Effect of water depth and the bottom boundary layer upon internal wave generation over abrupt topography

The role of water depth and bottom boundary layer turbulence upon lee-wave generation in sill regions is examined. Their effect upon vertical mixing is also considered. Calculations are performed using a non-hydrostatic model in cross-section form with a specified tidal forcing. Initial calculations in deeper water and a sill height such that the sill top is well removed from the surrounding bed region showed that downstream lee-wave generation and associated mixing increased as bottom friction coefficient k increased. This was associated with an increase in current shear across the sill. However, for a given k, increasing vertical eddy viscosity A _v reduced vertical shear in the across sill velocity, leading to a reduction in lee-wave amplitude and associated mixing. Subsequent calculations using shallower water showed that for a given k and A _v, lee-wave generation was reduced due to the shallower water depth and changes in the bottom boundary layer. However, in this case (unlike in the deepwater case), there is an appreciable bottom current. This gives rise to bottom mixing which in shallow water extends to mid-depth and enhances the mid-water mixing that is found on the lee side of the sill. Final calculations with deeper water but small sill height showed that lee waves could propagate over the sill, thereby reducing their contribution to mixing. In this case, bottom mixing was the major source of mixing which was mainly confined to the near bed region, with little mid-water mixing.     

On the importance of non-hydrostatic processes in determining tidally induced mixing in sill regions

The importance of using a non-hydrostatic model to compute tidally induced mixing and flow in the region of a sill is examined using idealized topography representing the sill at the entrance to Loch Etive. This site is chosen since detailed measurements were recently made there. Calculations are performed with and without the inclusion of non-hydrostatic dynamics using a vertical slice model for a range of sill widths corresponding to typical sill regions. Initial non-hydrostatic calculations showed that the model could reproduce the observed flow characteristics in the region. However, when calculations were performed using the model in hydrostatic form, the significant artificial convective mixing that occurred in order to remove density inversions led to excessively high vertical mixing. This influenced the computed temperature field and the intensity of the current jet that separated from the sill on its lee side. In addition it affected the magnitude and spatial characteristics of the lee waves generated on the lee side of the sill. Calculations with a range of sill widths, showed that as the sill width decreased the difference between the solution computed with the non-hydrostatic and hydrostatic model increased.     

Numerical modelling of stratified tidal flow over a fjord sill

Field observations of tidally driven stratified flow in the sill area of Knight Inlet (British Columbia) revealed a very complicated structure, which includes solitary waves, upstream bifurcation, hydraulic jump and mixing processes. Recent observations suggest that the flow instabilities on the plunging pycnocline at the lee side of the sill may contribute to solitary wave generation through a subharmonic interaction. The present study reports on a series of numerical experiments of stratified tidal flow in Knight Inlet performed with the help of a fine resolution fully non-linear non-hydrostatic numerical model. The model reproduces all important stages of the baroclinic tidal dynamics observed in Knight Inlet. Results demonstrate that solitary waves are generated apart from the area of hydrodynamic instability. Accelerating tidal flux forms a baroclinic hydraulic jump just above the top of the sill, whereas the bifurcations and zones of shear instabilities are formed downstream of the sill. The first baroclinic mode having the largest velocity escapes from the generation area and propagates upstream, disintegrating further into a packet of solitary waves reviling the classical “non-subharmonic” mechanism of generation. The remaining part of the disturbance (slow baroclinic modes) is arrested by tidal flow and carried away to the lee side of the obstacle, where shear instability, billows and mixing processes are developed. Some sensitivity runs were performed for different value of tidal velocity.     

Non-hydrostatic and non-linear contributions to the internal wave energy flux in sill regions

A three-dimensional non-linear, non-hydrostatic model in cross-sectional form is used to determine the factors influencing the relative importance of the linear, non-hydrostatic and non-linear contributions to the internal wave energy flux in sill regions due to tidal forcing. The importance of the free surface elevation term is also considered. Idealised topography representing the sill at the entrance to Loch Etive, the site of a recent measurement programme, is used. Calculations show that the non-linear terms in the energy flux become increasingly important as the sill Froude Number (F _s) increases and the sill aspect ratio is increased. The vertical profile of the stratification, in particular its value close to the sill crest where internal waves are generated, has a significant influence on unsteady lee wave and mixed tidal–lee wave generation and the non-linear contribution to the energy flux. Calculations show that as F _s increases, the energy flux due to the non-linear and non-hydrostatic terms increases more rapidly than the linear term. The importance of the non-linear terms in the energy flux also increases as the sill aspect ratio is increased. Increasing the buoyancy frequency reduces the contribution of the non-hydrostatic and non-linear terms to the total energy flux. Also, as the buoyancy frequency is increased, this reduces unsteady lee wave and mixed tidal–lee wave generation. In essence, these calculations show that the energy flux due to the non-hydrostatic and non-linear terms is appreciable in sill regions.     

On the generation and propagation of internal solitary waves in the southern Andaman Sea: A numerical study

Numerous internal solitary waves(ISWs) have been observed in the southern Andaman Sea. In this study, the two-dimensional Massachusetts Institute of Technology general circulation model is applied to investigate the dynamics of ISWs and explore the effects of the bottom topography and tidal forcing on the generation and propagation of ISWs in the southern Andaman Sea. The results show that the large-amplitude depression ISWs are mainly generated via the oscillating tidal flow over the sill of the Great Channel, and the generation of ISWs is subject to the lee wave regime. The Dreadnought Bank cannot generate ISWs itself; however, it can enhance the amplitudes of eastward-propagating ISWs generated from sill A, owing to constructive interference of internal tide generation between the sill of the Great Channel and the Dreadnought Bank. The eastward-propagating ISWs generated by the eastern shallow sill near the continental shelf can propagate to the shelf, where they evolve into elevation waves because of the shallow water. Sensitivity runs show that both the semidiurnal and diurnal tides over the sill of the Great Channel can generate ISWs in this area. However, the ISWs generated by diurnal tides are much weaker than those generated by semidiurnal tides. Mixed tidal forcing has no significant effect on the generation of ISWs.     

Tidal mixing in sill regions: influence of sill depth and aspect ratio

A non-hydrostatic model in cross-sectional form with an idealized sill is used to examine the influence of sill depth (h _s) and aspect ratio upon internal motion. The model is forced with a barotropic tide and internal waves and mixing occurs at the sill. Calculations using a wide sill and quantifying the response using power spectra show that for a given tidal forcing namely Froude number F _r as the sill depth (h _s) increases the lee wave response and vertical mixing decrease. This is because of a reduction in across sill velocity U _s due to increased depth. Calculations show that the sill Froude number F _s based on sill depth and across sill velocity is one parameter that controls the response at the sill. At low F _s (namely F _s ≪ 1) in the wide sill case, there is little lee wave production, and the response is in terms of internal tides. At high F _s, calculations with a narrow sill show that for a given F _s value, the lee wave response and internal mixing increase with increasing aspect ratio. Calculations using a narrow sill with constant U _s show that for small values of h _s, a near surface mixed layer can occur on the downstream side of the sill. For large values of h _s, a thick well-mixed bottom boundary layer occurs due to turbulence produced by the lee waves at the seabed. For intermediate values of h _s, “internal mixing” dominates the solution and controls across thermocline mixing.     

On the influence of stratification and tidal forcing upon mixing in sill regions

A cross-sectional non-hydrostatic model with idealized topography was used to examine the processes influencing tidal mixing in the region of sills. Initial calculations with appropriate parameters for the sill at the entrance to Loch Etive showed that the model could reproduce the main features of the observed mixing in the region. In particular, the hydraulic jump in the sill region was reproduced, as was an intense mid-water jet that was observed to separate from the lee side of the sill. Shear instabilities associated with the jet appeared to be a source of mixing within the thermocline. In addition, internal lee waves were generated on the lee side of the sill, with the observed amplification because of trapping during the flood stage. Their magnitude and hence the mixing increased with increasing Froude number (F _r). In the case of vertically varying buoyancy frequency, its value near the sill top determined the F _r number, with its value below influencing internal waves magnitude at depth. At high F _r values particularly with strong currents, short waves and overturning occurred.     

Internal solitary wave-induced flow over a corrugated bed

A combined numerical and experimental study of the propagation of an internal solitary wave (ISW) over a corrugated bed is presented, in which the amplitude and the wavelength of the corrugated bed, together with the wave amplitude and wave speed of the ISW, have been varied parametrically. Both ISWs of elevation and depression have been considered. The wave-induced currents over the corrugated bed cause flow separation at the apex of the corrugations and a sequence of lee vortices forms as a result. These vortices develop fully after the main wave has passed over the topographic feature, resulting in deformation of the overlying pycnocline and, in some instances, significant vertical mixing. It is found that the intensity of the vortex formation is dependent on both the amplitude and wavelength of the bottom topography. In the case of an ISW of depression, the generation of vertically (upward)-propagating vortices is seen to result in entrainment of fluid from a bottom boundary jet (Carr and Davies, Phys Fluids 18:016601, 2006), while, in the elevation case, a second mechanism is present to induce significant turbulent mixing in the water column. It occurs when the bottom corrugations reach into, or are very near, the pycnocline at rest. Large waves of elevation that are stable on approach to the corrugations exhibit evidence of a spatio-temporally developing shear instability as they interact with the bottom corrugation. The shear instability takes the form of billows that have a vertical extent that can reach 50% of the wave amplitude.     

Inclined internal tide waves at a narrow Mexican Pacific shelf

The dynamics of a semidiurnal internal tidal wave at a narrow Mexican Pacific shelf is discussed using the data of temperature obtained by an anchored instrument and data of field surveys. The internal tide on the shelf is dominated by an inclined wave, which propagates upward and onshore along a continental slope. Despite its reflection from the bottom and from the surface of the ocean, they remain inclined and totally destroyed over the course of one wavelength. Due to wave reflection from the inclined bottom, the horizontal and vertical wave number increase threefold when the wave goes into shallow waters. The wave undergoes nonlinear transformation and overturns forming several homogeneous temperature layers up to 20 m thick. The most intense disturbances of water layers are observed near the bottom, where the slope angle approaches its critical value. Because of nonlinear effects, the wave carries cool deep water out to the shallow depth and causes coastal upwelling. Intense solar warming together with vertical mixing results in a rapid rise of temperature in the 130-m water column that was observed.     

Numerical investigations of the turbulent kinetic energy dissipation rate in the Rhine region of freshwater influence

The turbulent kinetic energy dissipation rate, ε, in tidal seas is maximum at the bottom during full flood and during full ebb, i.e. when tidal currents are strongest. In coastal regions with tides similar to a Kelvin wave, this coincides with high water and low water. If there is a freshwater source at the coast, stratification in such a region will be most stable at high water and least at low water. Measurements of ε in the Rhine region of freshwater influence performed by previous studies have revealed bottom maxima at both high and low water. In addition, a maximum in the upper half of the water column was found around high water, which cannot be explained by tidal shear at the bottom, convective instabilities or wind mixing. This study investigates the dissipation rate and relevant physical properties in the Rhine region of freshwater influence by means of three-dimensional numerical simulations using the General Estuarine Transport Model and idealised conditions. The measurements are well reproduced; two distinct peaks of ε are evident in the upper layer shortly before and after high water. These maxima turn out to be due to strong peaks in the alongshore shear occurring when the fore- and the back-front of the plume transit the water column.     

The baroclinic circulation structure of Yellow Sea Cold Water Mass

The Yellow Sea is a semi-enclosed shallow sea with a deep trough of about 80 m. On the hy-drographic condition in the Yellow Sea, Lie[1] pointed out that it is strongly associated with winter cooling and summer heating, fresh input from rivers into the co…     

ESTIMATES OF TERRESTRIAL THERMAL GRADIENTS AND HEAT FLOW VARIATIONS WITH DEPTH IN THE HINTON-EDSON AREA OF THE ALBERTA BASIN DERIVED FROM PETROLEUM BOTTOM-HOLE TEMPERATURE DATA*

There is a significant increase in terrestrial heat flow with depth in the Hinton-Edson area of the deep part of the western Canadian sedimentary basin in Alberta. This is especially true near the Rocky Mountain foothills which is an area of high relief, high hydraulic head and regional water recharge. Gravity-imposed downward movement of meteoric water through the thick sedimentary strata with velocities as low as 10^–10 m/s to 0.5 × 10^–9 m/s may cause an increase of heat flow with depth. Such disturbance of heat flow with depth on a regional scale in the sedimentary strata means that it is not possible to determine the background conductive steady-state heat flow associated with crustal or upper mantle heat sources in such an area from measurement of conductive heat flow in the part of the sedimentary column where water movement occurs. This is because the convective portion cannot be determined, particularly when measurements are made in only part of the regional hydrodynamic system of the basin.     

The effects of large and small-scale topography upon internal waves and implications for tidally induced mixing in sill regions

A free surface non-hydrostatic model in a cross-sectional form, namely, two-dimensional, in the vertical is used to examine the role of larger-scale topography, namely, sill width, and smaller scale topography, namely, ripples on the sill upon internal wave generation and mixing in sill regions. The present work is set in the context of earlier work and the wider literature in order to emphasise the problems of simulating mixing in hydrographic models. Highlights from previous calculations and references to the literature for detail, together with new results presented here with smooth and “ripple” topography, are used to show that an idealised cross-sectional model can reproduce the dominant features found in observations at the Loch Etive sill. Calculations show that on both the short and long time scales, the presence of small-scale “ripple” topography influence the mixing and associated Richardson number distribution in the sill region. Subsequent calculations in which the position and form of the small-scale sill topography is varied show for the first time that it is the small-scale topography near the sill crest that is particularly important in enhancing mid-water mixing on the lee side of the sill. Both short-term and longer-term calculations with a reduced sill width and associated time series show that as the sill width is reduced, the non-linear response of the system increases. In addition, Richardson number plots show that the region of critical Richardson number, and hence enhanced mixing, increases with time and a reduction in sill width. Calculations in which buoyancy frequency N varies through the vertical show that buoyancy frequency close to the top of the sill is primarily controlling mixing rather than its mean value. Hence, a Froude number based on sill depth and local N is the critical parameter rather than one based on total depth and mean N.     

A fuzzy dynamic wave routing model

In this paper a fuzzy dynamic wave routing model (FDWRM) for unsteady flow simulation in open channels is presented. The continuity equation of the dynamic wave routing model is preserved in its original form while the momentum equation is replaced by a fuzzy rule based model which is developed on the principle that during unsteady flow the disturbances in the form of discontinuities in the gradient of the physical parameters will propagate along the characteristics with a velocity equal to that of velocity of the shallow water wave. The model gets rid off the assumptions associated with the momentum equation by replacing it with the fuzzy rule based model. It overcomes the necessity of calculating friction slope (S_f) in flow routing and hence the associated uncertainties are eliminated. The robustness of the fuzzy rule based model enables the FDWRM to march the solution even in regions where the aforementioned assumptions are violated. Also the model can be used for flow routing in curved channels. When the model is applied to hypothetical flood routing problems in a river it is observed that the results are comparable to those of an implicit numerical model (INM) which solves the dynamic wave equations using an implicit numerical scheme. The model is also applied to a real case of flow routing in a field canal. The results match well with the measured data and the model performs better than the INM. Copyright © 2007 John Wiley & Sons, Ltd.     

Hydrodynamic response of a fringing coral reef to a rise in mean sea level

Ningaloo Reef, located along the northwest coast of Australia, is one of the longest fringing coral reefs in the world extending ~300 km. Similar to other fringing reefs, it consists of a barrier reef ~1–6 km offshore with occasional gaps, backed by a shallow lagoon. Wave breaking on the reef generates radiation stress gradients that produces wave setup across the reef and lagoon and mean currents across the reef. A section of Ningaloo Reef at Sandy Bay was chosen as the focus of an intense 6-week field experiment and numerical simulation using the wave model SWAN coupled to the three-dimensional circulation model ROMS. The physics of nearshore processes such as wave breaking, wave setup and mean flow across the reef was investigated in detail by examining the various momentum balances established in the system. The magnitude of the terms and the distance of their peaks from reef edge in the momentum balance were sensitive to the changes in mean sea level, e.g. the wave forces decreased as the mean water depth increased (and hence, wave breaking dissipation was reduced). This led to an increase in the wave power at the shoreline, a slight shift of the surf zone to the lee side of the reef and changes in the intensity of the circulation. The predicted hydrodynamic fields were input into a Lagrangian particle tracking model to estimate the transport time scale of the reef-lagoon system. Flushing time of the lagoon with the open ocean was computed using two definitions in renewal of semi-enclosed water basins and revealed the sensitivity of such a transport time scale to methods. An increase in the lagoon exchange rate at smaller mean sea-level rise and the decrease at higher mean sea-level rise was predicted through flushing time computed using both methods.     

Simulation of annual biogeochemical cycles of nutrient balance, phytoplankton bloom(s), and DO in Puget Sound using an unstructured grid model

Nutrient pollution from rivers, nonpoint source runoff, and nearly 100 wastewater discharges is a potential threat to the ecological health of Puget Sound with evidence of hypoxia in some basins. However, the relative contributions of loads entering Puget Sound from natural and anthropogenic sources, and the effects of exchange flow from the Pacific Ocean are not well understood. Development of a quantitative model of Puget Sound is thus presented to help improve our understanding of the annual biogeochemical cycles in this system using the unstructured grid Finite-Volume Coastal Ocean Model framework and the Integrated Compartment Model (CE-QUAL-ICM) water quality kinetics. Results based on 2006 data show that phytoplankton growth and die-off, succession between two species of algae, nutrient dynamics, and dissolved oxygen in Puget Sound are strongly tied to seasonal variation of temperature, solar radiation, and the annual exchange and flushing induced by upwelled Pacific Ocean waters. Concentrations in the mixed outflow surface layer occupying approximately 5–20?m of the upper water column show strong effects of eutrophication from natural and anthropogenic sources, spring and summer algae blooms, accompanied by depleted nutrients but high dissolved oxygen levels. The bottom layer reflects dissolved oxygen and nutrient concentrations of upwelled Pacific Ocean water modulated by mixing with biologically active surface outflow in the Strait of Juan de Fuca prior to entering Puget Sound over the Admiralty Inlet. The effect of reflux mixing at the Admiralty Inlet sill resulting in lower nutrient and higher dissolved oxygen levels in bottom waters of Puget Sound than the incoming upwelled Pacific Ocean water is reproduced. By late winter, with the reduction in algal activity, water column constituents of interest, were renewed and the system appeared to reset with cooler temperature, higher nutrient, and higher dissolved oxygen waters from the Pacific Ocean.     

Source term balance in a severe storm in the Southern North Sea

This paper presents the results of a wave hindcast of a severe storm in the Southern North Sea to verify recently developed deep and shallow water source terms. The work was carried out in the framework of the ONR funded NOPP project (Tolman et al. 2013) in which deep and shallow water source terms were developed for use in third-generation wave prediction models. These deep water source terms for whitecapping, wind input and nonlinear interactions were developed, implemented and tested primarily in the WAVEWATCH III model, whereas shallow water source terms for depth-limited wave breaking and triad interactions were developed, implemented and tested primarily in the SWAN wave model. So far, the new deep-water source terms for whitecapping were not fully tested in shallow environments. Similarly, the shallow water source terms were not yet tested in large inter-mediate depth areas like the North Sea. As a first step in assessing the performance of these newly developed source terms, the source term balance and the effect of different physical settings on the prediction of wave heights and wave periods in the relatively shallow North Sea was analysed. The December 2013 storm was hindcast with a SWAN model implementation for the North Sea. Spectral wave boundary conditions were obtained from an Atlantic Ocean WAVEWATCH III model implementation and the model was driven by hourly CFSR wind fields. In the southern part of the North Sea, current and water level effects were included. The hindcast was performed with five different settings for whitecapping, viz. three Komen type whitecapping formulations, the saturation-based whitecapping by Van der Westhuysen et al. (2007) and the recently developed ST6 whitecapping as described by Zieger et al. (2015). Results of the wave hindcast were compared with buoy measurements at location K13 collected by the Dutch Ministry of Transport and Public Works. An analysis was made of the source term balance at three locations, the deep water location North Cormorant, the inter-mediate depth location K13 and at location Wielingen, a shallow water location close to the Dutch coast. The results indicate that at deep water the source terms for wind input, whitecapping and nonlinear four-wave interactions are of the same magnitude. At the inter-mediate depth location K13, bottom friction plays a significant role, whereas at the shallow water location Wielingen also depth-limited wave breaking becomes important.     

Darcian Flow Characteristics Upgradient of a Kettle Pond Determined by Direct Ground Water Flow Measurement

In glacial outwash deposits, the movement of ground water Is determined by small scale irregularities in the pattern of hydraulic conductivity. Permeability determinations on split spoon samples obtained from coring the site are not sufficient to predict the patchiness of flow since it cannot define continuity of the strata. The lattice work pattern can be determined by vertical profiling with direct ground water flow measurement. The rate and direction of flow is combined with head gradient changes to compute hydraulic conductivity changes across the site.
The results of the tests can be plotted on triangular graphs depicting the fundamental Darcy equation. The local conditions reflect a mathematical "patchiness" of hydraulic conductivity unique to outwash deposits.
The procedure was employed to determine flow characteristics and define the zone of contribution to porous bottom kettle lakes. The zone of contribution was defined by projecting backward from the vertical profiling and shallow measurements and taking into account the daily rain water recharge rate across the site.
For the unconfined aquifer north of the pond, shallow ground water flow measurements were necessary to define the recharge portion of the shoreline. Vertical profiling was required to define the recharge volume since the rate of flow was not even with depth. A simple differential equation for determining the recharge area is presented along with the calculations.     

Tides and mixing in the northwestern East China Sea Part I: Rotating and reversing tidal flows

Bottom-mounted ADV and ADCP instruments in combination with CTD profiling measurements taken along the Chinese coast of the East China Sea were used to study the vertical structure of temperature, salinity, and velocity in reversing tidal currents on a shallow inner shelf and in rotating tidal flows over a deeper sloping bottom of the outer shelf. These two regimes of barotropic tide affect small-scale dynamics in the lower part of the water column differently. The reversing flow was superimposed by seiches of ∼2.3 h period generated in semienclosed Jiaozhou Bay located nearby. As the tidal vector rotates over the sloping bottom, the height of the near-bottom logarithmic layer is subjected to tidal-induced variations. A maximum of horizontal velocity U_max appears at the upper boundary of the log layer during the first half of the current vector rotation from the minor to the major axis of tidal ellipse. In rotating tidal flow, vertical shear generated at the seafloor, propagated slowly to the water interior up to the height of U_max, with a phase speed of ∼5 m/h. The time-shifted shear inside the water column, relative to the shear at the bottom, was associated with periodically changing increases and decreases of the tidal velocity above the log layer toward the sea surface. In reversing flows, the shear generated near the bottom and the shear at the upper levels were almost in phase.     

Temporal Changes in VOC Discharge to Surface Water from a Fractured Rock Aquifer During Well Installation and Operation, Greenville, South Carolina

Analysis of the vapor in passive vapor samplers retrieved from a streambed in fractured rock terrain implied that volatile organic carbon (VOC) discharge from ground water to surface water substantially increased following installation of a contaminant recovery well using air rotary drilling. The air rotary technique forced air into the aquifer near the stream. The injection produced an upward hydraulic gradient that appears to have transported water and contaminants from deeper parts of the aquifer through fractures into shallow parts of the aquifer. Once in the shallow flow regime, the contamination was transported to the stream, where it discharged during the next several weeks following well installation. After the recovery well was activated and began continuously pumping contaminated ground water to a treatment facility, the VOC concentrations in the stream bottom passive vapor samplers decreased to below detectable concentrations, suggesting that the withdrawal had captured the contaminated ground water that previously had discharged to the stream.