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1.
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.  相似文献   

2.
A cross-sectional nonhydrostatic model using idealized sill topography is used to examine the influence of bottom friction upon unsteady lee wave generation and flow in the region of a sill. The implications of changes in shear and lee wave intensity in terms of local mixing are also considered. Motion is induced by a barotropic tidal flow which produces a hydraulic transition, associated with which are convective overturning cells, wave breaking, and unsteady lee waves that give rise to mixing on the lee side of the sill. Calculations show that, as bottom friction is increased, current profiles on the shallow sill crest develop a highly sheared bottom boundary layer. This enhanced current shear changes the downwelling of isotherms downstream of the sill with an associated increase in the hydraulic transition, wave breaking, and convective mixing in the upper part of the water column. Both short and longer time calculations with wide and narrow sills for a number of sill depths and buoyancy frequencies confirm that increasing bottom friction modifies the flow and unsteady lee wave distribution on the downstream side of a sill. Associated with this increase in bottom friction coefficient, there is increased mixing in the upper part of the water column with an associated decrease in the vertical temperature gradient. However, this increase in mixing and decrease in temperature gradient in the upper part of the water column is very different from the conventional change in near-bed temperature gradient produced by increased bottom mixing that occurs in shallow sea regions as the bottom drag coefficient is increased.  相似文献   

3.
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.  相似文献   

4.
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.  相似文献   

5.
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.  相似文献   

6.
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.  相似文献   

7.
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.  相似文献   

8.
Vertical mixing in Überlingersee is studied by releasing sulfur hexafluoride (SF6) as a tracer at a central hypolimnic depth of 60 m and measuring its subsequent vertical dispersion over a period of three months. The experiment started with a streaky tracer injection of 1 liter gaseous SF6 (STP) in August 1990. At that time the lake showed a typical strong summer stratification which in a weakened form lasts until November. From the SF6 profiles of fifteen surveys at three sampling sites vertical diffusivitiesK z are calculated compensating internal seiche displacement and horizontal tracer loss. Except of the bottom region no sampling site or time period is marked by significant differences in the hypolimnicK z profile. So vertical mixing in the whole Überlingersee is described by mean diffusivities decreasing from 1.7 cm2/s at 120 m depth to 0.4 cm2/s in 30 m. The minimal value of 0.3 cm2/s in the thermocline region at 20 m depth is only based on observations in autumn. For a strong summer stratification it is certainly lower. The gradient-flux-method for heat was applied to compute a meanK z (T) profile from continuously measured temperature profiles. Significant differences resulting from the two tracers showed, that theK z (T) values are underestimated by up to a factor of 5 if cooling by lateral exchange is neglected. Particularly, internal seiche pumping of colder water from the adjacent Lake Obersee over the separating sill of Mainau into the deep Überlingersee basin is observed in 1990 from August onward, obviously controlling the heat budget below the sill level.  相似文献   

9.
The local scouring downstream of bed sills forming a sequence for bed stabilization in steep channels has been investigated in a laboratory flume. The initial bed slopes ranged from 0·078 to 0·148. The bed alluvium was characterised by a non‐uniform grain size distribution. The results show that when the ratio between the critical water depth hc and the sill spacing L rises above a characteristic value the scouring dynamics become heavily affected by the presence of the downstream sill, associated with the onset of a form of “interference” which renders the scouring process less effective. The difference with an “undisturbed” case is demonstrated. Self‐affinity of scour holes is confirmed and the scour length appears to be the reference parameter from which the scour depth might be evaluated. Copyright © 2003 John Wiley & Sons, Ltd.  相似文献   

10.
The deformation of movable boundaries under the action of an applied turbulent shear stress is well known. The resulting bed forms often are highly organized and nearly two-dimensional, which makes them an intriguing focus of study considering that they are generated in both steady and oscillatory turbulent flows. Many past studies share a common approach in which an infinitesimal perturbation is prescribed and the resulting growth or decay patterns are examined. In this approach, the bed forms are usually sinusoidal and the perturbation analysis does not provide a theoretical prediction of equilibrium bed-form geometry. An alternative approach is suggested here in which the forcing terms (pressure and stress) are prescribed parametrically and the governing equations are solved for the flow velocity and the associated boundary deformation. Using a multilayered approach, in which the bottom boundary layer is divided into a discrete, yet, arbitrary number of finite layers, analytical solutions for the horizontal current and bed profile are derived. The derivations identify two nondimensional parameters, p0/u02 and 0/kh0u02, which modulate the amplitude of the velocity fluctuations and boundary deformation. For the case of combined pressure and stress divergence anomalies, the magnitude of the front face and lee slopes exhibit an asymmetry that is consistent with observed bed forms in steady two-dimensional flows.Responsible Editor: Jens Kappenberg  相似文献   

11.
Abstract

Despite their close proximity and similar dimensions (～ 200m deep × 10km long × 2km wide) the two eastern basins of Lake Lucerne, Gersauersee and Urnersee, exhibit considerable differences in their internal behaviour, particularly during late winter and spring. The two lakes are separated by a small intermediate basin (～ 120m deep × 4km long × 1km wide) with sills of approximately 90m depth at each end. We report results of a field program conducted over the period February—May, 1988, when observations were obtained from weekly CTD transects and from three thermistor string/current meter moorings deployed for two months, one near each sill and the third at the southern end of Urnersee near Fluelen. During the observation period the stratification, relative surface to bottom density difference, Δρ/ρ, was 12 × 10?6 in Gersauersee and 4 × 10?6 in Urnersee. Following wind events a large amplitude internal seiche in Gersauersee (vertical excursions of ～50m and period ～60 hours) effectively pumped the heavier Gersauersee bottom water onto the intermediate basin and eventually into the hypolimnion of Urnersee. Temperature spectra show a peak at this seiche frequency at all levels at the Gersauer sill but only near the bottom at the sill in Urnersee. Coherence estimates between the bottom temperatures at Gersauer sill and Fluelen showed a significant peak at period 60 hours suggesting transmission of energy from the Gersauersee seiching motion through the weaker stratification of Urnersee to Fluelen. The phase relationships indicate that the wave phase speed decreases as the wave propagates into the region of weaker stratification. Application of a simple two-layer Defant model which includes topographic variations confirms these observations. The estimated volume exchange due to seiche pumping is only a small fraction of the Urnersee hypolimnion. However, the dissipation of energy transferred from the Gersauersee seiche may be an important contribution to mixing in the deeper waters of Urnersee.  相似文献   

12.
Cai  Shuqun  Wu  Yuqi  Xu  Jiexin  Chen  Zhiwu  Xie  Jieshuo  He  Yinghui 《中国科学:地球科学(英文版)》2021,64(10):1674-1686
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.  相似文献   

13.
A numerical model of deep, uniform, oscillatory, rough-turbulent boundary-layer flow is described. The model is based upon the governing horizontal momentum equation and a closure scheme involving the turbulent-energy equation and various turbulence-scaling laws. Finite difference solutions of these equations are obtained for a range of values of the ‘relative roughness’ (A0/ks), whereA0 is the excursion amplitude of the water particles in the free-stream flow andks is the ‘equivalent bed roughness’. Typical vertical profiles of horizontal velocity, turbulence energy and eddy viscosity, and time-series of the bed shear stress are presented. The model results are then used to determine the wave drag coefficient, boundary-layer thickness and phase lead of the bed shear stress over the free-stream velocity, each as a function ofA0/ks. These results are shown to be in generally good agreement with previous experimental and theoretical results. Finally, the model is used to test for the existence of a universal velocity distribution for uniform oscillatory (sinusoidal) rough-turbulent flow. The ‘law of the wall’ and the ‘defect law’ proposed by Jonsson (1980, Ocean Engineering, 7, 109–152) are well supported by the model, and the existence of a logarithmic ‘velocity overlap layer’ in which both of these laws are valid is demonstrated forAo/ks30.  相似文献   

14.
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.  相似文献   

15.
Single bed load particle impacts were experimentally investigated in supercritical open channel flow over a fixed planar bed of low relative roughness height simulating high‐gradient non‐alluvial mountain streams as well as hydraulic structures. Particle impact characteristics (impact velocity, impact angle, Stokes number, restitution and dynamic friction coefficients) were determined for a wide range of hydraulic parameters and particle properties. Particle impact velocity scaled with the particle velocity, and the vertical particle impact velocity increased with excess transport stage. Particle impact and rebound angles were low and decreased with transport stage. Analysis of the particle impacts with the bed revealed almost no viscous damping effects with high normal restitution coefficients exceeding unity. The normal and resultant Stokes numbers were high and above critical thresholds for viscous damping. These results are attributed to the coherent turbulent structures near the wall region, i.e. bursting motion with ejection and sweep events responsible for turbulence generation and particle transport. The tangential restitution coefficients were slightly below unity and the dynamic friction coefficients were lower than for alluvial bed data, revealing that only a small amount of horizontal energy was transferred to the bed. The abrasion prediction model formed by Sklar and Dietrich in 2004 was revised based on the new equations on vertical impact velocity and hop length covering various bed configurations. The abrasion coefficient kv was found to be vary around kv ~ 105 for hard materials (tensile strength ft > 1 MPa), one order of magnitude lower than the value assumed so far for Sklar and Dietrich's model. Copyright © 2017 John Wiley & Sons, Ltd.  相似文献   

16.
Field data from the Rio Paraná, Argentina, are used to examine patterns of suspended sediment transport over a sand dune. Measurements of three‐dimensional velocity are made with an acoustic Doppler current profiler whilst suspended sediment concentration and particle size have been quantified using a laser in situ sediment scattering transmissometer. Suspended sediment concentration and streamwise and vertical sediment flux are highest close to the bed, with an upward vertical flux over the stoss side of the dune and downward flux over the lee side. Suspended sediment concentrations are higher over the crest compared with the trough and suspended sediment is coarsest near the bed. About 17% of the suspended‐load transported over the crest is deposited in the lee side before it reaches the trough. Most of this deposited sand is coarser sediment that originates close to the bed over the crest, a result consistent with simulations based on the model of Mohrig and Smith (Water Resources Research 1996; 32: 3207–3217) for the excursion lengths of sediment dispersed in the lee side of a dune. Copyright © 2009 John Wiley & Sons, Ltd.  相似文献   

17.
Analytical solutions that use diurnal temperature signals to estimate vertical fluxes between groundwater and surface water based on either amplitude ratios (Ar) or phase shifts (Δ?) produce results that rarely agree. Analytical solutions that simultaneously utilize Ar and Δ? within a single solution have more recently been derived, decreasing uncertainty in flux estimates in some applications. Benefits of combined (ArΔ?) methods also include that thermal diffusivity and sensor spacing can be calculated. However, poor identification of either Ar or Δ? from raw temperature signals can lead to erratic parameter estimates from ArΔ? methods. An add‐on program for VFLUX 2 is presented to address this issue. Using thermal diffusivity selected from an ArΔ? method during a reliable time period, fluxes are recalculated using an Ar method. This approach maximizes the benefits of the Ar and ArΔ? methods. Additionally, sensor spacing calculations can be used to identify periods with unreliable flux estimates, or to assess streambed scour. Using synthetic and field examples, the use of these solutions in series was particularly useful for gaining conditions where fluxes exceeded 1 m/d.  相似文献   

18.
Recent field investigations have shown that differential mixing causes a significant density driven exchange between the two eastern basins of Lake Lucerne, Gersauersee and Urnersee. The long term vertical mixing characteristics during the winter mixing period and the influence of the resulting exchange flow on water quality are examined through the analysis of ten years (1964 to 1974) of monthly limnological data. Vertical homogenization of the state variables (temperature, electric conductivity and density) occurred on average once every two years in Urnersee, but not once in Gersauersee where the ten year average winter mixed-layer depth extended to 120 m. In Urnersee intense mixing was evident over the whole water column for every year. In contrast intense mixing in the deeper layers of Gersauersee occurred approximately once every four years. A three layer model shows that theT/ 20 signature of the Gersauersee intermediate water correlates best with the Urnersee deep water confirming the regular occurrence of a density driven exchange. For the lower layers the oxygen consumption rate in Urnersee was approximately twice that for Gersauersee. It appears the exchange flow can act either as a source or sink for the oxygen balance of Urnersee deep water. The larger rate in Urnersee hypolimnion might also be associated with the larger sediment input to this system. Density driven exchange resulting from differential mixing is probably an important contribution to the vertical water replenishment in many lakes.  相似文献   

19.
A three-dimensional prognostic hydrodynamic model in cross sectional form is used to examine the influence of bottom friction, mixing and topography upon the spin-down and steady-state circulation in a cold water bottom-dome. Parameters characteristic of the Irish Sea or Yellow Sea cold water domes are used. In all calculations, motion is induced by specifying an initial temperature distribution characteristic of the dome, and an associated along frontal flow. The spin-down of the dome is found to be influenced by the coefficient of bottom friction, with a typical time scale of order 10 days, and in general to be independent of the chosen initial vertical profile of along frontal flow. However, in the case in which the along frontal flow is such that the near bed velocity is zero, then bottom stress is also zero, and there is no appreciable spin-down. Calculations showed that the formulation of viscosity and diffusivity had a greater effect upon the steady-state circulation than topography, suggesting that background mixing of tidal origin is important. The lack of topographic influence was due mainly to the formulation of the initial conditions which were taken to be independent of topography. The steady-state circulation was characterized by a cyclonic flow in the surface region, with an anti-cyclonic current near the bed, where frictional effects produced a bottom Ekman layer and an across frontal flow. This gave rise to vertical circulation cells in the frontal region of the dome with prevailing downwelling motion inside the dome. A detailed analysis of the dynamic balance of the various terms in the hydrodynamic equations yielded insight into the processes controlling the steady-state circulation in cold water domes. Responsible Editor: Phil Dyke  相似文献   

20.
A non-hydrostatic terrain-following model in cross sectional form is applied to study the processes in the lee of a sill in an idealized stratified fjord during super-critical tidal inflow. A sequence of numerical studies with horizontal grid sizes in the range from 100 to 1.5625 m are performed. All experiments are repeated using both hydrostatic and non-hydrostatic versions of the model, allowing a systematic study of possible non-hydrostatic pressure effects and also of the sensitivity of these effects to the horizontal grid size. The length scales and periods of the internal waves in the lee of the sill are gradually reduced and the amplitudes of these waves are increased as the grid size is reduced from 100 down to 12.5 m. With a further reduction in grid size, more short time and space scale motions become superimposed on the internal waves. Associated with the internal wave activity, there is a deeper separation point that is fairly robust to all parameters investigated. Another separation point nearer to the top of the sill appears in the numerical results from the high-resolution studies with the non-hydrostatic model. Associated with this shallower separation point, an overturning vortex appears in the same set of numerical solutions. This vortex grows in strength with reduced grid size in the non-hydrostatic experiments. The effects of the non-hydrostatic pressure on the velocity and temperature fields grow with reduced grid size. In the experiments with horizontal grid sizes equal to 100 or 50 m, the non-hydrostatic pressure effects are small. For smaller grid sizes, the time mean velocity and temperature fields are also clearly affected by the non-hydrostatic pressure adjustments.  相似文献   

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