A tidal front influenced by river discharge

The detailed structure of an oceanic front found in Osaka Bay, Japan, was observed on board R/V Toyoshio-Maru in May, 1987. The front separates the stratified nearshore region from the well-mixed region of the central part of the bay. The differences of water temperature, salinity and density (σ t) across the front are ∼ 1.5°C, 4.0‰ and 3.0, respectively. The strength of the tidal mixing may be represented by a reciprocal of the parameter H/U³ (where H is the water depth in m and U is the amplitude of the tidal current in m s⁻¹). The front runs in the domain where the value of log(H/U³) ranges from 2.5 to 3.0, showing that tidal stirring plays an important role in its formation. However, the critical value for Osaka Bay is considerably smaller than that for other tidal fronts. The influence of river discharge is taken into account, and it is shown that the front found in Osaka Bay has the nature of a tidal front highly influenced by river discharge. Furthermore, temporal observations of the current, temperature and salinity at the station near the front revealed its vivid and changeable structure.     

Modelling stratification and baroclinic flow in the estuarine transition zone of the St. Lawrence estuary

Abstract

This paper presents a hydrodynamic study of the St. Lawrence Estuary's estuarine transition zone, a 100 km region where fresh water from the river mixes with salt water from the estuary. The circulation of the estuarine transition zone is driven by strong tides, a large river flow, and well‐defined salinity gradients. For this study, a three‐dimensional hydrodynamic model was applied to the estuarine transition zone of the St. Lawrence Estuary and used to examine stratification and density‐driven baroclinic flow. The model was calibrated to field observations and subsequently predicted water level elevations, along‐channel currents, and salinity with mean errors of less than 9%, 11%, and 17%, respectively. The baroclinic density‐driven currents were distinguished from the tidal barotropic currents by using principal component analysis. Stratification and baroclinic flow were observed to vary throughout the estuarine transition zone on tidal and subtidal spring‐neap time scales. On a semidiurnal tidal time scale, stratification was periodic, and baroclinic flow was represented by pulses of sheared exchange flow, suggesting that neither buoyancy forcing nor turbulent mixing is dominant at this scale. On a subtidal spring‐neap time scale, stratification and baroclinic flow varied inversely with tidal energy, increasing on weak neap tides and decreasing on strong spring tides.     

Diurnal and Seasonal Variations of Thermal Stratification and Vertical Mixing in a Shallow Fresh Water Lake

Among several influential factors, the geographical position and depth of a lake determine its thermal structure. In temperate zones, shallow lakes show significant differences in thermal stratification compared to deep lakes. Here, the variation in thermal stratification in Lake Taihu, a shallow fresh water lake, is studied systematically. Lake Taihu is a warm polymictic lake whose thermal stratification varies in short cycles of one day to a few days. The thermal stratification in Lake Taihu has shallow depths in the upper region and a large amplitude in the temperature gradient, the maximum of which exceeds 5°C m^–1. The water temperature in the entire layer changes in a relatively consistent manner. Therefore, compared to a deep lake at similar latitude, the thermal stratification in Lake Taihu exhibits small seasonal differences, but the wide variation in the short term becomes important. Shallow polymictic lakes share the characteristic of diurnal mixing. Prominent differences on the duration and frequency of long-lasting thermal stratification are found in these lakes, which may result from the differences of local climate, lake depth, and fetch. A prominent response of thermal stratification to weather conditions is found, being controlled by the stratifying effect of solar radiation and the mixing effect of wind disturbance. Other than the diurnal stratification and convection, the representative responses of thermal stratification to these two factors with contrary effects are also discussed. When solar radiation increases, stronger wind is required to prevent the lake from becoming stratified. A daily average wind speed greater than 6 m s^–1 can maintain the mixed state in Lake Taihu. Moreover, wind-induced convection is detected during thermal stratification. Due to lack of solar radiation, convection occurs more easily in nighttime than in daytime. Convection occurs frequently in fall and winter, whereas long-lasting and stable stratification causes less convection in summer.     

Marginal mixing theories

Abstract

Mixing near the sloping boundaries of oceans or lakes may be a significant mechanism of diapycnal transport. The basic physics of this is reviewed, with emphasis on the reduction of the effectiveness of the process due to both reduced stratification and the restratifying secondary circulation driven by buoyancy forces. This re stratification is shown to reduce the effectiveness of intermittent mixing events as well as steady mixing. It is argued that for boundary mixing to be effective in the abyssal ocean it must extend sufficiently far from the boundary that the stratification can be maintained; this may be true for breaking bottom‐reflected internal waves. The alongslope flow implied by steady‐state boundary mixing theories is downwelling‐favourable and has a magnitude related to the thickness and other properties of the boundary layer. Mixing near a boundary may thus tend to drive a downwelling‐favourable mean circulation in the interior. If the interior circulation is imposed by other forces, the bottom boundary layer may evolve to a steady state if the interior flow is downwelling‐favourable, but if it is upwelling‐favourable initially a steady state seems unlikely and the downwelling‐favourable alongslope flow induced by the boundary mixing will tend to diffuse slowly into the interior. The nature of the solution in all these cases is sensitive to the Burger number, N² sin² θ/f², where θ is the bottom slope, and to the eddy Prandtl number.     

On the mean and tidal currents in Hudson strait

Abstract

The vertical structures of the mean and tidal flows in Hudson Strait are described from moored current‐meter data collected during an 8‐week period in August to October of 1982. The residual flow in the strongly stratified waters off Quebec is directed along the Strait to the southeast, is highly baroclinic and is concentrated near shore (within an offshore length scale of approximately an internal Rossby radius). Maximum mean speeds of 0.3 m s^?1 were observed near‐surface (30 m). In the weakly stratified waters on the northern side of the Strait along Baffin Island the mean flow is northwestward. The maximum speeds are 0.1 m s^?1 near‐surface (30 m) and the current amplitudes decrease to 0.05 m s^?1 at 100 m. The mean southeastward transport is estimated to be 0.93 ±0.23 × 10⁶ m³ s^?1 with a northwestward transport of 0.82 ± 0.24 × 10⁶ m³ s^?1. Over most of the Strait the across‐channel residual currents are directed towards the Quebec shore with velocities ranging from 0.02 to 0.1 ms^?1. Current variability is dominated by the tides, the M₂ being the major tidal constituent. In the vicinity of the mooring the M₂ tide is primarily barotropic, progressive in nature, and has along‐channel current amplitudes varying across the Strait from 0.20 to 0.45 m s^?1. Observed differences in tidal sea‐level elevations across the Strait can be accounted for by the cross‐channel variations characteristic of Kelvin waves.     

Instabilities of the tidally induced bottom boundary layer in the rotating frame and their mixing effect

To investigate the stability of the bottom boundary layer induced by tidal flow (oscillating flow) in a rotating frame, numerical experiments have been carried out with a two-dimensional non-hydrostatic model. Under homogeneous conditions three types of instability are found depending on the temporal Rossby number Ro_t, the ratio of the inertial and tidal periods. When Ro_t < 0.9 (subinertial range), the Ekman type I instability occurs because the effect of rotation is dominant though the flow becomes more stable than the steady Ekman flow with increasing Ro_t. When Ro_t > 1.1 (superinertial range), the Stokes layer instability is excited as in the absence of rotation. When 0.9 < Ro_t < 1.1 (near-inertial range), the Ekman type I or type II instability appears as in the steady Ekman layer. Being much thickened (100 m), the boundary layer becomes unstable even if tidal flow is weak (5 cm/s). The large vertical scale enhances the contribution of the Coriolis effect to destabilization, so that the type II instability tends to appear when Ro_t > 1.0. However, when Ro_t < 1.0, the type I instability rather than the type II instability appears because the downward phase change of tidal flow acts to suppress the latter. To evaluate the mixing effect of these instabilities, some experiments have been executed under a weak stratification peculiar to polar oceans (the buoyancy frequency N²  10⁻⁶ s⁻²). Strong mixing occurs in the subinertial and near-inertial ranges such that tracer is well mixed in the boundary layer and an apparent diffusivity there is evaluated at 150–300 cm²/s. This suggests that effective mixing due to these instabilities may play an important role in determining the properties of dense shelf water in the polar regions.     

Turbulence and mixing: Sources of nutrients on the Vancouver island continental shelf

Abstract

Estimates of the rate of dissipation of turbulent energy,?_v, were made on the continental shelf off the southwest coast of Vancouver Island throughout the diurnal tidal cycle at six stations. If turbulent mixing takes place away from boundaries, and a constant fraction of the energy supplied to turbulence is converted into potential energy, this dissipation rate per unit volume, ?_v, is shown to be proportional to the rate of turbulent mass and nutrient flux across the isopycnals.

We compute these fluxes to determine the source of nutrients in the upper mixed layer on the shelf. It is found that tidal mixing on the shelf throughout the water column contributes less than 10% of the flux of nutrients supplied by the estuarine outflow out of Juan de Fuca Strait. Strong winds during upwelling events supply nutrients at rates greater than those due to tidal mixing, but at rates that are likely smaller than the Juan de Fuca source. Therefore, the nutrient‐rich waters observed in the euphotic zone in spring and summer on this shelf derive mainly from Juan de Fuca Strait. Nutrients in bottom water derive from upwelling along shelf‐break canyons.     

On the possibilities of thermal energy conversion in lakes

Abstract

The paper discusses the possibility of extracting electrical energy from the thermal energy stored in stratified lakes. Three situations are examined, an open lake or pond acting as a solar collector, a combination of waste heat and solar energy, and selective withdrawal of warm and cold streams from a stratified hydroelectric reservoir. Approximate calculations of the energy returns are made for typical conditions. The returns are limited by environmental factors as well as a short operating season. By using the deep stratified Great Lakes (Superior, Huron, Michigan and Ontario) as solar collectors, a few thousand megawatts of electrical power could be produced in the Great Lakes Basin during the summer months. This power could be produced on a year‐round basis by a single large nuclear generating station.     

Effects of variable wind shear on the mesoscale circulation forced by slab‐symmetric diabatic heating

Abstract

We examine the response of stably stratified airflow to a slab‐symmetric diabatic forcing associated with condensation in long‐lasting precipitation bands. The steady‐state linearized Boussinesq equations are used to model the diagnostic relationship between the vertical motion field, the heating source and the ambient flow. The basic‐state flow is assumed to be horizontally uniform and non‐rotating, but the static stability and wind vary in the vertical. Linear theory shows that the speed of the along‐band wind component is unimportant for slab‐symmetric heating since it cannot contribute towards the advection of buoyancy or vertical motion.

For typical atmospheric stratification and a moving heating source associated with a cloud band, the Taylor‐Goldstein equation is solved numerically. The numerical results show that the cross‐band wind shear tilts the updraft core and broadens it. While the magnitude of the shear is increased, the circulation becomes stronger. The details of the wind profile are also important in determining the intensity and structure of the circulation. When the wind profile indicates a convex bulge (i.e. the low‐level shear is weaker than the upper‐level shear), the circulation becomes slightly weaker in comparison with the linear wind profile. Conversely, the circulation becomes stronger when the wind profile has a concave shape. Increasing the concave bulge tends to enhance the circulation but not in a monotonic fashion. This non‐monotonic relation between the vertical motion and the parabolic wind profile is interpreted in terms of kinetic energy changes of parcels that interchange their altitudes.     

Effects of Topographical Slope Angle and Atmospheric Stratification on Surface-Layer Turbulence

The effect of topographical slope angle and atmospheric stratification on turbulence intensities in the unstably stratified surface layer have been parameterized using observations obtained from a three-dimensional sonic anemometer installed at 8 m height above the ground at the Seoul National University (SNU) campus site in Korea for the years 1999–2001. Winds obtained from the sonic anemometer are analyzed according to the mean wind direction, since the topographical slope angle changes significantly along the azimuthal direction. The effects of the topographical slope angle and atmospheric stratification on surface-layer turbulence intensity are examined with these data. It is found that both the friction velocity and the variance for each component of wind normalized by the mean wind speed decrease with increase of the topographical slope angle, having a maximum decreasing rate at very unstable stratification. The decreasing rate of the normalized friction velocity (u _* /U) is found to be much larger than that of the turbulence intensity of each wind component due to the reduction of wind shear with increase in slope angle under unstable stratification. The decreasing rate of the w component of turbulence intensity (σ _w /U) is the smallest over the downslope surface whereas that of the u component (σ _u /U) has a minimum over the upslope surface. Consequently, σ _w /u _* has a maximum increasing rate with increase in slope angle for the downslope wind, whereas σ _u /u _* has its maximum for the upslope wind. The sloping terrain is found to reduce both the friction velocity and turbulence intensity compared with those on a flat surface. However, the reduction of the friction velocity over the sloping terrain is larger than that of the turbulence intensity, thereby enhancing the turbulence intensity normalized by the friction velocity over sloping terrain compared with that over a flat surface.     

A model of tidal flushing of an estuary by dipole formation

We discuss a laboratory model of the flushing and mixing between a bay and a sea connected by a narrow channel. Tidal changes in water elevation lead to periodic flow in and out of the bay through the narrow channel. Due to flow separation there is an asymmetry between the flow entering and leaving the channel on different phases of the tide. A consequence of this asymmetry is that every tidal cycle a fraction of fluid is not returned through the channel, so that a passive tracer in the bay is successively flushed away. We consider what happens when the creation of vorticity in the channel leads to the formation of a dipole that can propagate away from the returning flow of the later phase of the tide. When the dimensionless ratio of maximum channel velocity U, width of channel W and tidal period T is such that W/UT<0.13, we find that dipoles can propagate away from the source region without being drawn back into the sink. This process leads to a larger exchange of water between the estuary and sea, than the classical model of tidal flushing by the jet-sink asymmetry of [Stommel, H., Farmer, H. G., 1952. On the nature of estuarine circulation WHOI Tech. Rep. 52–88, 131].     

Different Generating Mechanisms for the Summer Surface Cold Patches in the Yellow Sea

ABSTRACT

It has been frequently observed that there are surface cold patches (SCPs) in the Yellow Sea in summer. Although previous studies based on monthly mean temperature distribution found that these SCPs are a result of tidal mixing and tide-induced upwelling, tidal mixing and upwelling alone cannot explain all the occurrences. In our study we found that the three typical patches, namely, the Shandong SCP, the Subei SCP, and the Mokpo SCP, have different temporal patterns over a spring–neap tidal cycle; hence, they have different generating mechanisms. Based on a multiple-year simulation, the latter two show conspicuous spring–neap variations. The highest temperature occurs during the neap tide phase (about two days after a quarter moon). Because of weak upwelling and mixing, strong stratification is established and the SCPs are suppressed or even disappear. The opposite holds for the spring tide phase (about two days after a new or full moon). This is quite different from the Shandong SCP, which does not display a distinct difference between spring and neap tides. Buoy observations and composite analyses with data from the Moderate Resolution Imaging Spectroradiometer (MODIS) further support this conclusion.     

Solar energy system design: The impact of mesoscale variations in solar radiation

Abstract

A 12‐station network located in and around Vancouver, B.C. has been used to define the local (mesoscale) variations in solar energy. Numerical models are used to convert the horizontal data to inclined surface irradiances which, along with temperature, are the inputs required by the simulation models used to assess the significance of these variations on the performance and economics of both active and passive solar heating systems.

Solar radiation differences over the study area have a marked influence on the operation of a domestic hot water heating system while the temperature variations between the same stations have a comparatively small impact. For both active and passive space heating the situation is reversed because temperature has a large impact on the energy demand and hence on the extent of solar energy utilization. The results suggest that local variations of solar radiation should be incorporated in solar domestic hot water design studies while spatial variations in temperature should receive relatively more attention in space heating studies.     

Surface inhomogeneity effects on convective diffusion

It is suggested that convective scaling, with appropriate extensions, provides the most useful framework for estimating the effects of urban-scale surface inhomogeneities on diffusion in convective conditions. Strong contrasts in surface heat flux exist between cropland, forests, urban areas, and water or marshland surfaces. It is argued that a typical fetch for convective turbulence to readjust to changed heat (or buoyancy) input from the surface below is 2(U/w ^*)h, where U is the mean wind speed in the mixing layer, w ^* is the convective scaling velocity, and h is the mixing depth. In contrast, the fetch required for wind speed to readjust to new underlying surface roughness is of the order (U/u ^*)²h/2, where u ^* is the friction velocity.The ratio w ^*/U is the best index of diffusion rates in moderately to very unstable conditions. General urban effects on heat flux, h, and U are discussed separately, then their combined effects on w ^*/U are estimated. While this ratio can double over a large city during light winds, its increase is much less for small cities, or during moderate winds. Finally, some examples of heat flux in- homogeneities causing stationary convective features are presented. Steady downdrafts associated with these features are of the order of 0.4w ^*, and could significantly increase surface concentrations from elevated sources.On assignment from the National Oceanic and Atmospheric Administration, U.S. Department of Commerce.This paper is based on a presentation made at the AMS Specialty Conference on Air Quality Modeling of the Urban Boundary Layer, in Baltimore, late 1983.     

A model of turbulence spectra in the atmospheric surface layer

The spectral equations of turbulent kinetic energy and temperature variance have been solved by using Onsager's energy cascade model and by extending Onsager's model to closure of terms that embody the interaction of turbulent and mean flow.The spectral model yields the following results: In a stably stratified shear flow, the peak wave numbers of the spectra of energy and temperature variance shift toward larger wave numbers as stability increases. In an unstably stratified flow, the peak wave numbers of energy spectra move toward smaller wave numbers as instability increases, whereas the opposite trend is observed for the peak wave numbers of temperature variance spectra. Hence, the peak wave numbers of temperature spectra show a discontinuity at the transition from stable to unstable stratification. At near neutral stratification, both spectra reveal a bimodal structure.The universal functions of the Monin-Obukhov similarity theory are predicted to behave as _m ~ _H ~ (- Z/L)^-1/3 in an extremely unstable stratification and as _m ~ _H ~ z/L in an extremely stable stratification. For a stably stratified flow, a constant turbulent Prandtl number is expected.     

Turbulence decay in stratified and homogeneous marine layers

A spectral approach is applied to shear-induced turbulence in stratified layers. A system of spectral equations for stationary balance of turbulent energy and temperature variances was deduced in the vicinity of the local shear scale L_U = (ε/U_Z³)^1/2. At wavenumbers between the inertial-convective (k^−5/3) and wak turbulence (k⁻³) subranges, additional narrow spectral intervals—‘production’ subranges—may appear (E k⁻¹, E_T k⁻²). The upper boundary of these subranges is determined as L_U, and the lower boundaries as L_R (ε/U_ZN²)^1/2(χ/T_Z²). It is shown that the scale L_U is a unique spectral scale that is uniform up to a constant value for every hydrophysical field. It appears that the spectral scale L_U is equivalent to the Thorpe scale L_Th for the active turbulence model. Therefore, if turbulent patches are generated in a background of permanent mean shear, a linear relation between temperature and mass diffusivities exists. In spectral terms, the fossil turbulence model corresponds to the regime of the Boldgiano-Obukhov buoyancy subrange (E k^−11/5, E_T k^−7/5). During decay the buoyancy subrange is expanded to lower and higher wavenumbers. At lower wavenumbers the buoyancy subrange is bounded by L_** = 3(χ^1/2/N^1/2T_Z), which is equivalent to the Thorpe scale L_Th. In such a transition regime only, when the viscous dissipation rate is removed from the set of main turbulence parameters, the Thorpe scale does not correlate with the buoyancy scale L_N ε^1/2/N^3/2 and fossil turbulence is realized. Oceanic turbulence measurements in the equatorial Pacific near Baker Island confirm the main ideas of the active and fossil turbulence models.     

Stratified airflow over one or two hills

Methods for calculating, interpolating and idealising air flow in complex terrain are reviewed. Then the general structure of stratified airflow over a single hill of height H and length L₁ is studied in detail and shown to be determined by the upwind velocity profile, the magnitude of a characteristic Froude number and the dimensions of the hill. Let N(L₁) be the buoyancy frequency upwind at a height L₁, and u_* and U₀ be the upwind friction and mean velocity respectively; then the flow is effectively neutral if u^*/NL₁>1. But if u_*/NL₁>1 and u₀/NL₁>1, the stratification is weak enough to affect the upwind turbulence and velocity profile but not the dynamics of the flow over the hill. If U₀/NL₁ <1 but U₀/NH>1 the buoyancy forces are strong enough to affect the mean flow over the hill but not strong enough to prevent it passing over the top. In this regime the flow is very sensitive to the form of the upwind temperature profile. If U₀/NH>1, much of the flow passes round the hill. A similar classification, with different flow patterns, is appropriate for unstably stratified flows. When the wind is weak enough, local slope winds can dominate. Results from the analysis of these different regimes are described and compared with laboratory of field measurements where possible. It is shown how some of these results can be extended to groups of hills.     

Winter‐time near‐surface currents in the strait of Juan de Fuca

Abstract

During November 1976 to February 1977 near‐surface wind, current and temperature measurements were made at three sites along the Strait of Juan de Fuca. Strong tidal currents and major intrusions of warmer, fresher offshore coastal water were superimposed upon the estuarine circulation of near‐surface seaward flow. The r.m.s. amplitudes of the diurnal and semidiurnal tidal currents were ～30 cms^‐1 and 30–47 cm s^‐1, respectively. The vector‐mean flow at 4 m‐depth was seaward and decreased in speed from 28 cm s^‐1 at 74 km from the entrance to 9 cm s^‐1 at 11 km from the entrance. On five occasions intrusions of 1–3 C warmer northeast Pacific coastal water occurred for durations of 1–10 days. The 25 cm s^‐1 up‐strait speed of the intrusive lens agreed to within 20% of the gravity current speed computed from Benjamin's (1968) hydraulic model. The near‐surface currents associated with the intrusions and the southerly coastal winds were significantly correlated, indicating that the intrusions were initiated when shoreward Ekman currents advected Pacific coastal water into the Strait. The reversals were not significantly coherent with the along‐strait sea surface slope measured along the north side of the Strait nor were they strongly related to local wind forcing.     

The Entrainment Rate for Buoyant Plumes in a Crossflow

We consider large-eddy simulations (LES) of buoyant plumes from a circular source with initial buoyancy flux F ₀ released into a stratified environment with constant buoyancy frequency N and a uniform crossflow with velocity U. We make a systematic comparison of the LES results with the mathematical theory of plumes in a crossflow. We pay particular attention to the limits [(U)\tilde] << 1{\tilde{U}\ll1} and [(U)\tilde] >> 1{\tilde{U}\gg 1}, where [(U)\tilde]=U/(F₀ N)^1/4{\tilde{U}=U/(F_0 N)^{1/4}}, for which analytical results are possible. For [(U)\tilde] >> 1{\tilde{U}\gg 1}, the LES results show good agreement with the well-known two-thirds law for the rise in height of the plume. Sufficiently far above the source, the centreline vertical velocity of the LES plumes is consistent with the analytical z ^−1/3 and z ^−1/2 scalings for respectively [(U)\tilde] << 1{\tilde{U}\ll 1} and [(U)\tilde] >> 1{\tilde{U}\gg 1}. In the general case, where the entrainment is assumed to be the sum of the contributions from the horizontal and vertical velocity components, we find that the discrepancy between the LES data and numerical solutions of the plume equations is largest for [(U)\tilde]=O(1){\tilde{U}=O(1)}. We propose a modified additive entrainment assumption in which the contributions from the horizontal and vertical velocity components are not equally weighted. We test this against observations of the plume generated by the Buncefield fire in the U.K. in December 2005 and find that the results compare favourably. We also show that the oscillations of the plume as it settles down to its final rise height may be attenuated by the radiation of gravity waves. For [(U)\tilde] << 1{\tilde{U}\ll 1} the oscillations decay rapidly due to the transport of energy away from the plume by gravity waves. For ${\tilde{U}>rsim 1}${\tilde{U}>rsim 1} the gravity waves travel in the same direction and at the same speed as the flow. In this case, the oscillations of the plume do not decay greatly by radiation of gravity waves.     

The oil spill behaviour model of the Canadian atmospheric environment service Part I: Theory and model evaluation

Abstract

This paper describes a model to simulate the behaviour of oil spills in marine environments. The model includes parametrizations of various physical processes representing the movement and weathering of an oil slick. The movement of the slick is affected by wind‐driven, tidal and residual water currents. Turbulent dispersion is an important mechanism influencing the horizontal spreading of the slick for time periods greater than about a day.

The model is used to simulate successfully the movement of spill‐following buoys deployed in the Bay of Fundy, where some of the strongest tidal currents in the world occur. The ability of the model to simulate the horizontal spreading of an oil slick was evaluated with observed data from the Argo Merchant oil spill for a 10‐day period. It was found that the observed shape and extent of the spill could be fairly well described by the parametrization of turbulent dispersion effects.