Internal Froude Number Research Articles

High propulsive performance by an oscillating foil in a stratified fluid

We investigate numerically the propulsion characteristics of an oscillating foil undergoing coupled heave and pitch motion in a linearly density-stratified flow. A parameter space defined by the internal Froude number ( $1 \le Fr \le 10$ ) and the maximum angle of attack ( $5^\circ \le {\alpha _0} \le 30^\circ$ ) is considered in our study. The results demonstrate a significant enhancement in both thrust production and propulsive efficiency due to the stratification influence. Notably, the highest efficiency exceeding $80\,\%$ is achieved under moderate stratification conditions, surpassing the performance observed in a homogeneous fluid. We attribute this optimum performance to the proper match between the stratification effect and foil kinematics, which gives rise to intense vortex interactions and sufficient wave–mean flow interactions in the near wake of the oscillating foil. Consequently, the energy is transferred towards wake structures to form a high-intensity momentum jet in close proximity to the foil's trailing edge, indicating efficient propulsion. Furthermore, we find that the stratifications within the moderate-to-strong transitional regime display a reduced dependence of propulsive efficiency on the maximum angle of attack, primarily due to the delaying and alleviating effects on dynamic-stall events. Such a mechanism enables the oscillating foil to maintain a satisfactory performance by sufficiently high angles of attack without the penalty of stall events. Based on our findings, we propose that animals or artificial vehicles utilising oscillatory propulsion can benefit from the presence of density stratification in the surrounding fluid.

Study of the structure and intensity of density currents in the shelf-slope region in the Antarctic

The research involves the examination of modeling outcomes regarding the density structure and baroclinic dynamics of Antarctic shelf waters (ASW) within the shelf-slope area, encompassing a wide range of extreme weather conditions. We used a small-scale non-hydrostatic Fluidity-ICOM model to understand the formation and persistence of quasi-stationary polynyas in the Antarctic, which play a role in enhancing the formation of ASW. The salt fluxes, or buoyancy, are calculated for different forms of ice formation, namely static ice formation in young ice-covered polynyas and dynamic intra-water ice formation, which is considered the most effective and occurs in open water polynyas. Based on the intensification of ASW formation and its spread, three distinct modes of propagation along the continental slope have been identified: non-wave or subcritical mode, vortex mode, and wave or supercritical mode, which is characterized by rapid flow. The classification into different modes is determined by the internal Froude number (Fr) estimates. At the moment when the most developed stage of near-bottom density currents are transformed on a slope, the spatial dimensions of meanders, eddies, or frontal waves were found to be similar in magnitude, as well as their thickness. This observation aligns with model calculations of the local baroclinic Rossby deformation radius (RdL) for these currents. These findings agree with comparable assessments of the baroclinic Rossby deformation radius (RdL) for the Antarctic Slope Front (ASF) in the Commonwealth Sea, which were based on field observations. Additionally, the calculated propagation velocities of density currents and the density gradients at their boundaries coincide with the data obtained from field measurements. By estimating the volumetric fluxes (qv) and specific fluxes (ql) of ASW along the continental slope near the Cape Darnley coastal polynya area in the Commonwealth Sea, we can determine the contribution of ASW cascading to the formation of bottom waters under different flux regimes. The precision and accuracy of the qv and ql estimates are ensured through small-scale calculations using the non-hydrostatic Fluidity-ICOM model. These calculations consider the occurrences of intensified ASW formation in open water polynyas. Numerical experiments have revealed that a four-fold increase in a spatial step X results in an underestimation of qv by approximately 30%. As a consequence, in large-scale and even mesoscale hydrostatic models, such underestimation of qv and ql may be unsatisfactory (several times lower).

Numerical investigation on the generation and evolution of nonlinear internal waves in the southern Strait of Georgia

The generation and subsequent evolution of nonlinear internal waves (NLIWs) in the Strait of Georgia (British Columbia, Canada) is investigated with both remote sensing images and a three-dimensional regional non-hydrostatic numerical simulation. Many satellite images depict clear snapshots of two successive NLIWs propagating northward about 1 h or 4 km apart during the flood tides. In the model results, local energy budget analysis demonstrates that the generation processes of internal waves are dominated by the energy conversion from barotropic tides to internal tides, while propagation processes are dominated by high-frequency NLIWs after radiating away the Boundary Pass. To further investigate the generation mechanisms of local internal waves, sensitivity studies with different tidal forcing are carried out. In the standard spring tide experiment, the rank-order NLIW packets have relatively large leading waves (∼15 m amplitude) and small trailing waves radiating from the Boundary Pass, related to a complex evolution of an internal Froude number over the sill. The internal Froude number analysis also demonstrates that only when the diurnal (D1) and semidiurnal (D2) tides act in phase can paired NLIW packets be formed. However, either single D1 or D2 tides, or D1 and D2 tides not in phase, are not able to generate NLIWs, as condition of the flow remain subcritical at all times. Moreover, a series of sensitivity experiments demonstrate that the role of non-hydrostatic mode is crucial in the high-resolution model but less important in the coarse-resolution model, via comparing wave properties and wave energetics in non-hydrostatic and hydrostatic models.

Numerical study on the energy extraction performance by flapping foils in a density stratified flow

An energy extractor based on fully-activated flapping foils operating in a density stratified flow is studied numerically. The effect of stratification strength characterizing as the internal Froude number on the energy extraction performance is first investigated by fixing a typical set of parameters. The hydrodynamic characteristics of flapping foils with different kinematics in the stratified regime are then examined by varying the pitching amplitude. Our results suggest that the stratification effect decreases the energy harvesting efficiency owing to resulting poor synchronization between forces and flapping motion. Within the considered parametric space, the minimum energy extraction performance is identified at the Froude number around Fr=2, giving rise to an attached boundary layer without the favorable flow separation and leading edge vortex shedding. Nevertheless, a sudden increase of extracted power is observed when the stratification level is enhanced to Fr=1, which is attributed to the distinct flow structures generated by the induced internal waves. For the varying kinematics, the Froude number corresponding to the minimum performance is found to increase as the pitching amplitude becomes higher. It is indicated that the induced internal waves tend to dominate the flow patterns at a highly strong stratification, whereas the kinematics of flapping foils still play a crucial role in determining the vortex dynamics for the moderate and weak stratification strength.

Grid-point and time-step requirements for large-eddy simulation and Reynolds-averaged Navier–Stokes of stratified wakes

Estimates of grid-point and time-step requirements exist for many canonical flows but not for stratified wakes. The purpose of this work is to fill in this gap. We apply the basic meshing principles and estimate the grid-point and time-step requirements for Reynolds-averaged Navier–Stokes (RANS) and large-eddy simulation (LES) of stratified wake flows at high Reynolds numbers, as arise in many geophysical, aircraft, and undersea vehicle systems. Scales representative of a submarine operating in a stably stratified ocean environment are considered, and the quantitative conclusions reached here can be adapted accordingly for particular applications. For a submarine, typical wake conditions are Re0=108 and Fr0=102, and wakes extend to Nt = 1000, where Re0 and Fr0 are the initial Reynolds number and the internal Froude number of the wake, respectively, and N is the buoyancy frequency. We consider both spatially developing and temporally evolving wakes. We show that the grid points required for LES and RANS do not depend on the Reynolds number. The ratio of the grid points needed for LES and RANS is proportional to (Nt2,LW)2/3, where t2,LW marks the end of the late wake and the end of a computational fluid dynamics calculation. According to the present conservative estimates, 0.36×1012 and 0.7×109 grid points are needed for LES and RANS of a spatially developing wake. The numbers are 8×109 and 3×106 for LES and RANS of a temporally evolving wake.

Drag force on a circular cylinder in stratified flow: A two-dimensional numerical study

Using two-dimensional numerical simulations, we investigate a circular cylinder in a stratified flow with a pycnocline of a smooth density profile. We are particularly concerned about the difference between stratified flows and their homogeneous, or unstratified, counterparts in drag coefficients. It is well known that the characteristics of a stratified flow depend on the Reynolds number Re and the internal Froude number Fr. First, we change the incoming flow velocity, with the Reynolds number and the internal Froude number varying simultaneously, in the ranges of 76≤Re≤579 and 0.14≤Fr≤1.046, respectively. We find that the flow experiences a sequence of flow patterns, namely “multiple centerline structures,” “isolated mixed regions,” and “vortex shedding,” as we increase this combination, agreeing well with the previous experiments in the low Re and Fr ranges. Meanwhile, the mean drag coefficient decreases, and it drops below the value for a homogeneous state as an empirical stability parameter, k, drops below unity, indicating the transition from a lee-wave dominant wake to an unsteady, vortex shedding wake. This unique variation of drag coefficient is more clearly shown in another situation, when we fix the Reynolds number at Re = 234 while varying the Froude number within 0.094≤Fr≤4.192. In such a situation, we observe a stable “double eddy” pattern at Fr = 1.87, around which a minimum of mean drag coefficient is reached. At this critical point, we understand that the stratification in the flow inhibits lee-side separation, while the internal waves have not yet played a significant role. Although we observe turbulence-like, strong mixing regions in the far downstream wake for some specific cases, it is argued that the current two-dimensional simulations might not be able to resolve the high Reynolds number or high Froude number cases.

Laboratory and numerical experiments on the near wake of a sphere in a stably stratified ambient

The flow around and behind a sphere in a linear density gradient has served as a model problem for both body-generated wakes in atmospheres and oceans, and as a means of generating a patch of turbulence that then decays in a stratified ambient. Here, experiments and numerical simulations are conducted for 20 values of Reynolds number, $Re$ , and internal Froude number, $Fr$ , where each is varied independently. In all cases, the early wake is affected by the background density gradient, notably in the form of the body-generated lee waves. Mean and fluctuating quantities do not reach similar states, and their subsequent evolution would not be collapsible under any universal scaling. There are five distinguishable flow regimes, which mostly overlap with previous literature based on qualitative visualisations and, in this parameter space, they maintain their distinguishing features up to and including buoyancy times of 20. The possible relation of the low $\{Re, Fr\}$ flows to their higher $\{Re, Fr\}$ counterparts is discussed.

Freshwater Composition and Connectivity of the Connecticut River Plume During Ambient Flood Tides

The Connecticut River plume interacts with the strong tidal currents of the ambient receiving waters in eastern Long Island Sound. The plume formed during ambient flood tides is studied as an example of tidal river plumes entering into energetic ambient tidal environments in estuaries or continental shelves. Conservative passive freshwater tracers within a high-resolution nested hydrodynamic model are applied to determine how source waters from different parts of the tidal cycle contribute to plume composition and interact with bounding plume fronts. The connection to source waters can be cut off only under low-discharge conditions, when tides reverse surface flow through the mouth after max ambient flood. Upstream plume extent is limited because ambient tidal currents arrest the opposing plume propagation, as the tidal internal Froude number exceeds one. The downstream extent of the tidal plume always is within 20 km from the mouth, which is less than twice the ambient tidal excursion. Freshwaters in the river during the preceding ambient ebb are the oldest found in the new flood plume. Connectivity with source waters and plume fronts exhibits a strong upstream-to-downstream asymmetry. The arrested upstream front has high connectivity, as all freshwaters exiting the mouth immediately interact with this boundary. The downstream plume front has the lowest overall connectivity, as interaction is limited to the oldest waters since younger interior waters do not overtake this front. The offshore front and inshore boundary exhibit a downstream progression from younger to older waters and decreasing overall connectivity with source waters. Plume-averaged freshwater tracer concentrations and variances both exhibit an initial growth period followed by a longer decay period for the remainder of the tidal period. The plume-averaged tracer variance is increased by mouth inputs, decreased by entrainment, and destroyed by internal mixing. Peak entrainment velocities for younger waters are higher than values for older waters, indicating stronger entrainment closer to the mouth. Entrainment and mixing time scales (1–4 h at max ambient flood) are both shorter than half a tidal period, indicating entrainment and mixing are vigorous enough to rapidly diminish tracer variance within the plume.

On surface flow induced by internal waves generated by a slender body moving at low internal Froude number in a sharply stratified fluid

The studies on internal waves(IWs) generated by a moving body in a stratified fluid generally focused on wave amplitude phase characteristics in underwater space. The surface flow induced by internal waves(IWs) generated by an underwater moving body in stratified fluid is generally weak, and is rarely studied. In the present paper, the surface flow induced by body-generated IWs of a slender body(SUBOFF model) moving at Fri = 0.547～2.189 and high Reynolds number (Re = 2.0 × 106～8.0 × 106) in a sharply stratified fluid with finite depth is investigated numerically and experimentally. For the theoretical calculation, the Euler equations and the free surface boundary conditions are linearized, and the source-sink distribution method is used to calculate the velocity field of body-generated IWs of SUBOFF model using the potential flow theory combined with the associated eigenvalue problem on vertical velocity. Meanwhile Particle Image Velocimetry (PIV) is used to measure the surface flow induced by body-generated IWs of SUBOFF model under the same conditions (object size, fluid stratification and movement parameters) at a large stratified fluid tank (25m × 3m × 1.5m) and validate the theoretical calculation method. The wave patterns, the maximum peak-to-peak velocity value of surface flow and its variation with Fri are analyzed.

Numerical study of surface thermal signatures of lee waves excited by moving underwater sphere at low Froude number

A submerged body moving in density-stratified water, such as in oceans, disturbs the surrounding water layers. Furthermore, the internal waves generate and modulate the flow field on the water surface. Thereafter, the thin water surface layer and underlying water, which differ in temperatures because of factors such as solar radiation and water vapor exchange, mix. Consequently, thermal signatures could be generated on the water surface and detected by high-resolution infrared equipment; hence, the presence of a submerged moving body could also be deduced. To thoroughly examine this phenomenon, a submerged sphere moving horizontally in linearly density-stratified water with a “hot skin” layer on its surface was numerically studied in this work. A suitable solver, i.e., “twoLiquidMixing_skin_Foam”, based on the well-known open-source computational fluid dynamics code, “Open-Source Field Operation and Manipulation”, was developed for the aforementioned problem. The internal waves excited by the sphere were validated by experimental results to illustrate the accuracy of the developed solver. Then, the impact of lee waves on the water surface thermal signatures was investigated in detail for the towed submerged sphere moving at various depths in fluid with different internal Froude numbers.

Small‐Scale Topographic Effects on the Generation of Along‐Shelf Propagating Internal Solitary Waves on the Amazon Shelf

AbstractThis study investigates along‐shelf propagating internal solitary waves (ISWs) on the Amazon Shelf using satellite observations and numerical modeling. These ISWs appear as streak‐like patterns in satellite images along a narrow path within the North Brazilian Current (NBC), propagating against the current. The streak‐like patterns of the along‐shelf propagating ISWs are a result of the quasi‐two‐dimensional bathymetry below, suggesting the possibility of using sea surface imprints to detect the topographic features beneath. In this study, both the effects of the NBC and tidal current on ISW generation are considered over irregular seafloor. Near‐critical conditions (internal Froude number close to 1) created by the joint effects of the NBC and the tides result in ISW generation, while the dominant subcritical conditions result in the upstream propagation of these ISWs. Both the NBC and tidal currents are needed to continuously generate ISWs. This study demonstrates that small‐scale topographic features can result in the generation of large numbers of ISWs, which are expected to significantly contribute to ocean mixing and, potentially, sediment resuspension. The ISW‐induced current also contributes to sea surface wave breaking as observed by satellites.

Gravity currents propagating at the base of a linearly stratified ambient

Gravity currents produced from a full-depth lock release propagating at the base of a linearly stratified ambient are investigated by means of newly conducted three-dimensional high-resolution simulations in conjunction with corresponding two-dimensional simulations and laboratory experiments. A passive tracer is implemented in the simulations to quantitatively measure the energies associated with the current and the ambient. The density of heavy fluid within the lock is ρ̃C, the density in the ambient of depth H̃ varies linearly from ρ̃b at the bottom to ρ̃0 at the top, and the ambient has an intrinsic frequency Ñ. Attention is focused on the initial slumping stage, during which the gravity currents propagate at a constant velocity Ṽ and the internal Froude number is defined as Fr=Ṽ/ÑH̃. The dynamics of the subcritical gravity currents, i.e., Fr<1/π, and the supercritical gravity currents, i.e., Fr>1/π, are qualitatively different and are examined with the help of three-dimensional and two-dimensional high-resolution simulations. For the subcritical gravity currents, the flow is dominated by the internal wave, the Kelvin–Helmholtz vortices are inhibited, and the two-dimensional simulation agrees well with and serves as a good surrogate model for the three-dimensional simulation in the slumping stage. For the supercritical gravity currents, the Kelvin–Helmholtz vortices are pronounced and prone to breakup into three-dimensional structures in the slumping stage. On the one hand, for the supercritical gravity currents, the kinetic energy associated with the current and the potential energy associated with the ambient are accurately captured by the two-dimensional simulation. On the other hand, the transition distance for the slumping stage and dissipation rate in the system are underpredicted while the kinetic energy associated with the ambient and the potential energy associated with the current are overpredicted by the two-dimensional simulation for the supercritical gravity currents. Therefore, information derived from the two-dimensional simulation for the supercritical gravity currents must be treated with care. The high-resolution simulations in this study also complement the existing shallow-water formulation, which has been reported to agree well with the two-dimensional simulations with good physical assumptions and simple mathematical models.

Reduced-order representation of stratified wakes by proper orthogonal decomposition utilizing translational symmetry

Visualizations of reduced-order representations of stratified wakes of Reynolds number $$Re \in \{5,25,100\}\times 10^3$$ are presented at a fixed internal Froude number. The reduced-order representations are constructed by applying proper orthogonal decomposition (POD) to numerical datasets that are high-resolution, three-dimensional and time-dependent. Due to the transient nature of the flow, the dynamics to be represented are highly non-stationary, posing a challenge for the effectiveness of POD. The translational symmetry inherent in the computational configuration is utilized for the POD analysis. This technique turns out to be effective in terms of improving the convergence of energy content represented by the POD modes and enhancing the interpretability of the temporal dynamics. Individual POD modes representing distinct dynamics of various scales are visualized. In the turbulent region, visualizations of the reconstructed vertical vorticity fields suggest that the dominant length scale of flow structures decreases with the modal index. For internal wave motions, visualizations of the reconstructed vertical velocity fields show the opposite trend, as the wavelength of internal waves observed in the wake’s ambient increases with the modal index. The temporal coefficients for a given mode are observed to vary minimally between $$Re = 2.5\times 10^4$$ and $$10^5$$ , suggesting a potential asymptote of the large-scale temporal dynamics in terms of Reynolds number.

Internal gravity wave radiation from a stratified turbulent wake

The near-field energetics and directional properties of internal gravity waves (IGWs) radiated from the turbulent wake of a sphere towed through a linearly stratified fluid are investigated using a series numerical experiments. Simulations have been performed for an initial Reynolds number and internal Froude number , defined using body-based scales – , the sphere diameter; , the tow speed; and , the Brunt–Vaisala frequency. Snapshots of temporally evolving wake flow fields are sampled over the full wake evolution. The energy extracted from the wake through internal wave radiation is quantified by computing the total wave power emitted through a wake-following elliptic cylinder. The total time-integrated wave energy radiated is found to increase with and decrease with . The peak radiated wave power occurs at early times, near to the onset of buoyancy control, and is found to be approximately unchanged in magnitude as is increased. For the two higher considered, at late times, IGWs continue to be emitted – accounting for a distinct increase in total radiated wave energy. The most powerful IGWs are radiated out of the wake at a wide range of angles for , at to the horizontal for , and nearly parallel to the horizontal late in the non-equilibrium regime of wake evolution. Internal wave radiation is found to be an important sink for wake kinetic energy after , suggesting wave radiation cannot be neglected when modelling stratified turbulent wakes in geophysical and ocean engineering applications.

Strong Internal Waves Generated by the Interaction of the Kuroshio and Tides over a Shallow Ridge

AbstractThe Kuroshio and tides significantly influence the oceanic environment off the Japanese mainland and promote mass/heat transport. However, the interaction between the Kuroshio and tides/internal waves has not been examined in previous works. To investigate this phenomenon, the two-dimensional high-resolution nonhydrostatic oceanic Stanford Unstructured Nonhydrostatic Terrain-Following Adaptive Navier–Stokes Simulator (SUNTANS) model was employed. The results show that strong internal tides propagating upstream in the Kuroshio are generated at a near-critical internal Froude number (Fri = 0.91). The upstream internal wave energy flux reaches a magnitude of 12 kW m−1, which is approximately 3 times higher than that of internal waves without the Kuroshio. On the other hand, under supercritical conditions, the Kuroshio suppresses the internal wave energy flux. The interaction of internal tides and the Kuroshio also generates upstream propagating high-frequency internal waves and solitary wave packets. The high-frequency internal waves contribute to the increase in the total internal wave energy flux up to 40% at the near-critical Fri value. The results of this study suggest that the interaction of internal tides and the Kuroshio enhances the upstream propagating internal tides under the specified conditions (Fri ~ 1), which may lead to deep ocean mixing and transport at significant distances from the internal wave generation sites.

A climatological study of the strongest local winds of Japan “Inami‐kaze”

AbstractThis study examines the meteorological and climatological features of the Inami‐kaze in the Tonami Plain, the strongest local winds in Japan. The plain faces the Sea of Japan on the north side, while the remaining three sides are surrounded by high mountain ranges. An interview survey to local residents and the distribution of windbreak trees both indicate that the Inami‐kaze is localized to a surprisingly small region near the Inami town (about 6 km parallel to the mountain ridge and 3 km perpendicular to it), at the base of a very small saddle‐like topography in the mountain ridge. Wind statistics with a dense observation network during 2006–2014 (28 Inami‐kaze events) supports the above finding. Indeed, the wind speed is mostly (95%) below 11 m/s at the Tonami town, just 5 km away from the Inami town, while the Inami‐kaze (≥15 m/s) blows at the Inami town. Such a spatial pattern should be formed as a result of downslope windstorm with hydraulic jumps, which is indicated from the internal Froude number change across the mountain (0.9 at the upstream, 1.4 at the mountain top, and 0.3 at downstream). The required synoptic atmospheric condition for the Inami‐kaze is the pressure pattern “extratropical cyclone in the Sea of Japan.” The sufficient condition is the SSW–SSE wind (≥25 m/s) or south wind (around 20 m/s) at the 800‐pressure level over the mountain chain, indicating the allowed directional window is very narrow. On the other hand, the Inami‐kaze has an aspect of foehn. While the Inami‐kaze occur, the potential temperature at the Inami town tends to be higher by 4.7 K on average than in the windward plain on the Pacific Ocean side.

An unambiguous definition of the Froude number for lee waves in the deep ocean

There is a long-standing debate in the literature of stratified flows over topography concerning the correct dimensionless number to refer to as a Froude number. Common definitions using external quantities of the flow include $U/(ND)$, $U/(Nh_{0})$, and $Uk/N$, where $U$ and $N$ are, respectively, scales for the background velocity and buoyancy frequency, $D$ is the depth, and $h_{0}$ and $k^{-1}$ are, respectively, height and width scales of the topography. It is also possible to define an internal Froude number $Fr_{\unicode[STIX]{x1D6FF}}=u_{0}/\sqrt{g^{\prime }\unicode[STIX]{x1D6FF}}$, where $u_{0}$, $g^{\prime }$, and $\unicode[STIX]{x1D6FF}$ are, respectively, the characteristic velocity, reduced gravity, and vertical length scale of the perturbation above the topography. For the case of hydrostatic lee waves in a deep ocean, both $U/(ND)$ and $Uk/N$ are insignificantly small, rendering the dimensionless number $Nh_{0}/U$ the only relevant dynamical parameter. However, although it appears to be an inverse Froude number, such an interpretation is incorrect. By non-dimensionalizing the stratified Euler equations describing the flow of an infinitely deep fluid over topography, we show that $Nh_{0}/U$ is in fact the square of the internal Froude number because it can identically be written in terms of the inner variables, $Fr_{\unicode[STIX]{x1D6FF}}^{2}=Nh_{0}/U=u_{0}^{2}/(g^{\prime }\unicode[STIX]{x1D6FF})$. Our scaling also identifies $Nh_{0}/U$ as the ratio of the vertical velocity scale within the lee wave to the group velocity of the lee wave, which we term the vertical Froude number, $Fr_{vert}=Nh_{0}/U=w_{0}/c_{g}$. To encapsulate such behaviour, we suggest referring to $Nh_{0}/U$ as the lee-wave Froude number, $Fr_{lee}$.

Hydraulics and mixing in a laterally divergent channel of a highly stratified estuary

AbstractEstuarine mixing is often intensified in regions where topographic forcing leads to hydraulic transitions. Observations in the salt‐wedge estuary of the Connecticut River indicate that intense mixing occurs during the ebb tide in regions of supercritical flow that is accelerated by lateral expansion of the channel. The zones of mixing are readily identifiable based on echo‐sounding images of large‐amplitude shear instabilities. The gradient Richardson number (Ri) averaged across the mixing layer decreases to a value very close to 0.25 during most of the active mixing phase. The along‐estuary variation in internal Froude number and interface elevation are roughly consistent with a steady, inviscid, two‐layer hydraulic representation, and the fit is improved when a parameterization for interfacial stress is included. The analysis indicates that the mixing results from lateral straining of the shear layer, and that the rapid development of instabilities maintains the overall flow near the mixing threshold value of Ri = 0.25, even with continuous, active mixing. The entrainment coefficient can be estimated from salt conservation within the interfacial layer, based on the finding that the mixing maintains Ri = 0.25. This approach leads to a scaling estimate for the interfacial mixing coefficient based on the lateral spreading rate and the aspect ratio of the flow, yielding estimates of turbulent dissipation within the pycnocline that are consistent with estimates based on turbulence‐resolving measurements.

Behavior of a wave‐driven buoyant surface jet on a coral reef

AbstractA wave‐driven surface‐buoyant jet exiting a coral reef was studied in order to quantify the amount of water reentrained over the reef crest. Both moored observations and Lagrangian drifters were used to study the fate of the buoyant jet. To investigate in detail the effects of buoyancy and alongshore flow variations, we developed an idealized numerical model of the system. Consistent with previous work, the ratio of alongshore velocity to jet velocity and the jet internal Froude number were found to be important determinants of the fate of the jet. In the absence of buoyancy, the entrainment of fluid at the reef crest creates a significant amount of retention, keeping 60% of water in the reef system. However, when the jet is lighter than the ambient ocean water, the net effect of buoyancy is to enhance the separation of the jet from shore, leading to a greater export of reef water. Matching observations, our modeling predicts that buoyancy limits retention to 30% of the jet flow for conditions existing on the Moorea reef. Overall, the combination of observations and modeling we present here shows that reef‐ocean temperature gradients can play an important role in reef‐ocean exchanges.

Flow processes and sedimentation in contourite channels on the northwestern South China Sea margin: A joint 3D seismic and oceanographic perspective

3D seismic data from the northwestern South China Sea margin, coupled with the quantification of oceanographic processes and morphological results, were used to infer three-dimensional flow processes and in turn sedimentation in contourite channels. Contour currents resulting from the Northern Pacific Deep Water (NPDW-CCs) flowing through the bends of contourite channels around a topographic high lead to an imbalance in the transverse direction, around the bend, between three competing forces (i.e., upslope directed Coriolis forces versus downslope directed centrifugal and pressure-gradient forces). The interface deflection of NPDW-CCs by Coriolis, pressure gradient, and centrifugal forces yields a helical flow cell consisting of upper return flows directed downslope and basal flows orientated upslope. Ekman boundary layers, at the base and flow interface, are also likely present leading to flows in the downslope direction. The helical flow cell in the bulk of contour currents, and Ekman boundary layers, constitute a Coriolis force-induced helical flow circulation, which we suggest promoted asymmetric intra-channel deposition (i.e., downslope deposition versus upslope erosion), forcing contourite channels to consistently migrate in an upslope direction. Such Coriolis force-induced helical flow circulation is evidenced by occurrence of volumetrically significant overbank deposits along downslope margins and by asymmetric channel cross-sections with steepened channel walls and truncation terminations along upslope margins. It exhibits subcritical flow conditions (represented by internal Froude numbers estimated as 0.04 to 0.19), and is sufficiently deep to spill out of the studied contourite channels, yielding overbank deposits along downslope flanks of the contourite channels.