The Rose Spit Eddy in Dixon Entrance: Evidence for its existence and underlying dynamics

Abstract

The existence and dynamics of the so‐called “Rose Spit Eddy” in Dixon Entrance, British Columbia, are investigated by (i) analysing published observations of low‐frequency Eulerian and Lagrangian currents in the region; (ii) interpreting tidal residuals produced by the Hecate Model (a non‐rotating hydraulic model of Hecate Strait and Dixon Entrance); and (iii) running a barotropic, non‐linear numerical tidal model over simplified topography to investigate residuals produced over the Rose Spit sill.

Observations have consistently revealed persistent basin‐wide, surface‐intensified cyclonic shears within central and eastern Dixon Entrance. The Hecate hydraulic tidal model also produced a tidal residual cyclonic gyre in central Dixon Entrance, but with velocities considerably larger than those observed. Barotropic numerical simulations of tidal streams flowing over a representation of the Rose Spit sill produced residual flows along the sill in reasonable agreement with observations and theory. A southward‐directed jet flow was produced off Cape Chacon. Elsewhere, tidal rectification was weak. Run without the Coriolis force, organized flow along the sill broke down, although the headland jet off Cape Chacon persisted.

We submit that the observed Rose Spit eddy results from interactions between buoyancy‐driven coastal currents and tidally rectified flows generated over the Rose Spit sill, and near Cape Chacon, and perhaps indirectly, over the western flank of Learmonth Bank (which although west of the Rose Spit eddy, contributes to the cross‐channel flow across the Entrance). These regions of localized tidal stress will each favour recirculation of a portion of the coastal current within the Entrance, helping to form the eddy.

We believe that the Hecate hydraulic model eddy was generated to a significant degree by phase errors introduced at the northern open boundary, where a rocking barrier was used to force currents. A second rocking barrier also produced a large cyclonic gyre, not supported by observations, near the model's southern boundary.     

Dissipative effects on inertial flows over a sill

A systematic investigation of the effects of various parametrizations of dissipation, e.g. quadratic and linear frictional drag, harmonic lateral viscosity, and harmonic lateral diffusion on inertial flow over a sill and possible hydraulic control is presented. Rotation effects are ignored and the geometry is assumed to vary only slowly with downstream distance so that the flow may be considered one-dimensional. Results are given both for a single-active layer and for two-active layers with a rigid lid.If the parametrization is only a function of the dependent variables and not of their spatial derivatives, then it may be possible to hydraulically control the flow. A general expression is derived for the possible control point and the two gradients there, which are functions of the slope and possibly of flow rate. Specific energy is irreversibly removed from the flow and non-controlled as well as controlled flows can exhibit significant asymmetry in fluid depth over a sill. The upstream specific energy, and hence depth of the lower layer, of the controlled flow is greater than for an ideal fluid. Frictional effects modify the behaviour of long gravity waves, such that they are dispersive and damped with time. The system will only exhibit hydraulic control if these effects are small.For a viscous single layer of fluid, the gradient in surface elevation is always uniquely defined, so classically defined hydraulic control, as such, cannot exist. However, for values of non-dimensional lateral eddy viscosity coefficient, , where q is the flow rate, there is a narrow band of specific energies centred around that for the control solution in an ideal fluid, E_crit, for which the surface elevation, h is very asymmetric over the sill; the solutions resemble the inviscid, hydraulically controlled solutions. Outside this range, either the fluid depth tends to zero, or the surface elevation is almost uniform over the sill. A ‘control’-type solution exists which has the conjugate values of the inviscid equation up- and downstream of the sill, where the gradient in fluid depth, and hence the viscous term, is zero. For larger values of A_M, the band of specific energies is much wider, and the upstream specific energy of the ‘control’-type solution is much lower than that for an inviscid fluid. Long gravity waves are dispersive and damped with time. There is a short-wave cut-off, k² > h/(4A_M²), above which waves are stationary in the flow. Longer waves, k² h/(4A_M²), are critical if , as for an ideal fluid. If these waves can propagate significant distances, then any observed asymmetry in h will be due to inertial and not to viscous effects. The behaviour of unidirectional, two-layer flow is similar. The governing equation for viscous, two-layer exchange flow is singular, and typically excludes the ‘control’-type solutions found for unidirectional flows.Establishing the existence and behaviour of steady inertial flows in the presence of lateral diffusion between layers is more difficult. It significantly alters the single-layer solutions once the non-dimensional coefficient A_H is large, i.e. . The flow rate may become zero on the downslope as all the fluid diffuses into the inert, infinitely deep, overlaying layer. The fluid depth is maintained by reverse flow from downstream. In this case, the depth of the active layer tends to zero downstream for all values of specific energy. For two-layer flow, both unidirectional and exchange, the governing equation is such that the lower-layer flow rate and interfacial height return to their upstream values.Motivation for the study is provided by the increasingly fine spatial resolution achievable in large-scale numerical models of the ocean general circulation, and the question of whether they are capable of simulating some form of hydraulic control. Application to modelling oceanic flows over a sill is discussed.     

Optimization of Upstream Profiles in Modelled Flow Over Complex Terrain

This paper describes an adjoint method for data assimilation intoupstream boundary conditions of numerical modelsusing optimal control theory. Mathematical formalisms are given along with the numerical implementation of the schemein a column model of the atmospheric boundary layer. The optimized mean and turbulence profiles are used as an upstream solutionin a model of turbulent flow in complex terrain. To contrast thiswith other methods, two solutions for flow over an isolatedhill are calculated, one with an optimized upstream solution andone with a simple surface-layer formulation for the upstream solution.These two solutions are compared to observations and analytical theory. The adjoint optimization method is shown to producesolutions of flow in complex terrain that are substantively differentat the two solutions, with the optimized solution giving more accurate results.     

Thermally induced flow in valleys with tributaries part I: Response to heating

Summary Flow in long and deep main valleys with tributaries is studied for constant surface heating switched on att=0. The valley flows are obtained from a numerical model which combines slope wind layer equations with equations for the valley flow off the slopes. Much simpler linear models are used for the intepretation of the model results. If there are no sidevalleys an up-valley wind regime evolves in the main valley after the switch-on of the heating which protrudes towards the head. It is shown that the topographic amplification factor which captures the geometry of the valley and stratification are important factors in determining the intensity of the along-valley flow. However the up-valley winds are also quite sensitive to the specification of the boundary conditions at the upper end of the slope wind layers. If sidevalleys are added strong inflow to these tributaries is found only if their topographic amplification factors are larger than that of the main valley. This flow into the tributaries is mainly balanced by downward motion on top of the main valley but flow entering through the mounth of the main valley can contribute as well. Tributaries can induce flow in the main valley long before the main valley's own up-valley wind regime has reached the location of the tributary.With 10 Figures     

关于发展人工影响天气数值模式的一些问题

人工影响天气的学科基础是中小尺度天气动力学与云降水物理学,需要将天气-动力-云降水物理耦合为一体。考虑到目前将天气动力学性质的基础数值模式用于人工影响天气中的问题,从数值模式动力方程、模式分辨率、云物理过程、数值求解方案、初边值条件等方面系统地探索了发展人工影响天气数值模式中一些需要重点解决、且不可忽视的特色问题,并举例对相关问题提出了解决思路和方法。期望提出的问题有助于构思更适合于人工影响天气数值模式,使数值模式功能真正向满足人工影响天气的要求靠近一步。     

祁连山云系云微物理结构和人工增雨催化个例模拟研究

人工影响天气的学科基础是中小尺度天气动力学与云降水物理学,需要将天气-动力-云降水物理耦合为一体。考虑到目前将天气动力学性质的基础数值模式用于人工影响天气中的问题,从数值模式动力方程、模式分辨率、云物理过程、数值求解方案、初边值条件等方面系统地探索了发展人工影响天气数值模式中一些需要重点解决、且不可忽视的特色问题,并举例对相关问题提出了解决思路和方法。期望提出的问题有助于构思更适合于人工影响天气数值模式,使数值模式功能真正向满足人工影响天气的要求靠近一步。     

Comparison of Speed-Up Over Hills Derived from Wind-Tunnel Experiments,Wind-Loading Standards,and Numerical Modelling

We evaluate the accuracy of the speed-up provided in several wind-loading standards by comparison with wind-tunnel measurements and numerical predictions, which are carried out at a nominal scale of 1:500 and full-scale, respectively. Airflow over two- and three-dimensional bell-shaped hills is numerically modelled using the Reynolds-averaged Navier–Stokes method with a pressure-driven atmospheric boundary layer and three different turbulence models. Investigated in detail are the effects of grid size on the speed-up and flow separation, as well as the resulting uncertainties in the numerical simulations. Good agreement is obtained between the numerical prediction of speed-up, as well as the wake region size and location, with that according to large-eddy simulations and the wind-tunnel results. The numerical results demonstrate the ability to predict the airflow over a hill with good accuracy with considerably less computational time than for large-eddy simulation. Numerical simulations for a three-dimensional hill show that the speed-up and the wake region decrease significantly when compared with the flow over two-dimensional hills due to the secondary flow around three-dimensional hills. Different hill slopes and shapes are simulated numerically to investigate the effect of hill profile on the speed-up. In comparison with more peaked hill crests, flat-topped hills have a lower speed-up at the crest up to heights of about half the hill height, for which none of the standards gives entirely satisfactory values of speed-up. Overall, the latest versions of the National Building Code of Canada and the Australian and New Zealand Standard give the best predictions of wind speed over isolated hills.     

Key issues in developing numerical models for artificial weather modification

The scientific foundation of artificial weather modification is meso- and small-scale dynamics and cloud–precipitation microphysics. Artificial weather modification requires the realistic coupling of weather patterns, dynamical processes, and microphysical processes. Now that numerical models with weather dynamical characteristics have been widely applied to artificial weather modification, several key points that should not be neglected when developing numerical models for artificial weather modification are proposed in this paper, including the dynamical equations, model resolution, cloud–precipitation microphysical processes, numerical computation method, and initial and boundary conditions. Based on several examples, approaches are offered to deal with the problems that exist in these areas.     

On the choice of relaxation coefficients for Davies' lateral boundary scheme for regional weather prediction models

Summary Relaxation coefficients for Davies' lateral boundary scheme for limited-area numerical weather prediction models are constructed in such a way that, under idealized conditions, the unwanted partial reflection of outgoing waves (leaving the limited area) at the boundary is minimized.With 2 Figures     

Steady flow between two reservoirs of fluid with different densities and levels through a rectangular channel section of varying depth and width

The steady hydrostatic flow through a channel of rectangular cross section connecting reservoirs of infinite width and depth and containing inviscid fluids of different densities and levels is studied. The main goal is the determination of the discharges of the lighter and denser fluids in terms of the external conditions (reservoir levels, fluid densities and variation of width and depth along a channel). It is shown that the key parameter is δ, which is the ratio of relative reservoir level difference, γ, to relative density difference, ε. If δ<0 then the denser fluid plunges under the stationary lighter layer. If δ>δ_* (1<δ_*<1.5) then the lighter fluid runs up on a wedge of stationary heavier fluid. Here δ_* depends on the geometry of the constriction. The solutions describing these regimes are stated. If 0<δ<δ_* then both layers are in motion. A qualitative analysis of the solution for arbitrary bottom shape and channel width and arbitrary ε is presented and the problem is reduced to a system of two equations which can be easily solved numerically for any particular channel profile. We give detailed analyses for the following two cases: 1) the narrowest width of the channel is on the side of the heavier fluid and the top of the sill is on the side of lighter fluid; 2) the minima in channel depth and width coincide. In the second case the discharges for one class of geometries in the Boussinesq approximation are calculated and discussed.     

Evaluation of turbulent Prandtl (Schmidt) number parameterizations for stably stratified environmental flows

In this study, we evaluate four different parameterizations of the turbulent Prandtl (Schmidt) number Pr_t = ν_t/Γ_t where ν_t is the eddy viscosity and Γ_t is the scalar eddy diffusivity, for stably stratified flows. All four formulations of Pr_t are strictly functions of the gradient Richardson number Ri, which provides a measure of the strength of the stratification. A zero-equation (i.e. no extra transport equations are required) turbulence model for ν_t in a one-dimensional, turbulent channel flow is considered to evaluate the behavior of the different formulations of Pr_t. Both uni-directional and oscillatory flows are considered to simulate conditions representative of practical flow problems such as atmospheric boundary layer flows and tidally driven estuarine flows, to quantify the behavior of each of the four formulations of Pr_t. We perform model-to-model comparisons to highlight which of the models of Pr_t allow for a higher rate of turbulent mixing and which models significantly inhibit turbulent mixing in the presence of buoyancy forces resulting from linear (continuous) stratification as well as two-layer stratification. The basis underlying the formulation of each model in conjunction with the simulation results are used to emphasize the considerable variability in the different formulations and the importance of choosing an appropriate parameterization of Pr_t given a model for ν_t in stably stratified flows.     

Numerical study of flow and gas diffusion in the near-wake behind an isolated building

To assist validation of the experimental data of urban pollution dispersion, the effect of an isolated building on the flow and gaseous diffusion in the wake region have been investigated numerically in the neutrally stratified rough-walled turbulent boundary layer. Numerical studies were carried out using Computational Fluid Dynamics (CFD) models. The CFD models used for the simulation were based on the steady-state Reynolds-Average Navier-Stoke equations (RANS) with κ-ε turbulence models; standard κ-ε and RNG κ-ε models. Inlet conditions and boundary conditions were specified numerically to the best information available for each fluid modeling simulation. A gas pollutant was emitted from a point source within the recirculation cavity behind the building model. The accuracy of these simulations was examined by comparing the predicted results with wind tunnel experimental data. It was confirmed that simulation using the model accurately reproduces the velocity and concentration diffusion fields with a fine-mish resolution in the near wake region. Results indicated that there is a good agreement between the numerical simulation and the wind tunnel experiment for both wind flow and concentration diffusion. The results of this work can help to improve the understanding of mechanisms of and simulation of pollutant transport in an urban environment.     

Dynamics of the Leeuwin Current: Part 2. Impacts of mixing,friction, and advection on a buoyancy-driven eastern boundary current over a shelf

The boundary currents over the Western Australian continental shelf and slope consist of the poleward flowing Leeuwin Current (LC) and the equatorward flowing Leeuwin Undercurrent (LUC). Key properties of the LC are its poleward strengthening, deepening to the south, and shelfbreak intensification. The alongshore flow reverses direction below about 300 m, forming the LUC at greater depths. To investigate the processes that cause these features, we obtain solutions to an idealized, regional ocean model of the South Indian Ocean. Solutions are forced by relaxing surface density to a prescribed, meridionally varying density profile ρ^*(y) with a timescale of δt. In addition, vertical diffusion is intensified near the ocean surface. This diffusion establishes the minimum thickness over which density is well-mixed. We define this thickness as the “upper layer”. Solutions are obtained with and without a continental shelf and slope off Western Australia and for a range of values of δt and mixing parameters. Within this upper layer, there is a meridional density gradient that balances a near-surface, eastward geostrophic flow. The eastward current downwells near the eastern boundary, leading to westward flow at depth. The upper layer's meridional structure and zonal currents crucially depend on coastal processes, including the presence of topography near the eastern boundary. Kelvin waves inhibit the upper layer from deepening at the coast. Rossby waves propagate the coastal density structure offshore, hence modifying the interior currents. A comparison of the solutions with or without a continental shelf and slope demonstrate that topographic trapping of Rossby waves is a necessary process for maintaining realistic eastern boundary current speeds. Significant poleward speeds occur only onshore of where the upper layer intersects the slope, that is, at a grounding line. Its poleward transport increases when surface-enhanced vertical mixing is applied over a greater depth. When the timescale δt is sufficiently short, the poleward current is nearly barotropic. The current's spatial structure over the shelf is controlled by horizontal mixing, having the structure of a Munk layer. Increasing vertical diffusion deepens the upper layer thickness and strengthens the alongshore current speed. Bottom drag leads to an offshore flow along the bottom, reducing the net onshore transport and weakening the current's poleward acceleration. When δt is long, poleward advection of buoyancy forms a density front near the shelf break, intensifying poleward speeds near the surface. With bottom drag, a bottom Ekman flow advects density offshore, shifting the jet core offshore of the shelf break. The resulting cross-shelf density gradient reverses the meridional current's direction at depth, leading to an equatorward undercurrent.     

Forward Lagrangian stochastic simulation of a transient source in the atmospheric surface layer

We show that a forward Lagrangian stochastic (LS) model simulates well the ensemble-averaged concentration transient due to a short time (5 min) point source in the uniform atmospheric surface layer. In LS models, computational particles, which may not descend below ground level, are necessarily reflected at an imposed (artificial) boundary above ground. Model results were rather insensitive to the placing of the lower reflection boundary, and no definite benefit stemmed from including a parametrization for unresolved delays/displacements beneath the lower boundary.     

Effects of mesoscale sea-surface temperature fronts on the marine atmospheric boundary layer

A numerical modelling study is presented focusing on the effects of mesoscale sea-surface temperature (SST) variability on surface fluxes and the marine atmospheric boundary-layer structure. A basic scenario is examined having two regions of SST anomaly with alternating warm/cold or cold/warm water regions. Conditions upstream from the anomaly region have SST values equal to the ambient atmosphere temperature, creating an upstream neutrally stratified boundary layer. Downstream from the anomaly region the SST is also set to the ambient atmosphere value. When the warm anomaly is upstream from the cold anomaly, the downstream boundary layer exhibits a more complex structure because of convective forcing and mixed layer deepening upstream from the cold anomaly. An internal boundary layer forms over the cold anomaly in this case, generating two distinct layers over the downstream region. When the cold anomaly is upstream from the warm anomaly, mixing over the warm anomaly quickly destroys the shallow cold layer, yielding a more uniform downstream boundary-layer vertical structure compared with the warm-to- cold case. Analysis of the momentum budget indicates that turbulent momentum flux divergence dominates the velocity field tendency, with pressure forcing accounting for only about 20% of the changes in momentum. Parameterization of surface fluxes and boundary-layer structure at these scales would be very difficult because of their dependence on subgrid-scale SST spatial order. Simulations of similar flow over smaller scale fronts (<5 km) suggest that small-scale SST variability might be parameterized in mesoscale models by relating the effective heat flux to the strength of the SST variance.     

Measurements of Flows Over Isolated Valleys

Wind-tunnel measurements of the flow over an isolated valley both normal and at an angle (45°) to a simulated neutrally stable atmospheric boundary layer are presented. Attention is concentrated on the nature of the flow within the valley itself. The work formed part of a wider study that included detailed field measurements around an African desert valley and some limited comparisons with that work are included. A scale of about 1:1000 was used for the laboratory work, in which an appropriate combination of hot wire and particle image velocimetry was employed. For a valley normal to the upwind flow, it is shown that the upstream influence of the valley extends to a distance of at least one half of the axial valley width upstream of the leading edge, whereas differences in mean flow and turbulence could be identified well beyond two valley widths from the downwind edge. Non-normal wind angles lead to significant along-valley flows within the valley and, even at two valley heights above the valley ridge level, there remains a significant spanwise flow component. Downwind turbulence levels are somewhat lower in this case, but are still considerably higher than in the undisturbed boundary layer. At both flow angles, there are significant recirculation regions within the valleys, starting from mean separation just beyond the leading edge, but the strong spanwise flow in the 45° case reduces the axial extent of the separated zone. The flow is shown to be in some ways analogous to flow over an isolated hill. Our results usefully enhance the field data and could be used to improve modelling of saltation processes in the field.     

Effects of a Fence on Pollutant Dispersion in a Boundary Layer Exposed to a Rural-to-Urban Transition

Simultaneous particle-image velocimetry and laser-induced fluorescence combined with large-eddy simulations are used to investigate the flow and pollutant dispersion behaviour in a rural-to-urban roughness transition. The urban roughness is characterized by an array of cubical obstacles in an aligned arrangement. A plane fence is added one obstacle height h upstream of the urban roughness elements, with three different fence heights considered. A smooth-wall turbulent boundary layer with a depth of 10h is used as the approaching flow, and a passive tracer is released from a uniform line source 1h upstream of the fence. A shear layer is formed at the top of the fence, which increases in strength for the higher fence cases, resulting in a deeper internal boundary layer (IBL). It is found that the mean flow for the rural-to-urban transition can be described by means of a mixing-length model provided that the transitional effects are accounted for. The mixing-length formulation for sparse urban canopies, as found in the literature, is extended to take into account the blockage effect in dense canopies. Additionally, the average mean concentration field is found to scale with the IBL depth and the bulk velocity in the IBL.     

有限元集中质量法在非饱和土壤水流中的应用

利用Ｇａｌｅｒｋｉｎ有限元集中质量法,讨论了非饱和土壤水流动的数值计算模型,用以模拟均质土壤,地下水埋藏很深且在不同的初始和边界条件下的水分运动。通过将第一类边界条件齐次化,而对于第二类非线性边界条件采用变分的办法将其直接转化为已知边界通量的计算,从而容易且较好地处理了带通量约束边界条件。对于入渗或蒸发问题,用通常的离散方法容易产生振荡非物理解。我们采用有限元集中质量法,将质量矩阵的非对角元集中到主对角元,避免了这种非物理解的产生。利用该方案统一地模拟如下情况：稳定入渗和蒸发、蒸发一段时间后达到风干率,以及波动入渗蒸发时土壤水势的变化状况。模拟表明,在已知有关土壤参数的情况下,该模型能较好地模拟非饱和流水势及含水量分布。     

A semi-analytical model of barotropic and baroclinic flows for an open Panama Gateway

A semi-analytical model of the Panama throughflow is presented. The model expresses the throughflow transport as a function of deep water formation in the North Pacific and in the North Atlantic, and of the Panama Gateway depth. The model is derived from the integral of the momentum equation along a circumpolar path, and can be interpreted from the point of view of the vorticity balance. The important conditions are whether the deep water, whose location is considered to be above the bottom water formed around Antarctica, originates from the North Atlantic or from the North Pacific, and whether the Panama Gateway is shallower than the lower boundary of the deep water. The present model indicates that the barotropic transport through the Panama Gateway is eastward, except for the case where the deep water is formed in the North Pacific and the sill of the Panama Gateway is shallow. The baroclinic structure of the Panama throughflow depends on whether the deep water is formed in the North Pacific or in the North Atlantic. These qualitative implications of the model are consistent with recent numerical studies and proxy-based paleoceanographic studies. Numerical experiments performed in the present study reinforce confidence in the semi-analytical model.