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In this study, the non-linear tide-surge interactions (NTSIs) over the eastern Canadian shelf (ECS) are examined numerically during two extreme weather events. A three-dimensional ocean circulation model for the ECS based on the Regional Ocean Modeling System (ROMS-ECS) is used. The model is driven by tides and atmospheric forcing in a barotropic mode by neglecting baroclinic effects on NTSIs in this study. The atmospheric forcing is based on the hourly atmospheric reanalysis known as ERA5 produced by the European Centre for Medium-Range Weather Forecasts. The performance of ROMS-ECS in simulating tides and storm surge is assessed using observed sea levels and previous numerical results over the ECS. Analyses of model results during Hurricanes Bill (2009) and Dorian (2019) demonstrate that relatively strong NTSIs occur over regions with strong tidal and wind-driven currents. The relatively intense NTSIs also modulate the magnitudes and timings of maximum storm surges as well as the amplitudes and phases of tides during the storm. In addition, the three-dimensional (3D) currents are modulated greatly by the NTSIs over the shelf break region. It is found that the non-linear friction and advection are the dominant factors in the NTSIs during the two storms. Relatively strong NTSIs also occur after the passage of the storm due to shelf waves generated by non-local storm winds. [ABSTRACT FROM AUTHOR]

Vertical axes of mesoscale eddies with the coherent structure were observed to tilt southwestward significantly from the sea surface to bottom in the South China Sea. The dynamic mechanism for vertical tilting of eddies, however, is not well understood. In this study, the influence of the planetary β-effect on the vertical structure of a coherent eddy is investigated based on analytical considerations and numerical results produced by the MIT general circulation model (MITgcm). Both the analytical and numerical results demonstrate that, during the westward propagation of a mesoscale eddy, the momentum advection and divergence in the inner region of the eddy impact the propagation direction of the eddy on a β-plane. In the upper layer of the mesoscale eddy, the eddy propagation is mainly controlled by the β-effect and nonlinear effect (momentum advection). In the lower layer of an anticyclonic eddy, the eddy propagation direction is dominated by the advection and divergence, which leads to the westward shift of the eddy center in the upper layer. For a cyclonic eddy, by comparison, the vertical axis tilts to eastward from surface to bottom. The tilting distance is up to 30 km in a flat bottom ocean with the β value of 2.15 × 10−11 m−1 s−1. In addition, model results indicate that vertical stratification, eddy strength, and rough topography have significant influences on the vertical structure of a mesoscale eddy. [ABSTRACT FROM AUTHOR]

Features of internal tides in the northern South China Sea are investigated using measurements of two moorings at 506 m (MR1) and 260 m (MR2) working between April and November of 2014. The diurnal internal tides at MR1 are significantly enhanced in June-July and display a regular fortnight modulation, whereas at shallower MR2, the June-July intensification is absent and the fortnight cycle becomes irregular. Fortnight cycle peaks of diurnal internal tides have a regular time-lag of ~ 2.8 days after those of diurnal barotropic tides (at MR1). We derive a mathematical relationship indicating that this time-lag of fortnight cycle peaks is around twice the time for the diurnal internal tides propagating from the generation place to the mooring site. Semidiurnal internal tides are dominated by the mode-1 (~ 70%), while diurnal internal tides exhibit multi-modal structures, with the contribution of ~ 20-30% for each of the first three modes. The diurnal mode-1 contribution varies fortnightly, and eddy passages are highly correlated with the increasing contribution of semidiurnal high modes (at MR1). Furthermore, we find that the nonlinear interaction between internal tides and near-inertial motions is weak in summer, even during periods of strong near-inertial motions (at MR2), because in summer, the shear of near-inertial currents is maximum at a depth shallower than the depth of maximum internal tide shear. [ABSTRACT FROM AUTHOR]

Thermocline bulk shear is investigated in the northern North Sea using historical observations. The conventional bulk shear is modified to define a thermocline bulk shear (TBS), in order to better represent the shear across the thermocline. The TBS computed by observed currents is decomposed into components at different frequency bands. The near-inertial TBS is the largest component. Its dominance is significant during the period of high wind. It is formed by the wind-driven near-inertial current which has a distinct phase shift (∼180°) across the thermocline. A linear model is presented, which well simulates the observed near-inertial TBS, especially during the period of relatively strong wind. The semidiurnal TBS makes a secondary contribution to the total TBS. It is only slightly smaller than the near-inertial TBS when the wind is relatively weak. The large values of semidiurnal TBS are associated with semidiurnal currents which have a phase shift (∼30-40°) or a magnitude difference (∼5 cm/s) across the thermocline. The low-frequency (<0.7 cpd) TBS also makes an episodic contribution to the total. Its variation coincides with the Ekman transport during the period of relatively strong wind. The low-frequency TBS is mainly formed by an Ekman-like clockwise spiraling of velocity with depth or a distinct magnitude difference in velocities between upper and lower layers. [ABSTRACT FROM AUTHOR]

A new relationship is presented to give a review study on the evolution of inertial oscillations in the surface ocean locally generated by time-varying wind stress. The inertial oscillation is expressed as the superposition of a previous oscillation and a newly generated oscillation, which depends upon the time-varying wind stress. This relationship is employed to investigate some idealized wind change events. For a wind series varying temporally with different rates, the induced inertial oscillation is dominated by the wind with the greatest variation. The resonant wind, which rotates anti-cyclonically at the local inertial frequency with time, produces maximal amplitude of inertial oscillations, which grows monotonically. For the wind rotating at non-inertial frequencies, the responses vary periodically, with wind injecting inertial energy when it is in phase with the currents, but removing inertial energy when it is out of phase. The wind rotating anti-cyclonically with time is much more favorable to generate inertial oscillations than the cyclonic rotating wind. The wind with a frequency closer to the inertial frequency generates stronger inertial oscillations. For a diurnal wind, the induced inertial oscillation is dependent on latitude and is most significant at 30 °. This relationship is also applied to examine idealized moving cyclones. The inertial oscillation is much stronger on the right-hand side of the cyclone path than on the left-hand side (in the northern hemisphere). This is due to the wind being anti-cyclonic with time on the right-hand side, but cyclonic on the other side. The inertial oscillation varies with the cyclone translation speed. The optimal translation speed generating the greatest inertial oscillations is 2 m/s at the latitude of 10 ° and gradually increases to 6 m/s at the latitude of 30 °. [ABSTRACT FROM AUTHOR]

A three-dimensional finite volume unstructured mesh model of the west coast of Britain, with high resolution in the coastal regions, is used to investigate the role of wind wave turbulence and wind and tide forced currents in producing maximum bed stress in the eastern Irish Sea. The spatial distribution of the maximum bed stress, which is important in sediment transport problems, is determined, together with how it is modified by the direction of wind forced currents, tide-surge interaction and a surface source of wind wave turbulence associated with wave breaking. Initial calculations show that to first order the distribution of maximum bed stress is determined by the tide. However, since maximum sediment transport occurs at times of episodic events, such as storm surges, their effects upon maximum bed stresses are examined for the case of strong northerly, southerly and westerly wind forcing. Calculations show that due to tide-surge interaction both the tidal distribution and the surge are modified by non-linear effects. Consequently, the magnitude and spatial distribution of maximum bed stress during major wind events depends upon wind direction. In addition calculations show that a surface source of turbulence due to wind wave breaking in shallow water can influence the maximum bed stress. In turn, this influences the wind forced flow and hence the movement of suspended sediment. Calculations of the spatial variability of maximum bed stress indicate the level of measurements required for model validation. [ABSTRACT FROM AUTHOR]

An unstructured mesh tidal model of the west coast of Britain, covering the Celtic Sea and Irish Sea is used to compare tidal distributions computed with finite element (FE) and finite volume (FV) models. Both models cover an identical region, use the same mesh, and have topography and tidal boundary forcing from a finite difference model that can reproduce the tides in the region. By this means, solutions from both models can be compared without any bias towards one model or another. Two-dimensional calculations show that for a given friction coefficient, there is more damping in the FV model than the FE model. As bottom friction coefficient is reduced, the two models show comparable changes in tidal distributions. In terms of mesh resolution, calculations show that for the M tide, the mesh is sufficiently fine to yield an accurate solution over the whole domain. However, in terms of higher harmonics of the tide, in particular the M component, its small-scale variability in near-shore regions which is comparable to the mesh of the model, suggests that the mesh resolution is insufficient in the near-coastal regions. Even with a finer mesh in these areas, without detailed bottom topography and a spatial varying friction depending on bed types and bed forms, which is not available, model skill would probably not be improved. In addition in the near-shore region, as shown in the literature, the solution is sensitive to the form of the wetting/drying algorithm used in the model. Calculations with a 3D version of the FV model show that for a given value of k, damping is reduced compared to the 2D version due to the differences in bed stress formulation, with the 3D model yielding an accurate tidal distribution over the region. [ABSTRACT FROM AUTHOR]

A non-hydrostatic model in cross-sectional form with an idealized sill is used to examine the influence of sill depth ( h) and aspect ratio upon internal motion. The model is forced with a barotropic tide and internal waves and mixing occurs at the sill. Calculations using a wide sill and quantifying the response using power spectra show that for a given tidal forcing namely Froude number F as the sill depth ( h) increases the lee wave response and vertical mixing decrease. This is because of a reduction in across sill velocity U due to increased depth. Calculations show that the sill Froude number F based on sill depth and across sill velocity is one parameter that controls the response at the sill. At low F (namely F ≪ 1) in the wide sill case, there is little lee wave production, and the response is in terms of internal tides. At high F, calculations with a narrow sill show that for a given F value, the lee wave response and internal mixing increase with increasing aspect ratio. Calculations using a narrow sill with constant U show that for small values of h, a near surface mixed layer can occur on the downstream side of the sill. For large values of h, a thick well-mixed bottom boundary layer occurs due to turbulence produced by the lee waves at the seabed. For intermediate values of h, 'internal mixing' dominates the solution and controls across thermocline mixing. [ABSTRACT FROM AUTHOR]

n unstructured mesh model of the west coast of Britain, covering the same domain and using topography and open boundary forcing that are identical to a previous validated uniform grid finite difference model of the region, is used to compare the performance of a finite volume (FV) and a finite element (FE) model of the area in determining tide-surge interaction in the region. Initial calculations show that although qualitatively both models give comparable tidal solutions in the region, comparison with observations shows that the FV model tends to under-estimate tidal amplitudes and hence background tidal friction in the eastern Irish Sea. Storm surge elevations in the eastern Irish Sea due to westerly, northerly and southerly uniform wind stresses computed with the FV model tend to be slightly higher than those computed with the FE model, due to differences in background tidal friction. However, both models showed comparable non-linear tide-surge interaction effects for all wind directions, suggesting that they can reproduce the extensive tide-surge interaction processes that occur in the eastern Irish Sea. Following on from this model comparison study, the physical processes contributing to surge generation and tide-surge interaction in the region are examined. Calculations are performed with uniform wind stresses from a range of directions, and the balance of various terms in the hydrodynamic equations is examined. A detailed comparison of the spatial variability of time series of non-linear bottom friction and non-linear momentum advection terms at six adjacent nodes at two locations in water depths of 20 and 6 m showed some spatial variability from one node to another. This suggests that even in the near coastal region, where water depths are of the order of 6 m and the mesh is fine (of order 0.5 km), there is significant spatial variability in the non-linear terms. In addition, distributions of maximum bed stress due to tides and wind forcing in nearshore regions show appreciable spatial variability. This suggests that intensive measurement campaigns and very high-resolution mesh models are required to validate and reproduce the non-linear processes that occur in these regions and to predict extreme bed stresses that can give rise to sediment movement. High-resolution meshes will also be required in pollution transport problems. [ABSTRACT FROM AUTHOR]

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