulations of steady bottom-boundary layer flow over a series of spherical triangle shell fragments to calculate the hydrodynamic forces. The simulations explicitly resolve the wall boundary layers using grid resolution on the order of y+=1 at the shell fragment surface and use the SST k-omega turbulence closure model. These fragments cover a range of aspect ratio and flatness characteristics. The shell fragments are generated as triangular selections of a spherical shell with azimuthal and longitudinal angles proscribed based on elongation and flatness parameters (varying between 1 to 5, and 0.02 to 0.2 respectively), while characteristic length of the fragment is held constant to define the overall fragment size. Fragment orientations are considered with independently varying pitch, roll, and yaw each ranging from 0 to 180 degrees. The numerical estimates for the forces from all simulations were used to develop robust parameterizations of the drag and lift as a function of aspect ratio and flatness characteristics, as well as orientation of the shell fragments.

Evolution of water wave packets by wind in shallow water

We use the Korteweg–de Vries (KdV) equation, supplemented with several forcing/friction terms, to describe the evolution of wind-driven water wave packets in shallow water. The forcing/friction terms describe wind-wave growth due to critical level instability in the air, wave decay due to laminar friction in the water at the air–water interface, wave stress in the air near the interface induced by a turbulent wind and wave decay due to a turbulent bottom boundary layer. The outcome is a modified KdV–Burgers equation that can be a stable or unstable model depending on the forcing/friction parameters. To analyse the evolution of water wave packets, we adapt the Whitham modulation theory for a slowly varying periodic wave train with an emphasis on the solitary wave train limit. The main outcome is the predicted growth and decay rates due to the forcing/friction terms. Numerical simulations using a Fourier spectral method are performed to validate the theory for various cases of initial wave amplitudes and growth and/or decay parameter ranges. The results from the modulation theory agree well with these simulations. In most cases we examined, many solitary waves are generated, suggesting the formation of a soliton gas.

Sediment oxygen uptake and hypoxia in coastal oceans, the Pearl River Estuary region

Hypoxia is increasing in coastal oceans due to high oxygen consumption and weak ventilation. Quantifying biological oxygen uptake and how its effects on hypoxia respond to stratification is important for management and predicting future trends. This work introduces a simple analysis to quantify and compare the biological and physical drivers of hypoxia, by using an example from the Pearl River Estuary (PRE) region (10–70 m deep). We show that in the PRE region, sediment respires ∼50 % of organic matter produced in the water column and oxidizes ∼88 % of the ammonium produced from sediment organic matter degradation. These processes lead to high sediment oxygen uptake (SOU; 41.1 ± 16.3 mmol m-2d-1). Under stratification, sediment's effect on the bottom oxygen is strongly regulated by the thickness of the bottom boundary layer (BBL), and the robust relationships can be used to parameterize SOU. We then construct a simple and generic mass-balance model to estimate the water column oxygen uptake in the BBL (WOUBBL) and quantify the total oxygen loss. By comparing model results to observations in the PRE and other similar systems, we show that the sensitivity of oxygen levels to SOU is largely controlled by the duration of stratification, while the organic matter settling velocity controls the contributions of SOU to total oxygen consumption. We further demonstrate how the model can help evaluate the primary drivers of hypoxia (stratification versus high oxygen consumption), determine the time scale of stratification required to develop hypoxia, and explain the within and across system variabilities.

On the three-dimensional structure of instabilities beneath shallow-shoaling internal waves

The stimulation of instability and transport in the bottom boundary layer by internal solitary waves has been documented for over twenty years. However, the challenge of shallow slopes and a disparity of scales between the large-scale wave and the small-scale boundary layer has proven challenging for simulations. We present laboratory scale simulations that resolve the three-dimensionalisation in the boundary layer during the entire shoaling process. We find that the late stage, in which the incoming wave fissions into boluses, provides the most consistent source of three-dimensionalisation. In the early stage of shoaling, three-dimensionalisation occurs not so much due to separation bubble instability, but due to the interaction of vortices shed from the separation bubble with the overlying pycnocline. This interaction overturns the pycnocline, and creates bursts in kinetic energy and viscous dissipation, suggesting that the shed vortices induce turbulent motion and sediment resuspension in the water column above and behind the separation bubble.

Abyssal Slope Currents

Abstract Realistic computational simulations in different oceanic basins reveal prevalent prograde mean flows (in the direction of topographic Rossby wave propagation along isobaths; a.k.a. topostrophy) on topographic slopes in the deep ocean, consistent with the barotropic theory of eddy-driven mean flows. Attention is focused on the Western Mediterranean Sea with strong currents and steep topography. These prograde mean currents induce an opposing bottom drag stress and thus a turbulent boundary-layer mean flow in the downhill direction, evidenced by a near-bottom negative mean vertical velocity. The slope-normal profile of diapycnal buoyancy mixing results in down-slope mean advection near the bottom (a tendency to locally increase the mean buoyancy) and up-slope buoyancy mixing (a tendency to decrease buoyancy) with associated buoyancy fluxes across the mean isopycnal surfaces (diapycnal downwelling). In the upper part of the boundary layer and nearby interior, the diapycnal turbulent buoyancy flux divergence reverses sign (diapycnal upwelling), with upward Eulerian mean buoyancy advection across isopycnal surfaces. These near-slope tendencies abate with further distance from the boundary. An along-isobath mean momentum balance shows an advective acceleration and a bottom-drag retardation of the prograde flow. The eddy buoyancy advection is significant near the slope, and the associated eddy potential energy conversion is negative, consistent with mean vertical shear flow generation for the eddies. This cross-isobath flow structure differs from previous proposals, and a new one-dimensional model is constructed for a topostrophic, stratified, slope bottom boundary layer. The broader issue of the return pathways of the global thermohaline circulation remains open, but the abyssal slope region is likely to play a dominant role.

Strong bottom currents in large, deep Lake Geneva generated by higher vertical-mode Poincaré waves

Although internal seiches are ubiquitous in large, deep lakes, little is known about the effect of higher vertical-mode seiches on deepwater dynamics. Here, by combining entire summer season current and temperature observations and 3D numerical modeling, we demonstrate that previously undetected vertical mode-two and mode-three Poincaré waves in 309-meter deep Lake Geneva (Switzerland/France) generate bottom-boundary layer currents up to 4 cm s−1. Poincaré wave amphidromic patterns revealed three strong cells excited simultaneously. Weak hypolimnetic stratification (N2 ≈ 10−6s−2), typical of deep lakes, significantly modified the wave structure by shifting the lower vertical node in the lake’s center from ~75-meter depth (without stratification) to ~150-meter depth (with stratification). This shift induces shear in the middle of the hypolimnion and strengthens bottom currents, with important implications for hypolimnetic mixing and sediment-water exchange. Our findings demonstrate that classical concepts based on constant temperature layers cannot correctly characterize higher vertical-mode Poincaré seiches in deep lakes.

Investigations into dynamic variation characteristics of near-bottom boundary flows over a long term at strait areas

Dynamic processes at the bottom boundary layers are crucial for various marine applications such as marine energy exploration and environmental protection. This paper explored hydrodynamic characteristics of near-bottom boundary currents based on the continuous measured velocity data at a site near the bottom boundary layer in the Strait of Georgia. Previous studies on the bottom boundary layer encompasses various aspects, including physical, chemical, and biological dimensions. However, the mechanism underlying the hierarchical structure of flow velocity remain poorly understood. Thus, the power spectrum and wavelet analysis were used to analyze the significant period of the averaged velocity and tidal characteristics, and to calculate the thickness of near-bottom boundary layer. The results indicate that the current velocities at the boundary layer tend to flow in south-eastern and north-western directions. There is a significant period of 15 days in August and September. At a depth of 301 m, the vertical velocities are stratified, indicating different velocity layers. The boundary layer thickness varies from 5.23 to 14.74 m, as indicated by the vertical structural characteristics. The structural characteristics of the seabed boundary layer are conducive to deepening our understanding of sediment's incipient motion, transport, and sedimentation process. The findings provide a theoretical foundation for future studies on sediment movement and the numerical simulation analysis of the bottom boundary layer. It is of great significance for the study of wave flow interaction and marine dynamic structure, and can provide scientific support for the development and utilization of the strait area.

Sediment remobilization over subaqueous sand waves: In-situ observation in the northern South China Sea

High-resolution tripod observations were conducted in a subaqueous sand-wave field in the northern South China Sea. The objective was to gain insight into the dynamic mechanism by which sandy sediments are remobilized by oceanic dynamic processes, in particular internal solitary waves and internal tides. Daily-recurring high suspended sediment concentrations were observed, likely due to lateral transport of sediments resuspended by critical reflection of diurnal internal tides at the shelf break. The passage of extreme internal solitary waves results in resuspension of sediments from the seabed and ejection of these sediments out of the boundary layer. The resuspension of sediments from the seabed is controlled by current-induced strong bed shear stress, while the ejection of sediments out of the bottom boundary layer is driven by the compression and subsequent expansion of the mixing layer, together with the developments of the separation bubbles behind the internal solitary waves. These findings provide new insights into understanding the dynamic mechanism of sediment remobilization by internal solitary waves. Moreover, they contribute to our understanding of the migration of subaqueous sand waves.

Wind Forcing Controls on Antarctic Bottom Water Export From the Weddell Sea via Bottom Boundary Layer Processes

AbstractThe Antarctic Bottom Water (AABW) exported from the Weddell Sea has experienced warming and contraction in the past 30 yrs. Superposed on this decadal trend is substantial annual and interannual variability in the volume and properties of Weddell‐sourced AABW. Several mechanisms have been suggested to explain these variations, many of which highlight a role of wind stress, but the comparative importance and possible simultaneity of the different mechanisms remains unclear. Using data from two mooring sites within the Weddell Sea, we find a rapid intensification of the abyssal boundary current carrying AABW through Orkney Passage (OP), the most direct export pathway of AABW from the Weddell Sea, in response to periods of strong zonal wind stress and anomalous wind stress curl along the South Scotia Ridge upstream of OP. This acceleration is concomitant with a 40% reduction in northward AABW transport in late 2015. The changes in transport follow anomalous wind forcing by approximately 3 months, with the short timescale indicative of a barotropic response in the flow through OP. The bottom boundary layer over the OP's sloping topography is found to have a key role in regulating export on monthly to interannual timescales. Increased boundary current velocity leading up to the passage forms a thickened bottom boundary layer, resulting in reduced AABW thickness and density, and thus restricting northward transport of AABW through the passage. Whilst other processes are likely to dominate on longer (decadal) periods, the dynamics identified here can explain significant variability on timescales up to interannual.

The boundary layer instability beneath internal solitary waves and its sensitivity to vortex wakes

We investigated the stability of the bottom boundary layer (BBL) beneath periodic internal solitary waves (ISWs) of depression over a flat bottom through two-dimensional direct numerical simulations. We explored the convective versus absolute/global nature of the BBL instability in response to changes in Reynolds number, and the sensitivity of the instability to seeding noise in the front of the ISW – spanning laboratory to geophysical scales. The BBL was laminar at $Re_{ISW}=90$ and convectively unstable at $Re_{ISW}=300$ . At laboratory-scale $Re_{ISW}=300$ , the convective wave packet was periodically amplified by each successive ISW, until vortex shedding occurred. The associated noise-amplification behaviour potentially explains the discrepancies of the critical $Re_{ISW}$ between the lock–release laboratory experiments and our Dubreil–Jacotin–Long-initialized numerical simulations as the result of the difference in background noise. Instability energy decreased under the front shoulder of the ISW, analogous to flow relaminarization under a favourable pressure gradient. At geophysical-scale $Re_{ISW}=900$ , the BBL was initially convectively unstable, and then the instability tracked with the ISW, appearing phenomenologically similar to a global instability. The simulated initial convective instability at both $Re_{ISW}=300$ and $Re_{ISW}=900$ is in agreement with local linear stability analysis which predicts that the instability group speed is always lower than the ISW celerity. Increased free stream perturbations in front of the ISW and larger $Re_{ISW}$ shift the location of vortex shedding (and enhanced bed shear stress) beneath the wave, closer to the ISW trough, thereby potentially changing the location of maximum sediment resuspension, in agreement with field observations at higher $Re_{ISW}$ .

Rough bed hydrodynamics under wave-current interactional flow field: double averaging approach

ABSTRACT The effect of surface wave on the double-averaged (DA) current-only flow properties is examined over two different types of rough beds comprising hemispherical elements with regular and staggered arrangements. For each case, the relative roughness spacing of p/r = 4 is maintained, where p = pitch distance and r = hemisphere height. The changes in turbulence characteristics against the water depth are analysed for superimposed surface waves propagating along the current with 1 and 2 Hz frequencies. The effect of regular and staggered roughness arrangements on different turbulence characteristics is explored. Results demonstrate that the DA stream-wise velocity decreases and increases at the outer region and within the roughness region, respectively, due to wave propagation. Owing to the surface wave, the DA intensity and form-induced intensity increase above the roughness layer and decrease within the bottom boundary layer. The values of form-induced intensities are smaller (greater) than the DA turbulence intensities at each considered flow depth within the roughness (outer) layer. For the entire flow depth, the values of DA Reynolds stress decrease due to wave interactions along a steady current. Again, the turbulence is observed to be close to isotropic for the current-only flow at the outer zone, while the flow transits to an anisotropic state with wave imposition on current. Further, the computed values of the turbulence indicator and dispersion functions are used for the identification of the level of turbulence and dispersion at each flow depth for the locations upstream and downstream of a hemisphere in the hemispherical bed.

Variability of the Bottom Boundary Layer Induced by the Dynamics of the Cross‐Isobath Transport Over a Variable Shelf

AbstractThe bottom boundary layer (BBL) dynamics play an important role in regulating the energy, momentum balance, and circulation in the shallow shelf areas. Unlike previous studies that disconnected BBL with background variable shelf circulation, we investigate the dynamic connection between the wind‐driven shelf circulation and BBL dynamics, and show the spatial characteristics of BBL dynamics in response to three‐dimensional (3D) heterogeneous transport over the highly variable shelf topography in the Northern South China Sea. Our process‐oriented modeling study demonstrates that the mixing dynamics and upslope buoyancy transport over varying shelf topography alter the spatial variability of BBL dynamics. Driven by southwesterly upwelling‐favorable winds, the along‐shelf current generated a frictional upslope Ekman transport. The along‐isobath pressure gradient force () formed by the flow‐topography interactions over the meandering shelf induces the geostrophic cross‐isobath transport. The downwave (upwave) enhances (offset) the frictional upslope transport over the east (west) of the shelf that has a concaving (uniform) bottom topography. Over the eastern shelf with concave isobaths, the intensified and upslope cross‐isobath dense water transport strengthen stratification and weaken the effect of bottom stress‐induced mixing, limiting the development of the BBL. The antithesis occurs over the western shelf, where a small bottom stress controls the BBL. River discharge and the tidal current modulate the alongshore current, upslope transport, bottom stress intensity, and BBL development. We model the trajectory of seabed particles as they respond to the BBL dynamic regimes, and find that high (low) concentration, short (long) suspension time, and strong (weak) shoreward transport occurover the eastern (western) shelf, respectively.

Intensified Currents Associated With Benthic Storms Underneath an Eddying Jet

AbstractBenthic storms are episodes of intensified near‐bottom currents capable of sediment resuspension in the deep ocean. They typically occur under regions of high surface eddy kinetic energy (EKE), such as the Gulf Stream. Although they have long been observed, the mechanism(s) responsible for their formation and their relationships with salient features of the deep ocean, such as bottom mixed layers (BMLs) and benthic nepheloid layers (BNLs), remain poorly understood. Here we conduct idealized experiments with a primitive‐equation model to explore the impacts of the unforced instability of a surface‐intensified jet on near‐bottom flows of a deep zonal channel. Vertical resolution is increased near the bottom to represent the bottom boundary layer. We find that the unstable near‐surface jet develops meanders and evolves into alternating, deep‐reaching cyclones and anticyclones. Simultaneously, EKE increases near the bottom due to the convergence of vertical eddy pressure fluxes, leading to near‐bottom currents comparable to those observed during benthic storms. These currents in turn form BMLs with thickness of O(100 m) from enhanced velocity shears and turbulence production near the bottom. The deep cyclonic eddies transport fluid particles both laterally and vertically, from near the bottom through the entire BML and may contribute to the formation of the lower part of BNLs. A sloping bottom reduces both the intensity of the near‐bottom currents and the extent of vertical transport. Overall, our study highlights a significant response of the abyssal environment to near‐surface current instability, with potential implications for sediment transport in the deep ocean.

Turbulence Over Camarinal Sill and Its Impact on Water Mixing—Strait of Gibraltar

AbstractStraits and narrows are the place of intensified turbulent mixing. Deep understanding of the turbulent dynamics at these locations is of crucial importance as it conditions the properties of the water masses flowing in the open ocean. A new extensive field experiment, PROTEVS GIB20, with high frequency measurements has been conducted in the Strait of Gibraltar. It allows us to infer dissipation rates of the turbulent kinetic energy, ϵ, from two consistent methods. The range of ϵ is depicted for the different processes which developed in the vicinity of Camarinal Sill, the main topographic feature of the Strait of Gibraltar. It evidences that the bottom boundary layer, hydraulic jumps and large overturns are the main loci of intensified turbulence reaching 10−3W.kg−1. The variability of the turbulence is mainly controlled by semi‐diurnal, diurnal and fortnightly tidal oscillations. Spatially, the western flank of Camarinal Sill is evidenced as the hotspot for turbulent mixing. We confirm a weak variation of the spatially averaged vertically integrated turbulent dissipation rate. This result needs to be qualified in view of the differentiated impact of the various processes on adjacent water masses. The dynamics of the spring tide directly mix Atlantic and Mediterranean waters, resulting in a large spreading of the T‐S diagram.

A snapshot of turbulence in the Northeastern Magellan Strait

First-ever measurements of the turbulent kinetic energy (TKE) dissipation rate in the northeastern Strait of Magellan (Segunda Angostura region) taken in March 2019 are reported here. At the time of microstructure measurements, the magnitude of the reversing tidal current ranged between 0.8 and 1.2 ms−1. The probability distribution of the TKE dissipation rate in the water interior above the bottom boundary layer was lognormal with a high median value εmedMS=1.2×10-6\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\varepsilon }_{med}^{MS}=1.2\ imes {10}^{-6}$$\\end{document} Wkg−1. Strong vertical shear, 1-2×10-2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\left(1-2\\right)\ imes {10}^{-2}$$\\end{document} s−1, in the weakly stratified water interior ensued a sub-critical gradient Richardson number Ri<10-1-10-2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Ri<{10}^{-1}-{10}^{-2}$$\\end{document}. In the bottom boundary layer (BBL), the vertical shear and the TKE dissipation rate both decreased exponentially with the distance from the seafloor ξ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\xi$$\\end{document}, leading to a turbulent regime with an eddy viscosity KM∼10-3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${K}_{M}\\sim {10}^{-3}$$\\end{document} m2/s, which varied with time and location, while being independent of the vertical coordinate in the upper part of BBL (for ξ>∼2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\xi >\\sim 2$$\\end{document} meters above the bottom).

Interaction between internal solitary waves and the seafloor in the deep sea

AbstractInternal solitary wave (ISW), as a typical marine dynamic process in the deep sea, widely exists in oceans and marginal seas worldwide. The interaction between ISW and the seafloor mainly occurs in the bottom boundary layer. For the seabed boundary layer of the deep sea, ISW is the most important dynamic process. This study analyzed the current status, hotspots, and frontiers of research on the interaction between ISW and the seafloor by CiteSpace. Focusing on the action of ISW on the seabed, such as transformation and reaction, a large amount of research work and results were systematically analyzed and summarized. On this basis, this study analyzed the wave–wave interaction and interaction between ISW and the bedform or slope of the seabed, which provided a new perspective for an in‐depth understanding of the interaction between ISW and the seafloor. Finally, the latest research results of the bottom boundary layer and marine engineering stability by ISW were introduced, and the unresolved problems in the current research work were summarized. This study provides a valuable reference for further research on the hazards of ISW to marine engineering geology.

The Shelf‐To‐Basin Transport of Iron From the Northern U.S. West Coast to the Pacific Ocean

AbstractRelease of iron (Fe) from continental shelves is a major source of this limiting nutrient for phytoplankton in the open ocean, including productive Eastern Boundary Upwelling Systems. The mechanisms governing the transport and fate of Fe along continental margins remain poorly understood, reflecting interaction of physical and biogeochemical processes that are crudely represented by global ocean biogeochemical models. Here, we use a submesoscale‐permitting physical‐biogeochemical model to investigate processes governing the delivery of shelf‐derived Fe to the open ocean along the northern U.S. West Coast. We find that a significant fraction (∼20%) of the Fe released by sediments on the shelf is transported offshore, fertilizing the broader Northeast Pacific Ocean. This transport is governed by two main pathways that reflect interaction between the wind‐driven ocean circulation and Fe release by low‐oxygen sediments: the first in the surface boundary layer during upwelling events; the second in the bottom boundary layer, associated with pervasive interactions of the poleward California Undercurrent with bottom topography. In the water column interior, transient and standing eddies strengthen offshore transport, counteracting the onshore pull of the mean upwelling circulation. Several hot‐spots of intense Fe delivery to the open ocean are maintained by standing meanders in the mean current and enhanced by transient eddies and seasonal oxygen depletion. Our results highlight the importance of fine‐scale dynamics for the transport of Fe and shelf‐derived elements from continental margins to the open ocean, and the need to improve representation of these processes in biogeochemical models used for climate studies.

Resemblance of the global depth distribution of internal-tide generation and cold-water coral occurrences

Abstract. Internal tides are known to be an important source of mixing in the oceans, especially in the bottom boundary layer. The depth of internal-tide generation therefore seems important for benthic life and the formation of cold-water coral mounds, but internal-tide conversion is generally investigated in a depth-integrated sense. Using both idealized and realistic simulations on continental slopes, we found that the depth of internal-tide generation increases with increasing slope steepness and decreases with intensified shallow stratification. The depth of internal-tide generation also shows a typical latitudinal dependency related to Coriolis effects. Using a global database of cold-water corals, we found that, especially in Northern Hemisphere autumn and winter, the global depth pattern of internal-tide generation correlates (rautumn = 0.70, rwinter = 0.65, p &lt; 0.01) with that of cold-water corals: shallowest near the poles and deepest around the Equator, with a decrease in depth around 25° S and N, and shallower north of the Equator than south. We further found that cold-water corals are situated significantly more often on topography that is steeper than the internal-tide beam (i.e. where supercritical reflection of internal tides occurs) than would be expected from a random distribution: in our study, in 66.9 % of all cases, cold-water corals occurred on a topography that is supercritical to the M2 tide whereas globally only 9.4 % of all topography is supercritical. Our findings underline internal-tide generation and the occurrence of supercritical reflection of internal tides as globally important for cold-water coral growth. The energetic dynamics associated with internal-tide generation and the supercritical reflection of internal tides likely increase the food supply towards the reefs in food-limited winter months. With climate change, stratification is expected to increase. Based on our results, this would decrease the depth of internal-tide generation, possibly creating new suitable habitat for cold-water corals shallower on continental slopes.

Mass transport at the bottom of propagating surface waves over a rippled bottom

The sea surface can be described by means of the superposition of many sinusoidal functions. However, quite often the amplitude of each component turns out to be much smaller than its wavelength, and any component evolves independently of the others. Hence, it is common to investigate the dynamics of a simple monochromatic surface wave. Hereinafter, the flow generated by a monochromatic surface wave within the bottom boundary layer over a rippled sea bed is determined by means of the numerical integration of vorticity and continuity equations. The forcing term that drives the fluid motion within the boundary layer is evaluated assuming that the steepness of the monochromatic surface wave is much smaller than one and considering the first term of the Stokes expansion. Even though the irrotational flow that forces the viscous rotational flow near the sea bottom is symmetric with respect to the ripple crests, Blondeaux and Vittori [“A route to chaos in an oscillatory flow: Feigenbaum scenario,” Phys. Fluids A 3(11), 2492–2495 (1991a)] showed that the symmetry of the flow field is broken when the Reynolds number becomes larger than a threshold value Rδ,t1 that depends on the geometrical characteristics of the ripples. The results of Blondeaux and Vittori [“A route to chaos in an oscillatory flow: Feigenbaum scenario,” Phys. Fluids A 3(11), 2492–2495 (1991a)] suggest that, when the Reynolds number is larger than Rδ,t1 but not too far from it, a steady current is also generated. Hereinafter, the steady velocity component is determined as a function of the ripple characteristics.

In situ hydrodynamic observations on three reef flats in the Nansha Islands, South China Sea

Waves and currents are responsible for sediment movement around and off coral reefs, affecting reef growth at both geological and modern timescales. Given the wide distribution and limited hydrodynamic information of reefs in the South China Sea, we carried out observations on tidal-cycle hydrodynamics in the Nansha Islands with tripod stationary instruments on the seafloor in order to fill the gap in our understanding of these processes. It was found that the magnitudes of near-bed orbital velocity were comparable with that of the mean tidal current, despite generally calm wave conditions. Waves dominated the combined wave-current skin-friction shear velocities acting on reef sediment, which were significantly higher than those generated by currents alone. Due to the large physical roughness of reef, drag coefficient and hydrodynamic roughness length estimated from logarithmic velocity profiles were two orders of magnitude higher than that in macro-tidal-estuary or inner shelf areas covered with siliceous muds or sands. The combined sinusoidal wave and asymmetric tidal current, along with the physical reef roughness, shaped velocity profile structures in the bottom boundary layer, which exhibited a logarithmic profile during the flood tide and a potential flow during the ebb. In absence of wave breaking, strong turbulence dissipation was observed across the rough reef, promoting strong mixing of water, which is crucial for delivering nutrients for coral growth. These findings imply the need to consider the unique characteristics of rough reef structure and combined effects of waves and currents to model the hydrodynamics in reef environment correctly. This understanding is critical for predicting energy and material transport in reef environments, which is essential for maintaining healthy coral ecosystems, and opens new paths for managing and preserving coral reefs in the face of environmental change.