Net Volume Flux Research Articles

A long-wave model for film flow inside a tube with slip

A long-wave asymptotic model is developed for the flow of an axisymmetric viscous film lining the interior of a tube for the case where slip occurs at the tube wall. Both the case of a falling film with a passive air core and that of a film driven up the tube by pressure-driven airflow are considered. The impact of slip on the net liquid volume flux is discussed, and linear stability analysis of the evolution equation is conducted to identify the impact of slip on the phase speed and growth rates of disturbances in each case. The presence of slip enhances the growth rates, though its impact on phase speed depends on the film thickness and the strength of the core airflow. For some parameter combinations, slip can modify the phase speed without altering the base flow. The nonlinear evolution of the free surface is then studied numerically. For falling films, increasing the slip length reduces the critical thickness required for plug formation to occur. Families of travelling wave solutions are found via continuation and are used to derive a simple formula for the dependence of this critical thickness on the slip length; this formula is shown to hold for small slip length. For air-driven films, the topology of streamlines in the film can be altered by slip at the wall; if the slip length is large enough, it can prevent regions of recirculation from forming at the wave crest.

Experiments on fluid entrainment and slip in continuous bubble plumes

A series of laboratory experiments are reported in which a continuous stream of bubbles rise from a small source at the base of a tank of water. Using different nozzles, bubble sizes $d$ ranging from 1.2 to 11.6 mm were produced for a number of gas volume fluxes, $Q_b$ , ranging between 1.1 and $21.1\times 10^{-6}\ {\rm m}^3\ {\rm s}^{-1}$ . Within a small distance from the source, the slip speed of these bubbles exceeds the speed of the equivalent single-phase plume with the same buoyancy flux, leading to formation of what we refer to as the ‘slip plume’ regime. Through a combination of high-speed photography, coupled with flow visualisation in the plume and the ambient fluid using dye, we find that the bubble speed and the fluid speed remain nearly constant with height, with the maximum fluid speed being of order $0.30\pm 0.03$ of the bubble speed. Using the filling box method, we also find that the net fluid volume flux in the slip plume increases linearly with distance from the source at a rate $Q_l = \lambda Bz/v_s^2$ , where $B$ is the buoyancy flux of the gas, $v_s$ the rise speed of the gas bubbles, $z$ the distance above the source and $\lambda$ is a constant related to the dimensionless volume of fluid in the wake of each bubble. This slip-dominated flow regime can be understood in terms of kinetic energy imparted to the fluid as the bubbles rise and release potential energy. Further experiments with particle-laden plumes illustrate similar scalings for the volume flux in a particle-driven slip plume once the slip speed of the particles exceeds the bulk speed of the equivalent single-phase buoyant plume with the same buoyancy flux. Near the source the slip speed may be smaller than the plume speed, and the flow follows the classical model for a turbulent buoyant plume, with the transition to the slip regime occurring at a distance $z^*\approx (32\pm 5)\lambda ^{3/2} B/v_s^3$ from the source, where the dimensionless parameter $\lambda$ relates to the dimensionless volume of the fluid wake, which we find varies with the Reynolds number of the particles.

Imminent reversal of the residual flow through the Marsdiep tidal inlet into the Dutch Wadden Sea based on multiyear ferry-borne acoustic Doppler current profiler (ADCP) observations

Abstract. The Dutch Wadden Sea is a UN World Heritage Site connected to the North Sea by multiple tidal inlets. Although there are strong tidal currents flowing through these inlets, the magnitude and direction of the residual circulation in the western Dutch Wadden Sea is important for sediment, salinity and nutrient balances. We found that the direction of this residual flow is reversing. This residual circulation has been the subject of various studies since the 1970s, in which substantially different net volume fluxes were presented. Differences in tidal conditions in the main inlets, tidal rectification and meteorology were identified as driving mechanisms. Here we analysed almost 13 years of acoustic Doppler current profiler (ADCP) observations collected on the ferry crossing the Marsdiep tidal inlet in the Dutch Wadden Sea since 2009. The results are combined with earlier investigations covering the period 1998–2009. We find a significant trend in the magnitude of the residual volume flux, with decreasing export to the North Sea and with occasional imports observed in recent years. We hypothesise that this trend is related predominantly to changes in tides in the North Sea, which are caused by increased strength and duration of stratification in response to global warming. With warming projected to continue, we expect the residual flow in the Marsdiep to continue to reverse to full inflow within the current decade, with potential knock-on effects for the sediment budget and ecosystem of the western Wadden Sea.

Local Volume Conservation in Concentrated Electrolytes Is Governing Charge Transport in Electric Fields.

While ion transport processes in concentrated electrolytes, e.g., based on ionic liquids (IL), are a subject of intense research, the role of conservation laws and reference frames is still a matter of debate. Employing electrophoretic NMR, we show that momentum conservation, a typical prerequisite in molecular dynamics (MD) simulations, is not governing ion transport. Involving density measurements to determine molar volumes of distinct ion species, we propose that conservation of local molar species volumes is the governing constraint for ion transport. The experimentally quantified net volume flux is found to be zero, implying a nonzero local momentum flux, as tested in pure ILs and IL-based electrolytes for a broad variety of concentrations and chemical compositions. This constraint is consistent with incompressibility, but not with a local application of momentum conservation. The constraint affects the calculation of transference numbers as well as comparisons of MD results to experimental findings.

A Direct Estimate of Volume, Heat, and Freshwater Exchange Across the Greenland‐Iceland‐Faroe‐Scotland Ridge

AbstractThe flow of warm salty water toward the Nordic Seas is of fundamental importance to the climate of central and northern Europe. In an effort to gain an improved quantitative assessment of these fluxes a program was started in 2008 to measure upper‐ocean currents from the high‐seas ferry Norröna, which operates out of the Faroes to Iceland and Denmark. The current measurements were made with an acoustic Doppler current profiler mounted in the Norröna's hull. Starting in fall of 2013 monthly deployments of Expendable BathyThermographs give comprehensive information on the temperature field. These velocity and temperature data can be combined to estimate mean volume and temperature fluxes (referenced to 0 °C) for the two sections. Archived hydrographic data give us the corresponding salt transport. Thanks to an array of 12 tall moorings across the Blosseville Basin that measured currents, temperature, and salinity net transport of volume, temperature, and salt between Iceland and Greenland can also be estimated. By combining the velocity data from these three sections the strength of the Nordic Seas branch of the meridional overturning circulation is estimated to be 7.7 ± 0.8 Sv where 1 Sv = 106 m3/s. Imposing the constraint of zero net volume and salt flux, the corresponding heat and freshwater fluxes are estimated to be 264 ± 27 TW (1 TW = 1012 W) and −0.104 ± 0.01 Sv, respectively. The uncertainties in heat and freshwater fluxes are largely governed by volume fluxes. The Norröna program is ongoing.

Subtidal circulation in a deep‐silled fjord: Douglas Channel, British Columbia

AbstractDouglas Channel, a deep fjord on the west coast of British Columbia, Canada, is the main waterway in the fjord system that connects the town of Kitimat to Queen Charlotte Sound and Hecate Strait. A 200 m depth sill divides Douglas Channel into an outer and an inner basin. This study examines the low‐frequency (from seasonal to meteorological bands) circulation in Douglas Channel from data collected at three moorings deployed during 2013–2015. The deep flows are dominated by a yearly renewal that takes place from May/June to early September. A dense bottom layer with a thickness of 100 m that cascades through the system at the speed of 0.1–0.2 m s−1, which is consistent with gravity currents. Estuarine flow dominates the circulation above the sill depth, and the observed landward net volume flux suggests that it is necessary to include the entire complex channel network to fully understand the estuarine circulation in the system. The influence of the wind forcing on the subtidal circulation is not only at the surface, but also at middepth. The along‐channel wind dominates the surface current velocity fluctuations and the sea level response to the wind produces a velocity signal at 100–120 m in the counter‐wind direction. Overall, the circulation in the seasonal and the meteorological bands is a mix of estuarine flow, direct wind‐driven flow, and the barotropic and baroclinic responses to changes to the surface pressure gradient caused by the wind stress.

A box model for representing estuarine physical processes in Earth system models

Appropriately treating riverine freshwater discharge into the oceans in Earth system models is a challenging problem. Commonly, the river runoff is discharged into the ocean models with zero salinity and arbitrarily distributed either horizontally or vertically over several grid cells. Those approaches entirely neglect estuarine physical processes that modify river inputs before they reach the open ocean. In order to realistically represent riverine freshwater inputs in Earth system models, a physically based Estuary Box Model (EBM) is developed to parameterize the mixing processes in estuaries. The EBM represents the estuary exchange circulation with a two-layer box structure. It takes as input the river volume flux from the land surface model and the subsurface salinity at the estuary mouth from the ocean model. It delivers the estuarine outflow salinity and net volume flux into and out of the estuary to the ocean model. An offline test of the EBM forced with observed conditions for the Columbia River system shows good agreement with observations of outflow salinity and high-resolution simulations of the exchange flow volume flux. To illustrate the practicality of use of the EBM in an Earth system model, the EBM is implemented for all coastal grid cells with river runoff in the Community Earth System Model (CESM). Compared to the standard version of CESM, which treats runoff as an augmentation to precipitation, the EBM increases sea surface salinity and reduces stratification near river mouths. The EBM also leads to significant regional and remote changes in CESM ocean surface salinities.

Switching and transport mechanism in the branching tube network due to attached eddies

An experimental study was performed on the quasi-two-dimensional symmetric branching tube under oscillatory flow. The velocity field and transport of materials in the Reynolds number Re = 1500 ∼ 3000 and the Womersley number α = 17 ∼ 23 were visualized by means of a dye or small spheres as well as measured by using Particle Image Velocimetry. The repeated growth and disappearance of the attached eddies near the junction of the branched channel are recognized, which play a role of the throttle valves to control the transport of newly taken gasses or suspended particles into, and older ones out of, the human lung in spite of zero net volume flux.

The shallow meridional overturning circulation in the South China Sea and the related internal water movement

The structure of the annual-mean shallow meridional overturning circulation (SMOC) in the South China Sea (SCS) and the related water movement are investigated, using simple ocean data assimilation (SODA) outputs. The distinct clockwise SMOC is present above 400 m in the SCS on the climatologically annual-mean scale, which consists of downwelling in the northern SCS, a southward subsurface branch supplying upwelling at around 10°N and a northward surface flow, with a strength of about 1×106 m3/s. The formation mechanisms of its branches are studied separately. The zonal component of the annual-mean wind stress is predominantly westward and causes northward Ekman transport above 50 m. The annual-mean Ekman transport across 18°N is about 1.2×106 m3/s. An annual-mean subduction rate is calculated by estimating the net volume flux entering the thermocline from the mixed layer in a Lagrangian framework. An annual subduction rate of about 0.66×106 m3/s is obtained between 17° and 20°N, of which 87% is due to vertical pumping and 13% is due to lateral induction. The subduction rate implies that the subdution contributes significantly to the downwelling branch. The pathways of traced parcels released at the base of the February mixed layer show that after subduction water moves southward to as far as 11°N within the western boundary current before returning northward. The velocity field at the base of mixed layer and a meridional velocity section in winter also confirm that the southward flow in the subsurface layer is mainly by strong western boundary currents. Significant upwelling mainly occurs off the Vietnam coast in the southern SCS. An upper bound for the annual-mean net upwelling rate between 10° and 15°N is 0.7×106 m3/s, of which a large portion is contributed by summer upwelling, with both the alongshore component of the southwest wind and its offshore increase causing great upwelling.

Sea level anomalies in straits of Malacca and Singapore

This paper studies sea level anomaly (SLA) behaviour in Malacca and Singapore straits which serve part of a major maritime trade route between Indian and Pacific Ocean using both observed data and numerical model. Spatio-temporal behaviour of SLA in the region is analyzed based on 15 years of in-situ and remote sensing data. Results show that SLA signatures can be distinctly different in the two straits, with vastly opposite behaviours during certain months. By further analyzing spatial dependency of observed SLA in the region, SLA in Malacca and Singapore straits are found to be under the influence of Indian Ocean and South China Sea, respectively. Based on this insight, a numerical model is built with the appropriate non-tidal forcing derived from meteorological model and satellite dataset to properly represent SLA in Malacca and Singapore straits with Root Mean Square Error of less than 10cm. With this well calibrated model, the effect of different types of forcing on volume flux through the straits is investigated. Combined tidal and non-tidal forcing in the model gives 4 to 7×1011m3 of annual net westward volume flux through the straits which is four to seven times higher than that of tidal forcing alone. Furthermore with this combined forcing, a distinct seasonal trend with westward net flow during northeast monsoon (November to March) and eastward net flow during southwest monsoon (May to September) can be observed through the straits in the model which is not observed with tidal forcing. The findings of this paper highlight the importance of these non-tidal forcing in the model to obtain accurate SLA and flow representation in the straits that is vital to environmental fate and transport modelling during operational forecast.

Multiple steady states in exchange flows across faults and the dissolution of

We develop a model of the steady exchange flows which may develop between two aquifers at different levels in the geological strata and across which there is an unstable density stratification, as a result of their connection through a series of fractures. We show that in general there are multiple steady exchange flows which can develop, depending on the initial conditions, and which may involve a net upwards or downwards volume flux. We also show that there is a family of equilibrium exchange flows with zero net volume flux, each characterised by a different interlayer flux of buoyancy. We present experiments which confirm our simplified model of the exchange flow. Such exchange flows may supply unsaturated water from a deep aquifer to drive dissolution of a structurally trapped pool of geologically stored $\text{CO}_{2}$, once the water in the aquifer containing the trapped pool of $\text{CO}_{2}$ has become saturated in $\text{CO}_{2}$, and hence relatively dense. Such exchange flows may also lead to cross-contamination of aquifer fluids, which may be of relevance in assessing risks of geological storage systems.

The salinity signature of the cross-shelf exchanges in the Southwestern Atlantic Ocean: Numerical simulations.

A high-resolution model is used to characterize the dominant patterns of sea surface salinity (SSS) variability generated by the freshwater discharges of the Rio de la Plata (RdlP) and the Patos/Mirim Lagoon in the southwestern Atlantic region. We identify three dominant modes of SSS variability. The first two, which have been discussed in previous studies, represent the seasonal and the interannual variations of the freshwater plumes over the continental shelf. The third mode of SSS variability, which has not been discussed hitherto, represents the salinity exchanges between the shelf and the deep ocean. A diagnostic study using floats and passive tracers identifies the pathways taken by the freshwater plumes. During the austral winter (JJA), the plumes leave the shelf region north of the BMC. During the austral summer (DJF), the plumes are entrained more directly into the BMC. A sensitivity study indicates that the high-frequency component of the wind stress forcing controls the vertical structure of the plumes while the low-frequency component of the wind stress forcing and the interannual variations of the RdlP discharge controls the horizontal structure of the plumes. Dynamical analysis reveals that the cross-shelf flow has a dominant barotropic structure and, therefore, the SSS anomalies detected by Aquarius represent net mass exchanges between the shelf and the deep ocean. The net cross-shelf volume flux is 1.21 Sv. This outflow is largely compensated by an inflow from the Patagonian shelf.

Diurnal cross‐shore thermal exchange on a tropical forereef

AbstractObservations of the velocity structure at the Kilo Nalu Observatory on the south shore of Oahu, Hawaii show that thermally driven baroclinic exchange is a dominant mechanism for cross‐shore transport for this tropical forereef environment. Estimates of the exchange and net volume fluxes are comparable and show that the average residence time for the zone shoreward of the 12 m isobath is generally much less than 1 day. Although cross‐shore wind stress influences the diurnal cross‐shore exchange, surface heat flux is identified as the primary forcing mechanism from the phase relationships and from analysis of momentum and buoyancy balances for the record‐averaged diurnal structure. Dynamic flow regimes are characterized based on a two‐dimensional theoretical framework and the observations of the thermal structure at Kilo Nalu are shown to be in the unsteady temperature regime. Diurnal phasing and the cross‐shore momentum balance suggest that turbulent stress divergence is an important driver of the baroclinic exchange. While the thermally driven exchange has a robust diurnal profile in the long term, there is high temporal variability on shorter time scales. Ensemble‐averaged diurnal profiles indicate that the exchange is strongly modulated by surface heat flux, wind speed/direction, and alongshore velocity direction. The latter highlights the role of alongshore variability in the thermally driven exchange. Analysis of the thermal balance in the nearshore region indicates that the cross‐shore exchange accounts for roughly 38% of the advective heat transport on a daily basis.

Improvements in LICOM2. Part II: Arctic Circulation

Abstract A known issue of the National Key Laboratory of Numerical Modeling for Atmospheric Sciences and Geophysical Fluid Dynamics/Institute of Atmospheric Physics Climate Ocean Model, version 2 (LICOM2, the standard version) is the use of an artificial island in the Arctic Ocean. The computational instability in the polar region seriously influences the model performance in terms of the Arctic circulation. The above-mentioned instability was originally attributed to the converging zonal grids in the polar region. However, this study finds that better computational stability could be achieved in an improved version of LICOM2 (i.e., LICOM2_imp) after four improvements on implementations of the vertical mixing, mesoscale eddy parameterization, and bottom drag schemes. LICOM2_imp is then able to reduce the aforesaid artificial island to a point (i.e., the North Pole). Two experiments of 650-yr integration by LICOM2_imp are carried out using different bathymetries: Exp IMPV0 with the artificial island (88°–90°N) and IMPV1 with only the single pole. The focus of this paper is on the Arctic circulation. Exp IMPV1 gives a more reasonable distribution of salinity and temperature in the Arctic Ocean, a more accurate location of the center of the Beaufort Gyre, and a better net volume flux of the transpolar drift. With more realistic bathymetry in the Arctic Ocean, the biases of net volume fluxes across the Fram Strait, Barents Sea Opening, and Barents Sea Exit are reduced from 1.71 to 1.56, from 0.23 to 0.10, and from 0.71 to 0.45 Sv (1 Sv ≡ 106 m3 s−1), respectively, closer to the observations. The large biases of the net volume fluxes at the Fram Strait in both experiments may be attributed to the closed Nares Strait and other straits/channels in the Canadian Arctic Archipelago.

Recirculation in the Fram Strait and transports of water in and north of the Fram Strait derived from CTD data

Abstract. The volume, heat and freshwater transports in the Fram Strait are estimated from geostrophic computations based on summer hydrographic data from 1984, 1997, 2002 and 2004. In these years, in addition to the usually sampled section along 79° N, a section between Greenland and Svalbard was sampled further north. Quasi-closed boxes bounded by the two sections and Greenland and Svalbard can then be formed. Applying conservation constraints on these boxes provides barotropic reference velocities. The net volume flux is southward and varies between 2 and 4 Sv. The recirculation of Atlantic water is about 2 Sv. Heat is lost to the atmosphere and the heat loss from the area between the sections averaged over the four years is about 10 TW. The net heat (temperature) transport is 20 TW northward into the Arctic Ocean, with large interannual differences. The mean net freshwater added between the sections is 40 mSv and the mean freshwater transport southward across 79° N is less than 60 mSv, indicating that most of the liquid freshwater leaving the Arctic Ocean through Fram Strait in summer is derived from sea ice melt in the northern vicinity of the strait. In 1997, 2001 and 2003 meridional sections along 0° longitude were sampled and in 2003 two smaller boxes can be formed, and the recirculation of Atlantic water in the strait is estimated by geostrophic computations and continuity constraints. The recirculation is weaker close to 80° N than close to 78° N, indicating that the recirculation is mainly confined to the south of 80° N. This is supported by the observations in 1997 and 2001, when only the northern part of the meridional section, from 79° N to 80° N, can be computed with the constraints applied. The recirculation is found strongest close to 79° N.

Fluid mechanical and electrostatic study on the osmotic flow through cylindrical pores

When two solutions differing in solute concentration are separated by a porous membrane, the osmotic pressure will generate a net volume flux of the suspending fluid across the membrane; this is termed osmotic flow. We consider the osmotic flow across a membrane with circular cylindrical pores when the solute and the pore walls are electrically charged, and the suspending fluid is an electrolytic solution containing small cations and anions. Under the condition in which the radius of the pores and that of the solute molecules greatly exceed those of the solvent as well as the ions, a fluid mechanical and electrostatic theory is introduced to describe the osmotic flow in the presence of electric charge. The interaction energy, including the electrostatic interaction between the solute and the pore wall, plays a key role in determining the osmotic flow. We examine the electrostatic effect on the osmotic flow and discuss the difference in the interaction energy determined from the nonlinear Poisson-Boltzmann equation and from its linearized equation (the Debye-Hückel equation).

Third-order theory for multi-directional irregular waves

AbstractA new third-order solution for multi-directional irregular water waves in finite water depth is presented. The solution includes explicit expressions for the surface elevation, the amplitude dispersion and the vertical variation of the velocity potential. Expressions for the velocity potential at the free surface are also provided, and the formulation incorporates the effect of an ambient current with the option of specifying zero net volume flux. Harmonic resonance may occur at third order for certain combinations of frequencies and wavenumber vectors, and in this situation the perturbation theory breaks down due to singularities in the transfer functions. We analyse harmonic resonance for the case of a monochromatic short-crested wave interacting with a plane wave having a different frequency, and make long-term simulations with a high-order Boussinesq formulation in order to study the evolution of wave trains exposed to harmonic resonance.

Observed volume fluxes in the Bosphorus Strait

[1] Pairs of moorings containing acoustic Doppler current profilers (ADCPs) were deployed at each end of the Bosphorus Strait as a part of the United States Naval Research Laboratory's “Exchange Processes in Ocean Straits (EPOS)” project. The moorings were deployed in September 2008 and remained in place for about half a year. For the first time, current velocity profiles were collected concurrently at both ends of the strait. They well resolved the two-layer exchange flow and were used to estimate volume flux time series. These estimates clearly indicated that there was a mean net volume flux of over 100 km3/yr directed from the Black Sea to the Sea of Marmara over this period. The upper-layer fluxes showed distinct temporal variability whereas the lower-layer fluxes varied less. Volume fluxes were maximized at over 1500 km3/yr in the upper layer and over 1100 km3/yr in the lower layer, with an upper-layer mean of about 400 km3/yr and a lower-layer mean of about 300 km3/yr. Fluxes in both layers were highly coherent with the bottom pressure difference between the southern and northern ends of Bosphorus Strait, and they can be fairly well predicted from this pressure difference. The fluxes in the upper layer were also influenced by atmospheric forcing, but generally less so than by the bottom pressure difference.

Experimental investigation of the flow in the near-field of a cross-shaped orifice jet

The flow in the near-field of a cross-shaped orifice jet is investigated experimentally in the present study. The three components of the velocity field are obtained at different longitudinal locations using time-resolved stereoscopic particle-image velocimetry measurements. The mean and the instantaneous entrainment rates are calculated to study the entrainment mechanism. The distribution of momentum thicknesses is also inspected in the region of the axis switching. It is found that both the instantaneous entrainment rate and the net volume flux are strongly dependent on the vortical structures present in the flow and particularly at different parts of the Kelvin–Helmholtz vortex ring. Hence, different phases of the flow are investigated in the region of the axis switching. The contribution of the turbulent normal and shear stresses to the streamwise vorticity generation is also studied in the near-field of the cross jet. The momentum flux and its streamwise evolution are obtained from the mean velocity field. The contribution of different turbulent intensities to the momentum flux is given. The proper orthogonal decomposition (POD) is then applied to show the streamwise evolution of energy content of the most energetic POD modes.

Numerical analysis of high frequency pulsating flows through a diffuser-nozzle element in valveless acoustic micropumps

The concept of a valveless acoustic micropump was investigated. Two-dimensional, time-varying, axisymmetric, incompressible viscous flows through a planar diffuser-nozzle element were analyzed for applications in valveless acoustic micropumps. The diffuser divergence half-angles (θ), and the maximum pressure amplitudes (P) were independently varied. The inflow was periodic and the excitation frequency (f) was varied over the range 10 kHz ≤ f ≤ 30 kHz. The net time-averaged volume flux and the rectification capability of the diffuser were found as functions of θ, f, and P. The phase difference between pressure and velocity waveforms, the life time and the size of large scale flow recirculation regions inside the microdiffuser, and energy losses were found to be strongly frequency dependent.