Buoyant Inflow Research Articles

Analytic solution for convection dominant heat transport induced by buoyant jet entrainment inside hot fluid storage tanks

Unsteady heat transfer process and the developed temperature field inside hot water storage tanks with a buoyant inflow jet can be described by a coupled first order partial and a first order ordinary differential equation system (PDE-ODE). Non-polynomial series solutions of this PDE-ODE system for an initial-boundary condition have been presented. The different solutions have been compared to the numerical solution of the PDE-ODE system and to the relevant measurement. The rate of the convergence of the analytic solutions is also investigated. Linear equation systems are constructed to calculate the constant coefficients of the series solution. Additionally the entire 3D flow and temperature field of the investigated thermo physical process have been calculated numerically and compared to the results of the analytic solution of the simplified model. Besides theoretical importance, the solutions can be benchmark solutions to develop the computational heat transfer.

Density, Salinity, and Entry Depths of Municipal Wastewater in an Urban Lake.

The depths of entry of municipal wastewater into receiving lakes importantly affects associated impacts on water quality. The plunging behavior of two negatively buoyant inflows that carry municipal waste, an urban tributary and an effluent discharge, in Onondaga Lake, NY, is characterized and quantified based on an integrated program of monitoring, density calculations, and modeling. In-lake signatures of plunging from the two inflows are differentiated according to constituents in which each is enriched. Under common contemporary conditions, the summer averages of the fraction of the urban stream and effluent discharge inflows plunging to stratified depths is predicted, with a calibrated hydrodynamic model, to be approximately 0.7 and 0.35, respectively. Recent short-term increases in salinity levels from construction site dewatering caused greater plunging of the effluent discharge and interfered with normal complete fall turnover in the lake.

On the buoyant sub-surface salinity maxima in the Gulf of Riga

Summary Thermohaline structure in the Gulf of Riga (GoR) was investigated by a multi-platform measurement campaign in summer 2015. Stratification of the water column was mainly controlled by the temperature while salinity had only a minor contribution. Buoyant salinity maxima with variable strength were observed in the intermediate layer of the Gulf of Riga. The salinity maxima were likely formed by a simultaneous upwelling–downwelling event at the two opposite sides of the Irbe strait. The inflowing salty water did not reach the deeper (> 35 m) parts of the gulf and, therefore, the near-bottom layer of the gulf remained isolated throughout the summer. Thus, the lateral water exchange regime in the near bottom layer of the Gulf of Riga is more complicated than it was thought previously. We suggest that the occurrence of this type of water exchange resulting in a buoyant inflow and lack of lateral transport into the near-bottom layers might contribute to the rapid seasonal oxygen decline in the Gulf of Riga.

Impacts of a Storm Merger on the 24 May 2011 El Reno, Oklahoma, Tornadic Supercell

Abstract On 24 May 2011, a tornadic supercell (the El Reno, Oklahoma, storm) produced tornadoes rated as category 3 and 5 events on the enhanced Fujita scale (EF3 and EF5, respectively) during a severe weather outbreak. The transition (“handoff”) between the two tornadoes occurred as the El Reno storm merged with a weaker, ancillary storm. To examine the impacts of the merger on the dynamics of these storms, a series of three-dimensional cloud-scale analyses are created by assimilating 1-min volumetric observations from the National Weather Radar Testbed’s phased array radar into a numerical cloud model using the local ensemble transform Kalman filter technique. The El Reno storm, its updrafts, and vortices in the analyzed fields are objectively identified, and the changes in these objects before, during, and after the merger are examined. It is found that the merger did not cause the tornado handoff, which preceded the updraft merger by about 5 min. Instead, the handoff likely resulted from midlevel mesocyclone occlusion, in which the midlevel mesocyclone split and a portion is shed rearward with respect to storm motion. During the merger process, the midlevel mesocyclone and updraft structure in the El Reno storm became relatively disorganized. New updraft pulses that formed above colliding outflow boundaries between the two storms tilted environmental vorticity from low levels to generate an additional midlevel vortex that later merged with the El Reno storm’s midlevel mesocyclone. Once the ~10-min merger process was complete, the El Reno storm and its mesocyclone rapidly reintensified, as access to buoyant inflow sector air was restored.

Numerical Simulation of Density Current Evolution in a Diverging Channel

Numerical Simulation of Density Current Evolution in a Diverging Channel: When a buoyant inflow of higher density enters a reservoir, it sinks below the ambient water and forms an underflow. Downstream of the plunge point, the flow becomes progressively diluted due to the fluid entrainment. This study seeks to explore the ability of 2D width-averaged unsteady Reynolds-averaged Navier-Stokes (RANS) simulation approach for resolving density currents in an inclined diverging channel. 2D width-averaged unsteady RANS equations closed by a buoyancy-modified <svg style="vertical-align:-0.13794pt;width:33.8125px;" id="M1" height="10.7375" version="1.1" viewBox="0 0 33.8125 10.7375" width="33.8125" xmlns="http://www.w3.org/2000/svg"> <g transform="matrix(1.25,0,0,-1.25,0,10.7375)"> <g transform="translate(72,-63.41)"> <text transform="matrix(1,0,0,-1,-71.95,63.6)"> <tspan style="font-size: 12.50px; " x="0" y="0">𝑘</tspan> <tspan style="font-size: 12.50px; " x="9.5522919" y="0">−</tspan> <tspan style="font-size: 12.50px; " x="20.892513" y="0">𝜀</tspan> </text> </g> </g> </svg> turbulence model are integrated in time with a second-order fractional step approach coupled with a direct implicit method and discretized in space on a staggered mesh using a second-order accurate finite volume approach incorporating a high-resolution semi-Lagrangian technique for the convective terms. A series of 2D width-averaged unsteady simulations is carried out for density currents. Comparisons with the experimental measurements and the other numerical simulations show that the predictions of velocity and density field are with reasonable accuracy.

Scales and structure of frontal adjustment and freshwater export in a region of freshwater influence

Sea surface temperature satellite imagery and a regional hydrodynamic model are used to investigate the variability and structure of the Liverpool Bay thermohaline front. A statistically based water mass classification technique is used to locate the front in both data sets. The front moves between 5 and 35 km in response to spring–neap changes in tidal mixing, an adjustment that is much greater than at other shelf-sea fronts. Superimposed on top of this fortnightly cycle are semi-diurnal movements of 5–10 km driven by flood and ebb tidal currents. Seasonal variability in the freshwater discharge and the density difference between buoyant inflow and more saline Irish Sea water give rise to two different dynamical regimes. During winter, when cold inflow reduces the buoyancy of the plume, a bottom-advected front develops. Over the summer, when warm river water provides additional buoyancy, a surface-advected plume detaches from the bottom and propagates much larger distances across the bay. Decoupled from near-bed processes, the position of the surface front is more variable. Fortnightly stratification and re-mixing over large areas of Liverpool Bay is a potentially important mechanism by which freshwater, and its nutrient and pollutant loads, are exported from the coastal plume system. Based on length scales estimated from model and satellite data, the erosion of post-neap stratification is estimated to be responsible for exporting approximately 19% of the fresh estuarine discharge annually entering the system. Although the baroclinic residual circulation makes a more significant contribution to freshwater fluxes, the episodic nature of the spring–neap cycle may have important implications for biogeochemical cycles within the bay.

Coastal circulation and hydrography in the Gulf of Tehuantepec, Mexico, during winter

Winter observations of shelf and slope hydrography and currents in the inner Gulf of Tehuantepec are analysed from two field studies in 1989 and 1996 to specify the variability of near-shore conditions under varying wind stress. During the winter period frequent outbursts of ‘Norte’ winds over the central Gulf result in persistent alongshore inflows along both its eastern and western coasts. Wind-induced variability on time scales of several days strongly influences the shelf currents, but has greater effect on its western coast because of the generation and separation of anticyclonic eddies there. The steadier inflow (∼0.2 m s −1) on the eastern shelf is evident in a strong down-bowing of shallow isosurfaces towards the coast within 100 km of shore, below a wedge of warmer, fresher and lighter water. This persistent entry of less saline (33.4–34.0), warmer water from the southeast clearly originates in buoyancy input by rivers along the Central American coast, but is augmented by a general shoreward tendency (0.2 m s −1) in the southeastern Gulf. The resultant shallow tongue of anomalous water is generally swept offshore in the head of the Gulf and mixed away by the strong outflow and vertical overturning of the frequent ‘Norte’ events but during wind relaxations the warm, low-salinity coastal flow may briefly extend further west. In the head of the Gulf, flow is predominantly offshore (<0.2 m s −1) as the alongshore component alternates eastward and westward in association with elevation or depression, respectively, of the pycnocline against the shore. More saline, open ocean water is introduced from the north-western side of the Gulf by the inflow along the west coast. During extended wind relaxations, the flow becomes predominantly eastward beyond the shelf while nearshore the coastally trapped buoyant inflow from the southeast penetrates across the entire head of the gulf at least as far as its western limit. On the basis of these and other recent observations, it seems that the accepted view of a broad, persistent Costa Rica Coastal Current (CRCC) is the result of averaging over many relatively sparse observations and that the instantaneous CRCC is a highly variable and convoluted flow around and between constantly changing eddies. The buoyancy-driven shelf current reported here forms a hitherto unrecognized, but major, component of this CRCC system.

Dissolved oxygen response to wind‐inflow interactions in a stratified reservoir

Results of a field campaign and numerical simulations are used to show how physical mechanisms impose length scales and timescales that determine the dominant biogeochemical process. As an example, the dynamics of the Snake River inflows into Brownlee Reservoir is investigated to explain the onset and maintenance of an oxygen‐depleted region (the oxygen block) in the surface layer of the upstream part of the reservoir. The oxygen block was located in a region of the reservoir in which the surface layer was warmer as a result of smaller wind stresses and reduced evaporation rates. Numerical simulations reproduced the hydrodynamic field observations resulting from inflow, outflow, wind stress, and atmospheric heat fluxes. When the wind stress opposed the inflow, the surface layer was arrested, forming a zone of convergence, stagnating the fluid and allowing the biological oxygen demand in the water to deplete the dissolved oxygen (DO) in the surface water; direct measurements showed that vertical mixing was small and contributed only marginally to the oxygen depletion. Net DO production in the water column was consistent with the observed variation with the buoyant inflow pattern, that is, a sink during overflows and overcast days and a source during interflows and intense sunlight. These observations provided further evidence that the water in this region was biologically isolated as confirmed by a scaling analysis. Modern numerical hydrodynamic simulations have reached a level of accuracy where they may be used to identify and quantify ecological niches.

Idealized three‐dimensional modeling of seasonal variation in the Alaska Coastal Current

Seasonal variation of the buoyancy‐ and downwelling‐wind‐forced Alaska Coastal Current (ACC) and the fate of freshwater contained in it is considered using idealized analytical and numerical models of the ACC formed from a half‐line source of buoyant inflow. The coastal current initially develops two‐dimensionally but becomes three‐dimensional from a balance between coastal influx of buoyancy and its downstream transport, which leads to a coastal current depth limit Hmax = ()1/2, where x is along‐shelf distance, Q is the line source strength for unit length, f is the Coriolis frequency, and g′ is the reduced gravity of the buoyant inflow. This limit is unchanged under downwelling wind stress and is reached on timescales of less than 1 month for the ACC. The coastal current width is roughly constant in x and increases in time at the same rate as the two‐dimensional solution. Imposition of a downwelling wind stress τ results in an approximate balance among wind stress and along‐ and cross‐shelf momentum advection so that the current width is reduced to Ywind ≈ LD ()1/2, where LD is the Rossby radius of deformation, τ is the wind stress and ρ0 is a reference density. Waves/eddying motions eventually grow in the half‐line source coastal current with wavelengths proportional to the coastal current width and with a downstream phase speed slower than the maximum current speed. These features cause an offshore flux of buoyant water, a broader coastal current, and further accumulation of buoyancy on the shelf. Increasing downwelling wind stress reduces the effects of the instabilities. Continual accumulation of buoyancy on the shelf occurs during all model runs but is nearly absent under maximum winter downwelling wind stress. It is suggested that freshwater accumulation on the shelf during spring, summer, and fall may be largely lost downstream during winter.

Interaction of transient shelf currents with a buoyancy-driven coastal current

Observations on the inner New Jersey shelf (1996) showed that transient wind-driven currents of 3–4-day periods strongly interacted with a buoyancy-driven coastal current (or buoyant plume) originating from the Hudson estuary. In particular, the depth-averaged current fluctuations were amplified in the buoyant water. This phenomenon is studied here using a primitive equation numerical model (SPEM5). Transient (periodic) shelf currents are introduced in the form of incident barotropic shelf waves (BSW). The model domain is an idealized channel with open upstream/ downstream boundaries and the depth exponentially increasing offshore, which allows the BSW propagation through the model domain. In most cases, the wave period is five days. The buoyancydriven coastal current is forced by constant buoyant discharge through a coastal gap. Propagating BSWs reduce the growth of a buoyant anticyclonic bulge at the source region while a coastal current downstream from the source contains more buoyant water with a sharper density gradient in the frontal zone compared to the case without BSWs. The amplitude of vertically averaged transient currents increases in the buoyant layer (for instance, by 20–30% for the inflow density anomaly of 3 to 4 kg m ). This amplification depends on the density anomaly of buoyant inflow. On the other hand, variations in the inflow velocity and/or the net transport do not affect the BSW amplification. The amplification of velocity amplitude is associated with the incident BSW scattering into higher wave modes. The total energy flux should remain approximately the same as BSWs propagate through the domain. The higher modes have lower group speeds and thus their amplitudes should be higher in order to maintain the same energy flux. Such interactions of transient currents with buoyant plumes are important for the mixing processes and the across-shelf exchange on the inner shelf.

The cyclonic turning and propagation of buoyant coastal discharge along the shelf

Buoyant coastal discharge typically forms a current flowing along the coast in the direction of Kelvin wave propagation (hereinafter referred to as the downstream direction). In this paper the opposite, upstream penetration of buoyancy-driven current is studied using numerical modeling. Previous models of coastal buoyancy-driven currents repeatedly predicted the upstream spreading while in the field this feature was not commonly observed. The mechanism responsible for the propagation of buoyant flow along the coast upstream from its source is identified as follows. In many cases, the boundary conditions applied for buoyant discharge oversimplify the actual dynamics at the mouth blocking landward flow in the lower layer. This generates a strong cyclonic vorticity disturbance with corresponding upstream turning of buoyant flow at the source. This process initiates the upstream spreading of buoyant flow. Alternative boundary condition maintaining constant net transport but allowing baroclinic adjustment of buoyant inflow is formulated and shown to reduce the generation of cyclonic vorticity at the mouth. The upstream propagation is further enhanced by the vertical mixing. The buoyant water forms an anticyclonic bulge at the river or estuary mouth. While spreading around the center of this anticyclone, the fresher water gradually becomes saltier due to vertical mixing/diffusion. As a result, the pool of lightest water does not coincide with the center of the anticyclone (in the sense of integral streamfunction) but tends to occupy the upstream and inshore segment of the bulge where the buoyant water comes first. This sets a new center for the anticyclonic turning at the surface and promotes the upstream shift of the anticyclonic bulge. This process sustains continuous growth of the buoyant plume upstream. It is shown that the upstream ambient current does not produce a similar effect. Instead, buoyant flow periodically sheds anticyclones advected upstream with the mean current. Under certain conditions, upstream spreading is also possible in nature. For example, Beardsley et al. (1985) reported substantial upstream penetration of the Changjiang River discharge in the East China Sea during the period of high runoff.

Numerical Investigation of Plunging Density Current

When a buoyant inflow of higher density enters a reservoir, it sinks below the ambient water and forms an underflow. Downstream of the plunge point, the flow becomes progressively diluted due to the fluid entrainment. The entrainment rate is strongly dependent on the Richardson number and reaches a constant value well downstream of the plunge point. This study is concerned with the analysis of the plunging phenomenon and the determination of the entrainment. A k-ε model including buoyancy effects, both in a sloping and a diverging channel, is used to reproduce the main flow characteristics. A relation between the depth at the plunge point in a channel of constant width and in a diverging channel is established, and theoretical results for the calculation of the dense layer thickness are provided. The latter indicates that the spreading rate of the dense layer in a diverging channel is a function of both the entrainment rate and the channel width. The predictions of the plunge line location are in agreement with most semiempirical equations.

A Simple Theory for the Fate of Buoyant Coastal Discharges*

Abstract A simple theory that predicts the vertical structure and offshore spreading of a localized buoyant inflow onto a continental shelf is formulated. The theory is based on two competing mechanisms that move the buoyant fluid offshore: 1) the radial spread of the lighter water over the ambient water, being deflected by the Coriolis force and producing an anticyclonic cyclostrophic plume, and 2) offshore transport of buoyant water in the frictional bottom boundary layer that moves the entire plume offshore while maintaining contact with the bottom. The surface expression of the cyclostrophic plume moves offshore a distance ys = 2(3g′h0 + υ 2i)/(2g′h0 + υ 2i)1/2f,where g′ is reduced gravity based on the inflow density anomaly, h0 is the inflow depth, υi is the inflow velocity, and f is the Coriolis parameter. The plume remains attached to the bottom to a depth given by hb = (2Lυih0f/g′)1/2,where L is the inflow width. Both scales are based solely on parameters of the buoyant inflow at its source. There...

湖成デルタと海成デルタの堆積シークエンス 現世デルタの典型例とその比較

The uppermost part of delta sequences is composed of overbank deposits, while muddy prodelta deposits form the lowermost part of the sequences. Crevasse splays, levees, bays, or abandoned channles occur commonly in the delta plain of the fluvial-dominated deltas. The delta front and upper prodelta are occupied mainly by distributary mouth bars. Slump blocks derived mainly from mouth bar deposits caused by slope failures may occur in the prodelta. Distal bar and bar front deposits of the distributary mouth bars have a distinct upward-coarsening sequence. Beach facies (dunes, beach ridges, foreshore, shoreface, etc.) or barrier island/lagoon systems are developed in the delta plain to upper prodelta of the wave-dominated deltas. In the tide-dominated deltas, tidal flats and tidal bars occur commonly in the lower delta plain to upper delta front, and in the delta front to upper prodelta, respectively. Bidirectional cross-bedding is often formed in the tidal bar deposits. The most distinct upward-coarsening sequence is observed in the wave-dominated deltas. Tide-dominated deltas do not have an upward-coarsening sequence.Marine deltas are not only of fluvial-dominated, wave-dominated and tide-dominated types, but also of mixed types. On the other hand, lacustrine deltas are restricted to the fluvial-dominated, wave-dominated, and their mixed type deltas. Nevertheless, the fluvial-dominated and wave-dominated lacustrine delta sequences have sedimentological features similar to those of the fluvial-dominated and wave-dominated marine delta sequences, respectively.Since marine water has a higher salinity than lake water, montmorillonite and illite occur more commonly as clay minerals in marine delta sediments than in lacustrine delta sediments. Authigenic minerals in lacustrine delta sediments could also be different from those of marine delta sediments because of the different chemical compositions of marine and lake waters.Furthermore, Gilbert-type deltas which resulted from homopycnal inflow are more commonly formed in lacustrine river-mouths rather than in marine river-mouths. Hyperpycnal or friction-dominated inflow occurs more commonly in lacustrine river-mouths resulting in deposition of turbidites and middle-ground mouth bars. However, large-scale broad mouth bars resulting from the hymopycnal or buoyant inflow are more often formed in marine river-mouths.

Negatively Buoyant Flow in Diverging Channel, IV: Entrainment and Dilution

A negatively buoyant inflow to a lake or reservoir sinks to the bottom and forms an underflow. In this process, the “plunging flow” entrains ambient water and becomes diluted. The dilution alters the buoyancy and hence the flow behavior of the underflow. Since literature on entrainment by underflows does not include the “plunging process” itself, great uncertainty exists when the initial conditions of underflows have to be estimated. Therefore, the density driven plunging phenomenon is experimentally investigated in a horizontal diverging channel. Entrainment rates are determined from velocity and temperature measurements and related to channel diffuser angle, inflow densimetric Froude number, and inflow channel aspect ratio. The experiments are conducted at inflow channel Reynolds numbers larger than 10,000. Experimental diffuser angles are varied from 3° to 180°, inflow densimetric Froude numbers from 1.8 to 21 and channel aspect ratios from 0.5 to 1.8. The information is of use as input to one‐dimensional stratified lake or reservoir water quality models.

Inflows, density currents, and fronts

The inflow of a fluid of different density into an ambient fluid of uniform density and finite depth is studied numerically using the full Navier–Stokes and diffusion equations. The problem is posed as an initial-boundary-value problem. In both the overflow (lighter buoyant inflow) and underflow (heavier inflow) cases, a gravity current is established with a pronounced headwave. A significant feature of the flows is the presence of strong downwelling (overflow case) and upwelling (underflow case) activity near the front. The overflow case has been applied by Kao, Park, and Pao to the study of small-scale oceanic fronts formed by the river discharge into the coastal region. The present paper deals with the fluid mechanical and numerical aspects of the overall problem in addition to presenting the results of the underflow case. It is found that the characteristics of the flow in the near field of the inflow are mainly governed by an inflow densimetric Froude number, Fe. In particular, the flow regime in the near field gradually changes from a plume-like to a jet-like behavior as Fe changes from less than to greater than unity. For the overflow case the local densimetric Froude number Fd of the current is shown to be a constant and a similarity solution is found in the far field behind the headwave giving a universal result for the density and velocity structure in the vertical for the range of parameters explored.