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.     

非均匀风场与急流强迫的水体涡旋动力特征模拟

通过数值模拟有限区域水气界面由强迫作用驱动形成的水体涡旋及环流动力结构特征,分析非均匀风场、水体急流、两者叠加以及环境边界和地转偏向力等因子的综合影响,探讨此类水体涡旋结构和动力特征。风应力驱动的水体涡旋尺度大,相对深厚,正涡旋具有下凹表面,负涡旋具有上凸表面。水体急流驱动的涡旋形成在急流两侧,对应急流所在深度及厚度尺度相对较小,也较浅,但流速与强度均大于风场驱动的涡旋环流。地形阻挡起着引导涡旋环流走向的作用;同时在北半球地转偏向力对急流侧向负涡旋形成和强度增强更为有利。此外正涡旋对应的辐合辐散势函数强于负涡旋,有利于正涡旋区垂直上升运动强于负涡旋中垂直下沉运动。非均匀风场及水体急流两种强迫叠加作用下,涡旋数量增加、尺度减小,底层的流场形态及强度与表层差异增大。形成的水体涡旋结构呈现多种形态：深厚的整层一致;浅薄的仅维持在上层,或上下层环流相反等。风应力驱动的涡旋以正压性为主,水体急流驱动的涡旋因急流的垂直强切变而具有强的斜压性,在正斜压动能的转换中,正压性涡旋区有斜压动能向正压动能转换,斜压性涡旋区有正压动能向斜压动能转换,均有利于这两个区域正负涡旋的维持。     

On the validity of layered models of ocean dynamics and thermodynamics with reduced vertical resolution

With the purpose of studying the upper part of the ocean, the shallow water equations (in a `reduced gravity' setting) have been extended in the last decades by allowing for horizontal and temporal variations of the buoyancy field ϑ, while keeping it as well as the velocity field u as depth-independent. In spite of the widespread use of this `slab' model, there has been neither a discussion on the range of validity of the system nor an explanation of points such as the existence of peculiar zero-frequency normal modes, the nature of the instability of a uniform u flow, and the lack of explicit vertical shear associated with horizontal density gradients. These questions are addressed here through the development of a subinertial model with more vertical resolution, i.e., one where the buoyancy ϑ varies linearly with depth. This model describes satisfactorily the problem of baroclinic instability with a free boundary, even for short perturbations and large interface slopes. An enhancement of the instability is found when the planetary β effect is compensated with the topographic one, due to the slope of the free boundary, allowing for a `resonance' of the equivalent barotropic and first baroclinic modes. Other low-frequency models, for which buoyancy stratification does not play a dynamical role, are invalid for short perturbations and have spurious terms in their energy-like integral of motion.     

Local kinetic energy budget of high-frequency and intermediate-frequency eddies: winter climatology and interannual variability

The local budget of eddy kinetic energy (EKE) for both high-frequency (HF, 2–6 days) and intermediate-frequency (IF, 7–29 days) eddies are evaluated for Northern Hemisphere boreal winter using the 31-year (1979/80–2010/11) NCEP-DOE reanalysis. A new form of EKE equation is used to isolate the kinetic energy generation/destruction due to interactions among eddies of different timescales. The main source of HF EKE is baroclinic conversion that is concentrated in the mid-lower troposphere. Barotropic conversion mainly damps HF EKE and shows positive contributions to IF EKE on the northern flank of the winter-mean tropospheric jet. Interaction between HF and IF eddies acts as a sink for HF EKE and a main source for IF EKE, especially over the eastern ocean basins, confirming the substantial role of synoptic-scale transients in the development of IF phenomena such as atmospheric blocking. Large interannual variability is found for various EKE budget terms. The HF EKE response to El Niño is characterized by a dipole (tri-pole) anomaly over the North Pacific (North Atlantic). Baroclinic conversion is the main driver of the observed changes in HF EKE while barotropic conversion, interaction between HF and IF eddies, and energy flux convergence all play non-negligible roles in determining the final meridional structure of the HF EKE anomalies. Associated with El Niño, IF EKE generally decreases over the North Pacific and increases over the North Atlantic, which mainly result from changes in baroclinic conversion and EKE conversion due to eddy–eddy interactions. The latter is dominated by interaction between IF and LF (low-frequency, 30–90 days) eddies over the North Pacific, and by interactions between HF and IF eddies, and between IF and LF eddies over the North Atlantic.     

The influence of the coast on the dynamics of upwelling fronts: Part II. Numerical simulations

We investigated the dynamics of upwelling fronts near a coast. This work was first motivated by laboratory experiments [Bouruet-Aubertot, Linden, Dyn. Atmos. Oceans, 2002] in which the front is produced by the adjustment of a buoyant fluid initially confined within a bottomless cylinder. It was shown that cyclonic eddies consisting of coastal waters are enhanced when the front is unstable near the coast (the outer vertical boundary). The purpose of this paper is to provide further insights into this process. We reproduced the experimental configuration using a three-dimensional model of the primitive equations. We first show that for coastal fronts more potential energy, in terms of the maximum available potential energy, is released than for open-ocean fronts. Therefore, waves of larger amplitude are generated during the adjustment and the mean flow that establishes has a higher kinetic energy in the former case. Then as baroclinic instability starts and wave crests reach the boundary, cyclonic eddies are enhanced as in the laboratory experiments and in a similar way. However, in contrast to the laboratory experiments, offshore advection of cyclonic eddies can occur in two stages, depending on the spatial organization of the baroclinic wave. When the baroclinic wave consists of the sum of different modes and is thus highly asymmetric, the offshore advection of cyclonic eddies occurs just after their enhancement at the boundary, as in the laboratory experiments. By contrast, when a single-mode baroclinic wave develops, neighboring cyclonic eddies first merge before being advected offshore. Very different behavior is observed for open-ocean fronts. First a mixed baroclinic–barotropic instability grows. Then the eddies transfer their energy to the mean flow and the barotropic and baroclinic instabilities start again. An excellent agreement is obtained with the main result obtained in the laboratory experiments: the ratio between growth rates of surface cyclonic and anticyclonic vorticity increases as the instability develops nearer to the coast.     

Changes in the normal mode energetics of the general atmospheric circulation in a warmer climate

Changes in the normal mode energetics of the general atmospheric circulation are assessed for the northern winter season (DJF) in a warmer climate, using the outputs of four climate models from the Coupled Model Intercomparison Project, Phase 3. The energetics changes are characterized by significant increases in both the zonal mean and eddy components for the barotropic and the deeper baroclinic modes, whereas for the shallower baroclinic modes both the zonal mean and eddy components decrease. Significant increases are predominant in the large-scale eddies, both barotropic and baroclinic, while the opposite is found in eddies of smaller scales. While the generation rate of zonal mean available potential energy has globally increased in the barotropic component, leading to an overall strengthening in the barotropic energetics terms, it has decreased in the baroclinic component, leading to a general weakening in the baroclinic energetics counterpart. These global changes, which indicate a strengthening of the energetics in the upper troposphere and lower stratosphere (UTLS), sustained by enhanced baroclinic eddies of large horizontal scales, and a weakening below, mostly driven by weaker baroclinic eddies of intermediate to small scales, appear together with an increased transfer rate of kinetic energy from the eddies to the zonal mean flow and a significant increase in the barotropic zonal mean kinetic energy. The conversion rates between available potential energy and kinetic energy, C, were further decomposed into the contributions by the rotational (Rossby) and divergent (gravity) components of the circulation field. The eddy component of C is due to the conversion of potential energy of the rotational adjusted mass field into kinetic energy by the work realized in the eddy divergent motion. The zonal mean component of C is accomplished by two terms which nearly cancel each other out. One is related to the Hadley cell and involves the divergent component of both wind and geopotential, while the other is associated to the Ferrel cell and incorporates the divergent wind with the rotationally adjusted mass field. Global magnitude increases were found in the zonal mean components of these two terms for the warmer climate, which could be the result of a strengthening and/or widening of both meridional cells. On the other hand, the results suggest a strengthening of these conversion rates in the UTLS and a weakening below, that is consistent with the rising of the tropopause in response to global warming.     

Shear instability and gravity wave saturation in an asymmetrically stratified jet

Motivated by the mean current and stratification structure associated with the equatorial undercurrent (EUC), we examine the stability and wave propagation characteristics of a highly idealized model flow: the asymmetrically stratified jet. This is a parallel shear flow in which the depth-varying current has the sech² form of a Bickley jet. The stratification has a step function structure: the buoyancy frequency takes uniform values above and below the center of the jet, with the larger value occurring below. The spectrum contains three classes of unstable normal modes. Two are extensions of the sinuous and varicose modes of the unstratified Bickley jet; the third has not been described previously. The asymmetric stratification structure allows instabilities to radiate gravity wave energy from the upper flank of the jet to the lower flank, where it encounters a critical layer. From here, wave energy may be reflected, absorbed or transmitted. Absorption results in wave saturation and momentum transfer to the mean flow, in close analogy with the breaking of orographic gravity waves in the middle atmosphere. Transmission beyond the lower flank may partly account for wave signals observed in the deep equatorial oceans. All of these processes exert zonal forces on the jet that alter its speed and shape. The wave structures and associated fluxes developed by the idealized model are compared with observations of the EUC.     

基于潜标资料的中南半岛外海水文特征分析

基于2012年9月—2013年12月中南半岛外海累计16个月的长时间序列潜标观测数据,结合AVISO海表面高度异常（sea level anomaly,SLA）数据,首次详细分析了中南半岛外海典型中尺度涡的运动规律和垂向特征及其对环境水文特征的影响,揭示了该海域深层海流的时间变化特征。在观测期间共捕捉到3次中尺度涡过程,中尺度涡对站位所在海域主温跃层深度变化的最大影响振幅可达50 m。研究发现：1)观测站位所在海域各深度的温度异常时间变化与站位SLA时间变化的相关性随深度增加逐渐减弱。2)上层和中层的海水流动受中尺度涡影响显著。1 500 m和2 000 m的深层环流主要表现为季节变化;在强中尺度涡暖涡经过期间,中尺度涡能影响到1 500 m的环流场,同时出现30 d周期震荡。2 000 m流场则不受中尺度涡影响。3)中南半岛以东南海1 500 m处深层海流月平均流速夏季大于冬季,月平均可达3～5 cm·s-1;2 000 m处深层海流最大流速出现在冬季,月平均可达2～6 cm·s-1。深层海流受潮汐影响显著,潮汐作用主要影响深层海流东西向流速的变化。     

A multi-limit formulation for the equilibrium depth of a stably stratified boundary layer

Currently no expression for the equilibrium depth of the turbulent stably-stratified boundary layer is available that accounts for the combined effects of rotation, surface buoyancy flux and static stability in the free flow. Various expressions proposed to date are reviewed in the light of what is meant by the stable boundary layer. Two major definitions are thoroughly discussed. The first emphasises turbulence and specifies the boundary layer as a continuously and vigorously turbulent layer adjacent to the surface. The second specifies the boundary layer in terms of the mean velocity profile, e.g. by the proximity of the actual velocity to the geostrophic velocity. It is shown that the expressions based on the second definition are relevant to the Ekman layer and portray the depth of the turbulence in the intermediate regimes, when the effects of static stability and rotation essentially interfere. Limiting asymptotic regimes dominated by either stratification or rotation are examined using the energy considerations. As a result, a simple equation for the depth of the equilibrium stable boundary layer is developed. It is valid throughout the range of stability conditions and remains in force in the limits of a perfectly neutral layer subjected to rotation and a rotation-free boundary layer dominated by surface buoyancy flux or stable density stratification at its outer edge. Dimensionless coefficients are estimated using data from observations and large-eddy simulations. Well-known and widely used formulae proposed earlier by Zilitinkevich and by Pollard, Rhines and Thompson are shown to be characteristic of the above interference regimes, when the effects of rotation and static stability (due to either surface buoyancy flux, or stratification at the outer edge of the boundary layer) are roughly equally important.     

Nonlinear oscillations of semigeostrophic Eady waves in the presence of diffusivity

Analyses are performed to examine the physical processes involved in nonlinear oscillations of Eady baxoclinic waves obtained from viscous semigeostrophic models with two types of boundary conditions (free-slip and non-slip). By comparing with previous studies for the case of the free-slip boundary condition, it is shown that the nonlinear oscillations are produced mainly by the interaction between the baroclinic wave and zonal-mean state (total zonal-mean flow velocity and buoyancy stratification) but the timescale of the nonlinear oscillations is largely controlled by the diffusivity. When the boundary condition is non-slip, the nonlinear oscillations are further damped and slowed by the diffusive process. Since the free-slip (non-slip) boundary condition is the zero drag (infinite drag) limit of the more realistic drag boundary condition,the nonlinear oscillations obtained with the two types of boundary conditions are two extremes for more realistic nonlinear oscillations.     

Effects of the baroclinic adjustment on the tropopause in the NCEP–NCAR reanalysis

In this work, we study the mean tropopause structure from the National Center for Environmental Prediction–National Center for Atmospheric Research reanalysis in the framework of baroclinic adjustment theories, focusing on the impact of baroclinic eddies on the mean tropopause height. In order to measure the effects of such perturbations, we introduce an appropriate global index that selects events of high baroclinic activity and allows us to distinguish the phases of growth and decay of baroclinic waves. We then composite the tropopause mean structure before and after baroclinic events, finding that baroclinic disturbances cause the zonally averaged midlatitude winter tropopause height to rise. Our results establish the importance of baroclinic adjustment processes for midlatitude tropopause dynamics.     

An analysis of vertical velocity spectra obtained in the bomex fair-weather,trade-wind boundary layer

Spectra of vertical velocity fluctuations measured on board an aircraft flying over the sea along and across the wind during the Barbados Oceanographic and Meteorological Experiment (BOMEX) are stratified and composited according to estimates of the Monin-Obukhov stability length. This was done to test the hypothesis that a hierarchy of physical mechanisms, responding to wind shear and buoyancy, is active in the turbulent transfer processes of the oceanic subcloud layer. Despite the possibility that the data contain a heading-independent bias, it is concluded that a major change of eddy structure occurs over a narrow range of stability. This agrees well with an early theory on convection over land and observations of herring gull flight characteristics. The vertical variation of the spectral-composites compares favorably with other observations over land and sea. Physical models are suggested to explain the data. One of these models is in agreement with theoretical results concerning ringlike convection. The spectral data, which begin to lose confidence at about 10 km, suggest that a limiting size of eddies over the ocean is approximately twice the depth of the subcloud layer (in this case 600 m) regardless of the kind of eddy structure.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

On the problem of the Neva river flood waves identification

Based on the analysis of the measurements of hydrometeorological characteristics, the identification is corroborated of the Neva River flood waves as the baroclinic topographic waves. It is demonstrated that during the formation and maximum development of the most significant sea level rises in the Neva Bay, the stratification in the Gulf of Finland still remains pronounced despite the storm conditions. The baroclinic nature of the flood wave is indicated by the significant changes in the dispersion of currents with depth with their direction changing to the reverse one as it occurs in the first baroclinic mode wave. Directions of major axes of the standard deviation ellipses are oriented not along the isobaths as it should be in case of long gravity waves (being the longitudinal ones) but are extended across the bottom topography contours that is typical of gradient-vorticity waves assigned to the class of horizontal transverse waves.     

大气静力稳定度的铅直分布和不同风速铅直廓线对天气系统发展的影响

采用一个准地转三层模式,对于高低空不同层结及不同风速铅直廓线下的斜压不稳定性问题进行了分析和讨论。指出:(1)大气层结特征对斜压不稳定的影响不仅表现在对不稳定临界波长和临界风速切变的制约上,而且其铅直分布的不均一性决定了大气的各个层次对斜压不稳定的贡献大小;扰动的斜压发展主要取决于静力稳定度较小的那些层次内的热力、动力学条件,在这些层次内,扰动也最为明显。(2)高低空风速比中空为大的“高低空强风型”风速铅直分布最有利于扰动的不稳定发展,在这种风速铅直廓线下,不稳定波波谱较宽,不稳定波临界波长和最不稳定波波长也较短。     

On the role of the unresolved eddies in a model of the residual currents in the central strait of Georgia,B.C.: Research Note

Abstract

A depth‐independent numerical model of the Juan de Fuca/Strait of Georgia system reproduces the broad structure of the observed depth‐averaged residual circulation in the Central Strait of Georgia but underestimates its magnitude (Marinone and Fyfe, 1992). Here we present some new calculations based on a re‐parameterization of the unresolved eddies in terms of “statistical dynamical tendencies” instead of the previous eddy‐viscosity treatment. With the new parameterization, the simulated time‐mean flow is closer to the observed circulation both in structure and magnitude. While not specifically designed to do so, the new parameterization also leads to a modest improvement in the low‐pass filtered component of the flow. Based on these results, the depth‐averaged residual currents in the region are conjectured to involve a four‐way balance between the hitherto ignored effect of “statistical dynamical tendencies” and conventional tidal, atmospheric and buoyancy forcing.     

One-dimensional baroclinically unstable waves on the Gulf Stream potential vorticity gradient near Cape Hatteras

Application of linear baroclinic instability theory to the observed distributions of velocity, stratification, and potential vorticity in the Gulf Stream near 74° W is successful in predicting the time and length scales of the most rapidly growing disturbances. A continuously-stratified, one-dimensional model with realistic bottom slope predicts propagation speeds of 10–50 cm s⁻¹ associated with two regimes of rapid temporal growth centered at periods of 28 days and 5–7 days. This prediction is consistent with observations of the propagation and growth of Gulf Stream meanders derived from inverted echo sounder measurements in this region. The instability model also predicts that for realistic bottom slopes the baroclinic energy transfer should be weakly negative (eddy-to-mean) in deep water, but for low-frequency waves should change to significant positive (mean-to-eddy) transfer above depths of 1500 m, consistent with observations.     

Comments on the Numerical Simulation of Homogeneous Stably-Stratified Turbulence

The standard design for the direct numerical simulation of homogeneous stably-stratified turbulence assumes that the simulated turbulence is fully characterised by the gradient Richardson number. This assumption is justified only in sufficiently strong stratification when the Obukhov turbulent length scale, L, is essentially smaller than the depth of the computational domain, H. Otherwise simulations are not quite realistic because they cut off the large-scale part of the turbulence spectrum, namely, the scales comparable with or larger than H but smaller than L, that is just the eddies most sensitive to the stratification.     

Effects of fluctuating daily surface fluxes on the time-mean oceanic circulation

The effect of fluctuating daily surface fluxes on the time-mean oceanic circulation is studied using an empirical flux model. The model produces fluctuating fluxes resulting from atmospheric variability and includes oceanic feedbacks on the fluxes. Numerical experiments were carried out by driving an ocean general circulation model with three different versions of the empirical model. It is found that fluctuating daily fluxes lead to an increase in the meridional overturning circulation (MOC) of the Atlantic of about 1 Sv and a decrease in the Antarctic circumpolar current (ACC) of about 32 Sv. The changes are approximately 7% of the MOC and 16% of the ACC obtained without fluctuating daily fluxes. The fluctuating fluxes change the intensity and the depth of vertical mixing. This, in turn, changes the density field and thus the circulation. Fluctuating buoyancy fluxes change the vertical mixing in a non-linear way: they tend to increase the convective mixing in mostly stable regions and to decrease the convective mixing in mostly unstable regions. The ACC changes are related to the enhanced mixing in the subtropical and the mid-latitude Southern Ocean and reduced mixing in the high-latitude Southern Ocean. The enhanced mixing is related to an increase in the frequency and the depth of convective events. As these events bring more dense water downward, the mixing changes lead to a reduction in meridional gradient of the depth-integrated density in the Southern Ocean and hence the strength of the ACC. The MOC changes are related to more subtle density changes. It is found that the vertical mixing in a latitudinal strip in the northern North Atlantic is more strongly enhanced due to fluctuating fluxes than the mixing in a latitudinal strip in the South Atlantic. This leads to an increase in the density difference between the two strips, which can be responsible for the increase in the Atlantic MOC.     

The effect of Antarctic Circumpolar Current transport on the frontal variability in Drake Passage

The Antarctic Circumpolar Current (ACC) is composed of three major fronts: the Sub-Antarctic Front (SAF), the Polar Front (PF), the Southern ACC Front (SACCF). The locations of these fronts are variable. The PF can shift away from its historical (mean) location by as much as 100 km. The transport of the ACC in Drake Passage varies from its mean (134 Sv) by as much as 60 Sv. A regional numerical circulation model is used to study frontal variability in Drake Passage as affected by a range of volume transports (from 95 Sv to 155 Sv with an interval of 10 Sv). Large transport shifts the fronts northward while the smaller transport causes a southward shift. The mean shifting distance of the PF from the historical mean location is minimum with 135 Sv transport. The SAF and the SACCF are confined by northern and southern walls, respectively, while the PF is loosely controlled by the topography. Due to impact of the eddies and meanders on the PF at several regions in Drake Passage, the PF may move northward to join the SAF or move southward to combine with the SACCF, especially in central Scotia Sea. The SAF and PF are more stable with higher transport. The SAF behaves as a narrow, strong frontal jet with large transport while displaying meanders with smaller transport. In the model simulations, the Ertel Potential Vorticity (EPV) is strongly correlated with the volume transport stream function. EPV at depths between 1000 and 2500 m is correlated with the transport stream function with a coefficient above 0.9. Near the bottom, the correlation is about 0.6 due to the disruptive influence of bottom topography. Within 750 m of the surface, the correlation is much reduced due to the effect of K-Profile Parameterization (KPP) mixing and eddy mixing.     

Tilting separation flows: a mechanism for intense vertical mixing in the coastal ocean

Observations of a front associated with boundary layer separation from a headland illustrate a mechanism by which horizontal density gradients create intense turbulence and vertical mixing, thus, contributing to water property modification in the coastal zone. Tidal current past an island separates from the coast, creating a shear zone between the primary flow and the slowly moving water in the lee of the island. The density structure on either side of the front may differ due to different origins or degrees of prior mixing. Consequently, there can be horizontal density gradients across the front. Boundary layer separation from the headland begins as a vertical vortex sheet on which instabilities grow to form a sequence of eddies. The presence of horizontal density gradients causes the shear layer to tilt. Tilting and stretching of the sheared flow generates intense circulation. Whirlpools and boils appear at the surface accompanied by vertical motions in which broad areas of upwelling alternate with narrow areas of downwelling. These mix the water throughout its depth; bubbles entrained at the surface reach depths of over 120 m. Such violent mixing weakens stratification associated with the estuarine circulation and aerates water masses passing through the area.