The impact of freshwater discharges on the ocean circulation in the Skagerrak/northern North Sea area Part I: model validation

We assess the performance of an eddy-recognizing numerical ocean model in simulating the pattern and variability of the hydrography in the Skagerrak/northern North Sea area. The model we use is a version of the widely used Princeton ocean model employing a terrain-following vertical coordinate. Results from a series of five multi-year simulations of the mesoscale response are described. The simulations differ in their representation of the lateral freshwater supply to the model ocean of which the first is a reference simulation. The next four are variations in which the river discharges and/or the Baltic outflow are given more realistic representations. For validation, we have used in situ hydrographic data. A novelty is that we use the concepts of freshwater height and potential energy anomaly as objective validation tools. We find that, in general, the model faithfully reproduces many of the observed hydrographic features including their mean patterns and their variance. Not surprisingly, we find that the Baltic outflow is by far the most significant freshwater source in terms of its influence on the hydrography in the area, a result corroborating earlier findings. The best validation is obtained when all freshwater supply is made as realistic as possible, in particular the Baltic outflow. We also find that the large scale cyclonic circulation and the location of fronts are robust characteristics of the Skagerrak/northern North Sea circulation given the impact changes in the freshwater input has on the hydrography. Finally, we find that a further exploration of the impact of the lateral open boundary forcing, e.g., the input of Atlantic water, is needed.     

Numerical analysis of the Black Sea currents and mesoscale eddies in 2006 and 2011

Two prognostic experiments taking into account real atmospheric forcing for 2006 and 2011 were carried out based on the eddy-resolving numerical model with a horizontal resolution of 1.6 km for the Black Sea. The main dynamic features such as the Rim Current, the Sevastopol, and Batumi anticyclones are reproduced in both experiments. The model results are confirmed via observation data. We accomplished the analysis of simulated circulation and energetics. The results demonstrate that both the vertical viscosity and vertical diffusion along with the energy inflow from the wind have been the main contributors to the annual and seasonal budgets of kinetic and potential energies of the Black Sea circulation. It is shown that two regimes of the Black Sea general circulation are implemented depending on a magnitude of wind contribution to the kinetic energy in winter. Intensive mesoscale eddy formation was observed along the Anatolian, Caucasian, and Crimean coasts. The analysis of the Black Sea circulation and eddy energetics allowed us to conclude that the generation and development of the mesoscale coastal eddies is associated with the barotropic instability in case of intensive coastal currents and is associated with both the barotropic and baroclinic instability in case of weak coastal currents.     

Regional turbulence patterns driven by meso- and submesoscale processes in the Caribbean Sea

The surface ocean circulation in the Caribbean Sea is characterized by the interaction between anticyclonic eddies and the Caribbean Upwelling System (CUS). These interactions lead to instabilities that modulate the transfer of kinetic energy up- or down-cascade. The interaction of North Brazil Current rings with the islands leads to the formation of submesoscale vorticity filaments leeward of the Lesser Antilles, thus transferring kinetic energy from large to small scales. Within the Caribbean, the upper ocean dynamic ranges from large-scale currents to coastal upwelling filaments and allow the vertical exchange of physical properties and supply KE to larger scales. In this study, we use a regional model with different spatial resolutions (6, 3, and 1 km), focusing on the Guajira Peninsula and the Lesser Antilles in the Caribbean Sea, in order to evaluate the impact of submesoscale processes on the regional KE energy cascade. Ageostrophic velocities emerge as the Rossby number becomes O(1). As model resolution is increased submesoscale motions are more energetic, as seen by the flatter KE spectra when compared to the lower resolution run. KE injection at the large scales is greater in the Guajira region than in the others regions, being more effectively transferred to smaller scales, thus showing that submesoscale dynamics is key in modulating eddy kinetic energy and the energy cascade within the Caribbean Sea.     

Eddy energy sources and mesoscale eddies in the Sea of Okhotsk

Based on eddy-permitting ocean circulation model outputs, the mesoscale variability is studied in the Sea of Okhotsk. We confirmed that the simulated circulation reproduces the main features of the general circulation in the Sea of Okhotsk. In particular, it reproduced a complex structure of the East-Sakhalin current and the pronounced seasonal variability of this current. We established that the maximum of mean kinetic energy was associated with the East-Sakhalin Current. In order to uncover causes and mechanisms of the mesoscale variability, we studied the budget of eddy kinetic energy (EKE) in the Sea of Okhotsk. Spatial distribution of the EKE showed that intensive mesoscale variability occurs along the western boundary of the Sea of Okhotsk, where the East-Sakhalin Current extends. We revealed a pronounced seasonal variability of EKE with its maximum intensity in winter and its minimum intensity in summer. Analysis of EKE sources and rates of energy conversion revealed a leading role of time-varying (turbulent) wind stress in the generation of mesoscale variability along the western boundary of the Sea of Okhotsk in winter and spring. We established that a contribution of baroclinic instability predominates over that of barotropic instability in the generation of mesoscale variability along the western boundary of the Sea of Okhotsk. To demonstrate the mechanism of baroclinic instability, the simulated circulation was considered along the western boundary of the Sea of Okhotsk from January to April 2005. In April, the mesoscale anticyclonic eddies are observed along the western boundary of the Sea of Okhotsk. The role of the sea ice cover in the intensification of the mesoscale variability in the Sea of Okhotsk was discussed.     

Mean and eddy motion in the Skagerrak/northern North Sea: insight from a numerical model

Insight regarding the mean and eddy motion in the Skagerrak/northern North Sea area is gained through an analysis of model-simulated currents, hydrography, kinetic energy and relative vorticity for the 2 years 2000 and 2001. In this a -coordinate ocean model is used. Since the tidal currents are generally strong in the area, care is exercised to distinguish the mesoscale (eddy) motion from higher-frequency motion such as tides, before computing the mean and eddy kinetic energy. The model-simulated response is first compared with available knowledge of the circulation in the area, and when available, also with sea-surface temperature obtained from satellite imagery. It is concluded that the model appears to faithfully reproduce most of what is known, in particularly the upper mixed layer circulation. An analysis of the mean and eddy kinetic energy reveals that many of the mesoscale structures found in the area are recurrent. This is particularly true for the structures off the southern tip of Norway. Also in general, areas of strong mean and eddy kinetic energy are co-located. The exception is the area off the southern tip of Norway, where the eddy kinetic energy is much larger than its mean counterpart. An analysis of the relative vorticity reveals that the variability found is due to the occurrence of recurrent anticyclonic eddies. It is hypothesized that these eddies are generated due to an offshore veering of the Norwegian coastal current (NCC) as it reaches the eastern end of the Norwegian Trench plateau. Here it becomes a free jet, which is then vulnerable to either barotropic instability caused by the horizontal shear in the jet-like structure of the NCC at this point, or a baroclinic (frontal) instability. The latter may come into play when the NCC veers offshore and its relatively fresh water meets the inflowing saline water of Atlantic origin, a frontogenesis that may become strong enough for cyclogenesis to take place. Due to the depth-independent nature of the model-generated eddies, the barotropic instability is the most likely candidate. It remains to resolve the reason for the offshore veering of the NCC. The most likely candidate mechanisms are vortex squeezing or simply that the coastline curvature is large enough for the NCC to separate from the coast in a hydraulic sense.Responsible Editor: Phil Dyke     

The intrinsic nonlinear multiscale interactions among the mean flow,low frequency variability and mesoscale eddies in the Kuroshio region

Using a new functional analysis tool, multiscale window transform(MWT), and the MWT-based localized multiscale energetics analysis and canonical transfer theory, this study reconstructs the Kuroshio system on three scale windows, namely,the mean flow window, the interannual-scale(low-frequency) window, and the transient eddy window, and investigates the climatological characteristics of the intricate nonlinear interactions among these windows. Significant upscale energy transfer is observed east of Taiwan, where the mean Kuroshio current extracts kinetic energy from both the interannual and eddy windows.It is found that the canonical transfer from the interannual variability is an intrinsic source that drives the eddy activities in this region. The multiscale variabilities of the Kuroshio in the East China Sea(ECS) are mainly controlled by the interaction between the mean flow and the eddies.The mean flow undergoes mixed instabilities(i.e., both barotropic and baroclinic instabilities) in the southern ECS, while it is barotropically stable but baroclinically unstable to the north. The multiscale interactions are found to be most intense south of Japan, where strong mixed instabilities occur; both the canonical transfers from the mean flow and the interannual scale are important mechanisms to fuel the eddies. It is also found that the interannual-scale energy mainly comes from the barotropically unstable jet, rather than the upscale energy transfer from the high frequency eddies.     

The diapcynal nutrient flux and shear-induced diapcynal mixing in the seasonally stratified western Irish Sea

We estimate the diapcynal nitrate flux in the seasonally stratified western Irish Sea using the dissipation method. By comparing the divergence of the reported benthic and diapcynal nitrate fluxes, we are able to explain much of the observed annual summer decline in deep-water nitrate at this location. We then show that the new production, fuelled by the diapcynal nitrate flux, is of a similar magnitude to that associated with the spring bloom. This suggests that the physical processes responsible for the diapcynal nitrate flux will set the limit on new production at this location. High-resolution mid-water column ADCP measurements show an average thermocline gradient Richardson number of 1, thus suggesting episodes of enhanced shear could result in shear instability, and therefore mixing within the thermocline. Bulk shear measurements reveal episodes of enhanced shear in the form of spikes, during which time the bulk shear vector takes the form of a clockwise rotating vector which has a period close to the local inertial period. The episodes of shear spikes are correlated to the wind and are consistent with observations made elsewhere. Estimates of profiles of the rate of dissipation of turbulent kinetic energy, based on microstructure velocity measurements, show that during a shear spike the dissipation rate within the thermocline, and therefore the buoyancy (and nitrate) flux, is enhanced by a factor of 4 when compared to periods with no shear spikes. Intermittent shear spikes are, therefore, an important mechanism for enhancing mixing across the shelf sea seasonal thermocline, and therefore delivery of nitrate to the euphotic zone, at this location.     

Multi-nest high-resolution model of submesoscale circulation features in the Gulf of Taranto

Recent oceanographic field measurements and high-resolution numerical modelling studies have revealed intense, transient, submesoscale motions characterised by a horizontal length scale of 100–10,000 m. This submesoscale activity increases in the fall and winter when the mixed layer (ML) depth is at its maximum. In this study, the submesoscale motions associated with a large-scale anticyclonic gyre in the central Gulf of Taranto were examined using realistic submesoscale-permitting simulations. We used realistic flow field initial conditions and multiple nesting techniques to perform realistic simulations, with very-high horizontal resolutions (> 200 m) in areas with submesoscale variability. Multiple downscaling was used to increase resolution in areas where instability was active enough to develop multi-scale interactions and produce 5-km-diameter eddies. To generate a submesoscale eddy, a 200-m resolution was required. The submesoscale eddy was formed through small-scale baroclinic instability in the rim of a large-scale anticyclonic gyre leading to large vertical velocities and rapid restratification of the ML in a time-scale of days. The submesoscale eddy was confirmed by observational data from the area and we can say that for the first time we have a proof that the model reproduces a realistic submesoscale vortex, similar in shape and location to the observed one.     

Vertical mixing and elements of mesoscale dynamics over North Carolina shelf and contiguous Gulf Stream waters

Results of microstructure measurements conducted in October–November of 2015 as a part of the Coupled Air Sea Processes and Electromagnetic Ducting Research (CASPER) project are discussed. The measurements were taken on the North Carolina shelf and across the Gulf Stream front. On the shelf, the oceanic stratification was influenced by highly variable surface salinity and along-bottom advection. Vertical mixing was mostly governed by variable winds. The vertical eddy diffusivity was estimated using the VMP-based dissipation measurements, and the diffusivity values obtained during calm periods and stormy winds were compared. Parameterization of the diffusivity for various mesoscale dynamical conditions is discussed in terms of shear instabilities and internal wave-generated turbulence based on data obtained in deep waters of the Gulf Stream and on the continental slope.     

Turbulence and mixing in a freshwater-influenced tidal bay: Observations and numerical modeling

In situ observations and numerical simulations of turbulence are essential to understanding vertical mixing processes and their dynamical controls on both physical and biogeochemical processes in coastal embayments. Using in situ data collected by bottom-mounted acoustic Doppler current profilers(ADCPs) and a free-falling microstructure profiler, as well as numerical simulations with a second-moment turbulence closure model, we studied turbulence and mixing in the Xiamen Bay, a freshwater-influenced tidal bay located at the west coast of the Taiwan Strait. Dynamically, the bay is driven predominantly by the M2 tide, and it is under a significant influence of the freshwater discharged from the Jiulong River. It is found that turbulence quantities such as the production and dissipation rates of the turbulent kinetic energy(TKE) were all subject to significant tidal variations, with a pronounced ebb-flood asymmetry. Turbulence was stronger during flood than ebb. During the flooding period, the whole water column was nearly well mixed with the depth-averaged TKE production rate and vertical eddy viscosity being up to 5?10?6 W kg?1 and 2?10?2 m2 s?1, respectively. In contrast, during the ebb strong turbulence was confined only to a 5?8 m thick bottom boundary layer, where turbulence intensity generally decreases with distance from the seafloor. Diagnosis of the potential energy anomaly showed that the ebb-flood asymmetry in turbulent dissipation and mixing was due mainly to tidal straining process as a result of the interaction between vertically shared tidal currents and horizontal density gradients. The role of vertical mixing in generating the asymmetry was secondary. A direct comparison of the modeled and observed turbulence quantities confirmed the applicability of the second-moment turbulence closure scheme in modeling turbulent processes in this weakly stratified tidally energetic environment, but also pointed out the necessity of further refinements of the model.     

Modelling-based assessment of suspended sediment dynamics in a hypertidal estuarine channel

We investigate the dynamics of suspended sediment transport in a hypertidal estuarine channel which displays a vertically sheared exchange flow. We apply a three-dimensional process-based model coupling hydrodynamics, turbulence and sediment transport to the Dee Estuary, in the north-west region of the UK. The numerical model is used to reproduce observations of suspended sediment and to assess physical processes responsible for the observed suspended sediment concentration patterns. The study period focuses on a calm period during which wave-current interactions can reasonably be neglected. Good agreement between model and observations has been obtained. A series of numerical experiments aim to isolate specific processes and confirm that the suspended sediment dynamics result primarily from advection of a longitudinal gradient in concentration during our study period, combined with resuspension and vertical exchange processes. Horizontal advection of sediment presents a strong semi-diurnal variability, while vertical exchange processes (including time-varying settling as a proxy for flocculation) exhibit a quarter-diurnal variability. Sediment input from the river is found to have very little importance, and spatial gradients in suspended concentration are generated by spatial heterogeneity in bed sediment characteristics and spatial variations in turbulence and bed shear stress.     

地球磁层顶的漂移动力学Alfvn波不稳定性及其反常输运效应

本文用回旋动力学研究了磁层顶等离子体低频漂移动力学不稳定性.在β≥1附近发现两支不稳定的漂移动力学Alfvèn模（DKA）.它们可在▽T（∥-▽n）≠0时激发,速度剪切提供主要的自由能源.两支DKA均具有非零的（δE_y,δE_∥）和（δB_x,δB_∥）.在湍动的非线性饱和状态下,δB_x的起伏可导致很强的反常输运,当|δB_x|=1nT时,D_⊥可达到10⁹m²/s的数量级.因此,DKA可能在太阳风-磁层耦合过程中起重要作用.     

Richardson number profiles in laboratory experiments applied to shallow seas

Abstract

A unified analysis is given of the critical conditions for the onset of stratification due to either a vertical or a horizontal buoyancy flux, with tidal or wind stirring.

The critical conditions for the onset of stratification with a horizontal buoyancy flux are found to be of the form of ratios of the tidal slope, or wind setup, to the equivalent surface slope due to the lateral density gradient. These ratios, which are easily determined from sea data, indicate that the profiles of critical flux Richardson Number, averaged over the stirring cycle, are similar to those inferred from the laboratory experiments of Hopfinger and Linden (1982) in which there is zero mean shear turbulence with a stabilising buoyancy flux, and also that the efficiency for the conversion of kinetic energy to potential energy for tidal stirring is similar to that for wind stirring.

The observed much greater efficiency for wind stirring, compared with tidal stirring with a vertical buoyancy flux, is also consistent with the existence of flux Richardson Number profiles in the sea similar to those occurring in the corresponding laboratory experiments. Using the solution of the turbulent kinetic energy equation for the water column, the relative importance of the production of turbulent kinetic energy, and its diffusion by turbulence are assessed, and the critical conditions for the onset of stratification with a vertical buoyancy flux are shown to reduce the classical Simpson—Hunter form.     

The influence of mesoscale topography on the stability and growth rates of a two-layer model of the open ocean

Abstract

The influence of mesoscale topography on the baroclinic instability of a two-layer model of the open ocean is considered. For westward velocities in the top layer (U), and for a sinusoidal topography independent of x or longitude (a cross-stream topography), the critical value of U (U_c ) leading to instability is the same as when there is no topography. The wavelength of the unstable perturbation corresponding to U _c is shortened. For a given wavevector (k) of the perturbation the system becomes stable (as also in the absence of topography) for large values of |U|. The minimum value of the shear leading to stability is, however, significantly reduced by the topography.

For sufficiently large values of the height of the topographic features, instabilities appear which are localized within a narrow range of the shear. These instabilities are studied for a topography that depends both on x and y.

For a cross-stream topography the growth rates are somewhat smaller than those without topography and they depend only weakly on k_y . For the topographies considered here which depend both on x and y, perturbations with different values of k_y can again have roughly the same growth rate.

In the case of stable oscillations, variations in the eddy energy with very long periods are made possible by the coexistence of topographic modes with closely lying periods.     

Multi-core structure of the Kuroshio in the East China Sea from long-term transect observations

Long-term hydrographic temperature and salinity transect data in the East China Sea from June 1955 to November 2001 are analyzed in order to examine the geostrophic velocity and the structure of the Kuroshio current. The structure of the Kuroshio Current is divided into three basic forms, a single-core structure, a double-core structure and a multi-core structure; the appearance percentage of the three forms are 53.1%, 31.4%, and 15.4%, respectively. The analysis suggests that multi-core structures have significant seasonal and interannual variabilities that are not fully understood but may relate to variations in transport and associated flow instabilities. The Kuroshio's spatial character is also analyzed in detail by applying a simplified model of motion instability into this multi-core structure of the East China Sea Kuroshio. The theoretical results are found to be consistent with the observations, suggesting that the instability of the Kuroshio in the East China Sea may bring forth the formation of the observed multi-core structure.     

Processes contributing to the evolution and destruction of stratification in the Liverpool Bay ROFI

Liverpool Bay, a region of freshwater influence subject to semi-diurnal and enduring periods of stratification, is home to a long-term coastal observatory. The observatory provides a new array of data which include vertical profiles of velocity from an Acoustic Doppler Current Profiler and a high frequency radar system (which provides measurements of surface currents). Using this dataset in conjunction with an analytical potential energy model that uses advances in the formulation of a freshwater buoyancy term, the processes controlling stratification can be assessed. The results indicate that a depth-resolving freshwater buoyancy term should be used for the calculation stratification. Advection, in addition to depth-mean straining, is an important process affecting the stratification in Liverpool Bay. Specifically, when semi-diurnal stratification occurs, the two terms are in phase whilst when enduring stratification occurs, they are out of phase. The phase of the advective component, and thus its influence relative to depth-mean straining, was found to be a function of the vertical variation of the horizontal density gradient.     

On the mathematical stability of stratified flow models with local turbulence closure schemes

Occasionally, numerical simulations using local turbulence closure schemes to estimate vertical turbulent fluxes exhibit small-scale oscillations in space, causing the eddy coefficients to vary over several orders of magnitude on short distances. Theoretical developments suggest that these spurious oscillations are essentially due to the way the eddy coefficients depend on the vertical gradient of the model’s variables. An instability criterion is derived based on the assumptions that the artefacts under study are due to the development of small-amplitude, small time- and space-scale perturbations of a smooth solution. The relevance of this criterion is demonstrated by applying it to a series a closure schemes, ranging from the Pacanowski–Philander formulas to the Mellor–Yamada level 2.5 model.     

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

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

Nonlinear diffusive instabilities in differentially rotating stars

Abstract

Angular momentum driven instabilities in a stratified differentially rotating star are investigated. In the strong buoyancy limit axisymmetric instabilities of the Goldreich-Schubert type are the most important. A detailed discussion of the linear and small amplitude theories at an arbitrary latitude is given. The bifurcation to finite amplitude steady modes is typically transcritical, and occurs whenever the angular momentum or its gradient is neither parallel not perpendicular to local gravity. Such misalignments enhance the time scale for transport of angular momentum by the Goldreich-Schubert instability. Depending on the turbulent viscosity produced by secondary shear instabilities time scales as short as the Kelvin-Helmholtz time scale are possible.     

Interaction between a surface quasi-geostrophic buoyancy filament and an internal vortex

This paper focuses on the nonlinear interaction between a surface quasi-geostrophic buoyancy filament and an internal vortex. We first revisit the stability of an isolated buoyancy filament. The buoyancy profile considered is continuous and leads to a continuous velocity field, albeit one with infinite shear just outside its edge. The stability properties of an isolated filament help to interpret the unsteady interaction with a sub-surface (internal) vortex studied next. We find that, in all cases, the filament breaks into billows, analogous in form to those occurring in Kelvin–Helmholtz shear instability. For intense buoyancy filaments, the vortex itself may undergo strong deformations, including being split into several pieces. Generally, the nonlinear interaction causes both the filament and the vortex to lose their respective “self”-energies to the energy of interaction. The flow evolution depends sensitively on whether the vertical vorticity of the filament and the vortex have the same or opposite signs – termed “cooperative” and “adverse” shear respectively. In cooperative shear, the filament rolls up into a coherent surface eddy above a vortex initially placed below it, whereas in adverse shear, buoyancy is expelled above the vortex. Although sufficiently great shear induced by the buoyancy filament may split the vortex in both cases, adverse shear is significantly more destructive.