Barotropic Model Research Articles

Dissipation and Bathymetric Sensitivities in an Unstructured Mesh Global Tidal Model

AbstractThe mechanisms and geographic distribution of global tidal dissipation in barotropic tidal models are examined using a high resolution unstructured mesh finite element model. Mesh resolution varies between 2 and 25 km and is especially focused on inner shelves and steep bathymetric gradients. Tidal response sensitivities to bathymetric changes are examined to put into context response sensitivities to frictional processes. We confirm that the Ronne Ice Shelf dramatically affects Atlantic tides but also find that bathymetry in the Hudson Bay system is a critical control. We follow a sequential frictional parameter optimization process and use TPXO9 data‐assimilated tidal elevations as a reference solution. From simulated velocities and depths, dissipation within the global model is estimated and allows us to pinpoint dissipation at high resolution. Boundary layer dissipation is extremely focused with 1.4% of the ocean accounting for 90% of the total. Internal tide friction is much more distributed with 16.7% of the ocean accounting for 90% of the total. Often highly regional dissipation can impact basin‐scale and even ocean wide tides. Optimized boundary layer friction parameters correlate very well with the physical characteristics of the locality with high friction factors associated with energetic tidal regions, deep ocean island chains, and ice covered areas. Global complex M2 tide errors are 1.94 cm in deep waters. Total global boundary layer and internal tide dissipation are estimated, respectively, at 1.83 and 1.49 TW. This continues the trend in the literature toward attributing more dissipation to internal tides.

Asymmetric Inner-Core Structure and its Impact on Rapid Intensification of a Sheared Tropical Cyclone

Based on ground-based Doppler radar data with high spatial and temporal resolution, our study focuses on rapid intensification (RI) of a sheared tropical cyclone (TC). The asymmetric inner-core structure and its impact on RI are presented using the Advanced Regional Prediction System-3DVAR. The time evolution of the TC inner-core characteristics shows that Meranti experiences two stages of RI: the asymmetric dominant period and the axisymmetric dominant period. The comparison between the two RI stages shows that the vortex intensified more in the asymmetric stage than the axisymmetric stage. The wavenumber-1 component introduced by the vertical wind shear dominates the asymmetric structure. In the moderate-to-strong shear environment, deep convection occurs mainly in the downshear-left quadrant, generating substantial diabatic heating in the downshear region. Under a suitable inner-core structure configuration, the downshear vortices are entrained cyclonically inward, resulting in RI. It is the interaction between the axisymmetric inner-core structure of the TC and the mesoscale vortex that controls the intensification process, which can be replicated by the nondivergent barotropic model with a similar initial field. This infrequent case provided observation of RI during a strong shear period, which suggests that the inner core structure is vital for TC RI.

The transition of tidal Kelvin waves to hybrid Kelvin edge and internal waves in the global ocean

In this study, we investigate the transition of semidiurnal Kelvin waves into Hybrid Kelvin-Edge (HKE) waves and associated generation of internal tides at widening shelves using theory, a realistic global baroclinic ocean model simulation, and quasi-realistic regional barotropic model simulations. Using the global model simulation, we identify several areas where a tidal HKE wave transition co-exists with internal wave generation. Of all areas considered, the Celtic Sea/Bay of Biscay shelf has the widest shelf and the strongest internal tide generation. We find that the global simulation agrees better with the theoretical Kelvin modes on the narrow than with the hybrid edge modes on the wide shelves. To help us understand the effect of complex, realistic bathymetry on the HKE wave transition, we perform quasi-realistic 1/25° barotropic simulations of the Celtic Sea/Bay of Biscay shelf areas. In these simulations, we gradually change the realistic bathymetry to a more idealized bathymetry. The idealized simulations show that the complex bathymetry steers the barotropic energy flux and causes standing wave patterns, which mask the HKE wave transition. Based on this analysis, we conclude that the HKE wave transition in the Celtic Sea/Bay of Biscay and other shelf areas in the global ocean is most likely masked by the effects of complex bathymetry and that offshelf baroclinic fluxes cannot be exclusively attributed to the HKE wave transition.

Lagrangian formulation and implications of barotropic fluid cosmologies

In this paper, we investigate the behavior of cosmologies in homogeneous and isotropic background with a barotropic fluid. We solve the continuity equation and study several aspects of model including behavior of cosmological quantities like Hubble parameter, deceleration parameter, equation of state parameter along with statefinder diagnostic and validity of energy conditions. The [Formula: see text] plane is checked for identification of thawing and freezing regions. We derive the Lagrangian formulation with standard and non-standard kinetic terms for barotropic fluid model. It is demonstrated that the model possesses periodic potential in its Lagrangian description with standard kinetic terms. Using dynamical system analysis, we find the stability of solutions, too. We further explore the thermodynamic aspects at apparent horizon by investigating the validity of generalized second law of thermodynamics with equilibrium description. The model exhibits complete cosmological scenario for different values of model parameters and the inflationary scenario decays smoothly into radiation-dominated phase during its evolution. The model approaches to [Formula: see text] cold dark matter model during late times of its evolution.

The Boreal Summer Zonal Wavenumber-3 Trend Pattern and Its Connection with Surface Enhanced Warming

Abstract The Northern Hemisphere warms faster under global warming and suffers from more frequent heatwaves, causing considerable social and economic damage. The Northern Hemisphere surface warming exhibits strong regionality, with multiple “hotspots” (areas of enhanced warming), but the relations among them remain unclear. This study finds a dominating zonal wavenumber-3 (ZW3) trend pattern in the upper-level geopotential heights during the boreal summer. The summer geopotential heights show significant increasing trends along the latitudinal circle around 60°N, with three centers located over northeastern America, western Eurasia, and eastern Siberia. The regionally enhanced surface warming trends are closely linked to the increased geopotential through the reduced cloud cover, exhibiting a consistent ZW3 pattern. The model simulations forced by sea surface temperature (SST) and Arctic sea ice cover (SIC) indicate that the SST forcing plays an important role in generating the ZW3 pattern, while the contribution of the SIC is minimal. A theoretical barotropic model can fairly well reproduce the observed ZW3 structure forced by a heating source located over the subtropical North Atlantic, where the SSTs show prominent warming trends and a close relationship with the ZW3 pattern. Our results indicate that the hotspots may be interconnected and are related to a Rossby wave train with a ZW3 structure. It highlights a vital role of tropical/subtropical SSTs on the atmospheric circulation and the associated surface enhanced warming over the mid- to high latitudes, which may have great implications for the coordinated heatwave events and tropical–extratropical teleconnections.

Variations in Amplitudes and Wave Energy along the Energy Dispersion Paths for Rossby Waves in the Quasigeostrophic Barotropic Model

Variations in Amplitudes and Wave Energy along the Energy Dispersion Paths for Rossby Waves in the Quasigeostrophic Barotropic Model

The Role of Random Vorticity Stretching in Tropical Depression Genesis

Abstract Tropical deep convection plays a key role in the tropical depression stage of tropical cyclogenesis by aggregating vorticity, but no existing theory can depict such a stochastic vorticity aggregation process. A vorticity probability distribution function (PDF) is proposed as a tool to predict the horizontal structure and wind speed of the tropical depression. The reason lies in the tendency for a vortex to adjust to an axisymmetric and monotonic vorticity structure. Assuming deep convection as independent and uniformly distributed vortex tube stretching events in the low–midtroposphere, repetitive vortex tube stretching will make the air column area shrink many times and significantly increase vorticity. A theory of the vorticity PDF is established by modeling the random stretching process as a Markov chain. The PDF turns out to be a weighted Poisson distribution, in good agreement with a randomly forced divergent barotropic model (weak temperature gradient model), and in rough agreement with a cloud-permitting simulation. The result shows that a stronger and sparser deep convective mode tends to produce more high-vorticity air columns, which leads to a more compact major vortex with a higher maximum wind. Based on the vorticity PDF theory, a parameterization of the eddy acceleration effect on the tangential flow is proposed.

A Lagrangian Tool for Simulating the Transport of Chemical Pollutants in the Arabian/Persian Gulf

A rapid-response Lagrangian model for the use in simulation of the transport of a chemical pollutant in the Arabian/Persian Gulf is described. The model is well suited to the provision of a fast response after an emergency due to an accident or a deliberate spill. It is easy to set up for any situation since only requires the modification of a few input files specifying the pollutant properties and release characteristics. Running times are short, even on a desktop PC, which makes it appropriate for a rapid assessment of a hypothetical accident occurring in the region. Baroclinic circulation was obtained from an HYCOM ocean model, and tides were calculated using a barotropic model. The interactions of pollutants with sediments (uptake/release processes) were described using a dynamic approach based on kinetic transfer coefficients and a stochastic numerical method. Some examples of model applications are shown, showing the influence of the geochemical behaviour of the pollutant in its distribution patterns.

Self-attraction and loading feedback on ocean dynamics in both shallow water equations and primitive equations

We introduce the effects of self-attraction and loading (SAL) to the momentum equations of a barotropic global ocean tide model as well as a baroclinic general circulation model. We show for the M2 tidal dynamics, that an explicit treatment of SAL is favourable compared to a scalar approximation or even disregarding the effects all together. For the general circulation the influence on the ocean bottom pressure is shown to be about 1 hPa for short time periods along the coasts and about 0.5 hPa for longer periods in resonant basins in the southern ocean. In contrast to previous studies, we additionally examine the effects of surface pressure anomalies over the continents in the computation of SAL which is shown to have an influence of about 0.5 hPa along the coasts. With those results, we demonstrate that the explicit treatment of SAL is important for satellite applications.

Numerical simulation of cavitating flow in maritime high-pressure direct fuel injection nozzles and assessment of cavitation-erosion damage

The internal flow of Heavy Fuel Oil (HFO) in two maritime direct fuel injector nozzles is studied by 3D flow simulations for the assessment of erosion-sensitive wall regions. The nozzle geometries differ in number, diameter and inclination angle of holes as well as sac wall curvature. Long-term endurance experiments reveal characteristic damage locations for both nozzles. Simulations are performed by a compressible density-based flow solver with a barotropic cavitation model to capture shock wave dynamics. Real geometries and the entire injection cycle with time-dependent rail pressure and transient needle movement are considered. A statistical evaluation of individual collapsing voids in terms of their condensation rate yield an erosion probability that is compared against experimental damage locations. Due to the scatter in the values of viscosity of real fuels a viscosity variation is carried out, which shows that while a lower viscosity leads to a rise of erosion probability, the location of erosion-sensitive wall zones is not significantly changed. The analysis of 3D velocity and void field evolutions motivates the introduction of distinct injection sub-phases of the entire cycle. Erosion probability is separately evaluated within each sub-phase. By this simulation procedure, experimentally found erosion spots are associated with particular sub-phases and can be traced back to characteristic flow and void structures that are linked to particular nozzle geometry features.

The Problem of Diagnosing Jet Waveguidability in the Presence of Large-Amplitude Eddies

AbstractThe waveguidability of an upper-tropospheric zonal jet quantifies its propensity to duct Rossby waves in the zonal direction. This property has played a central role in previous attempts to explain large wave amplitudes and the subsequent occurrence of extreme weather. In these studies, waveguidability was diagnosed with the help of ray tracing arguments using the zonal average of the observed flow as the relevant background state. Here, it is argued that this method is problematic both conceptually and mathematically. The issue is investigated in the framework of the nondivergent barotropic model. This model allows the straightforward computation of an alternative “zonalized” background state, which is obtained through conservative symmetrization of potential vorticity contours and that is argued to be superior to the zonal average. Using an idealized prototypical flow configuration with large-amplitude eddies, it is shown that the two different choices for the background state yield very different results; in particular, the zonal-mean background state diagnoses a zonal waveguide, while the zonalized background state does not. This result suggests that the existence of a waveguide in the zonal-mean background state is a consequence of, rather than a precondition for, large wave amplitudes, and it would mean that the direction of causality is opposite to the usual argument. The analysis is applied to two heatwave episodes from summer 2003 and 2010, yielding essentially the same result. It is concluded that previous arguments about the role of waveguidability for extreme weather need to be carefully reevaluated to prevent misinterpretation in the future.

A Barotropic Tide Model for Global Ocean Based on Rotated Spherical Longitude-Latitude Grids

Ocean modeling and simulation are important for understanding the dynamic processes in the geophysical system, and the simulation of tidal dynamics is of great significance for understanding the dynamic evolution of the ocean. However, there are some problems in existing simulations, including lack of specific standards to produce a desirable discrete spherical mesh for global ocean modelling. Many global ocean numerical models based on conventional longitude-latitude (LL) coordinates suffer from the “pole problem” in regions adjacent to the North Pole due to the convergence of meridians, which seriously hinders global ocean simulations. In this paper, a new longitude-latitude spherical grid coupled with rotated coordinate mapping is proposed to overcome the problem. In the design of the numerical model, for spatial approximation, the finite volume method on staggered C grid is proposed to solve the two-dimensional tidal wave equations for the global ocean. For temporal integration, the third-order Adams-Bashforth method is used to explicitly extrapolate the value on the next time interval half layer, and then the fourth-order implicit Adams-Moulton method is used to correct the water level. Finally, the constructed model is used to simulate the dynamics of two-dimensional tidal waves in the global ocean, and the co-tidal maps of two major diurnal tide and semidiurnal tide components are shown. The results demonstrate that the proposed model can support the simulation of tidal dynamics in the global ocean, especially for the Arctic Ocean.

Stability of [formula omitted]-dimensional gravastars with variable equation of state

In this paper, we are interested to explore stable configurations of d-dimensional gravastars constructed from the interior d-dimensional de Sitter and exterior d-dimensional Schwarzschild/Reissner–Nordström (de Sitter) black holes through cut and paste approach. We consider the linearized radial perturbation preserving the original symmetries to explore their stability by using three different types of matter distributions. The resulting frameworks represent unstable structures for barotropic, Chaplygin, and phantomlike models for every considered choice of exterior geometries. However, matter contents with variable equations of state have a remarkable role to maintain the stability of gravastars. We conclude that stable structures of gravastars are obtained only for generalized variable models with exterior d-dimensional Schwarzschild/Reissner–Nordström–de Sitter black holes.

Australian tidal currents – assessment of a barotropic model (COMPAS v1.3.0 rev6631) with an unstructured grid

Abstract. While the variations of tidal range are large and fairly well known across Australia (less than 1 m near Perth but more than 14 m in King Sound), the properties of the tidal currents are not. We describe a new regional model of Australian tides and assess it against a validation dataset comprising tidal height and velocity constituents at 615 tide gauge sites and 95 current meter sites. The model is a barotropic implementation of COMPAS, an unstructured-grid primitive-equation model that is forced at the open boundaries by TPXO9v1. The mean absolute error (MAE) of the modelled M2 height amplitude is 8.8 cm, or 12 % of the 73 cm mean observed amplitude. The MAE of phase (10∘), however, is significant, so the M2 mean magnitude of vector error (MMVE, 18.2 cm) is significantly greater. The root sum square over the eight major constituents is 26 % of the observed amplitude. We conclude that while the model has skill at height in all regions, there is definitely room for improvement (especially at some specific locations). For the M2 major axis velocity amplitude, the MAE across the 95 current meter sites, where the observed amplitude ranges from 0.1 to 156 cm s−1, is 6.9 cm s−1, or 22 % of the 31.7 cm s−1 observed mean. This nationwide average result is encouraging, but it conceals a very large regional variation. Relative errors of the tidal current amplitudes on the narrow shelves of New South Wales (NSW) and Western Australia exceed 100 %, but tidal currents are weak and negligible there compared to non-tidal currents, so the tidal errors are of little practical significance. Looking nationwide, we show that the model has predictive value for much of the 79 % of Australia's shelf seas where tides are a major component of the total velocity variability. In descending order this includes the Bass Strait, the Kimberley to Arnhem Land, and southern Great Barrier Reef regions. There is limited observational evidence to confirm that the model is also valuable for currents in other regions across northern Australia. We plan to commence publishing “unofficial” tidal current predictions for chosen regions in the near future based on both our COMPAS model and the validation dataset we have assembled.

Thermodynamically consistent modeling for complex fluids and mathematical analysis

The goal of this paper is to derive governing equations for complex fluids in a thermodynamically consistent way so that the conservation of energy and the increase of entropy is guaranteed. The model is a system of first-order partial differential equations on density, velocity, energy (or equivalently temperature), and conformation tensor. A barotropic model is also derived. In the one-dimensional case, we express the barotropic model in the form of hyperbolic balance laws, and show that it satisfies the stability condition. Consequently, the global existence of solutions around equilibrium states is proved and the convergence rates is obtained.

Numerical investigation of non-condensable gas effect on vapor bubble collapse

We numerically investigate the effect of non-condensable gas inside a vapor bubble on bubble dynamics, collapse pressure, and pressure impact of spherical and aspherical bubble collapses. Free gas inside a vapor bubble has a damping effect that can weaken the pressure wave and enhance the bubble rebound. To estimate this effect numerically, we derive and validate a multi-component model for vapor bubbles containing gas. For the cavitating liquid and the non-condensable gas, we employ a homogeneous mixture model with a coupled equation of state for all components. The cavitation model for the cavitating liquid is a barotropic thermodynamic equilibrium model. Compressibility of all phases is considered in order to capture the shock wave of the bubble collapse. After validating the model with an analytical energy partitioning model, simulations of collapsing wall-attached bubbles with different stand-off distances are performed. The effect of the non-condensable gas on rebound and damping of the emitted shock wave is well captured.

Roles of vertical distributions of atmospheric transient eddy dynamical forcing and diabatic heating in midlatitude unstable air\u2013sea interaction

Atmospheric transient eddy dynamical forcing (TEDF)-driven midlatitude unstable air–sea interaction has recently been recognized as a crucial positive feedback for the maintenance of the extratropical decadal variabilities. Our recent theoretical work (Chen et al., Clim Dyn https://doi.org/10.1007/s00382-020-05405-0, 2020) has characterized such an interaction through building an analytical midlatitude barotropic atmospheric model coupled to a simplified upper oceanic model. This study extends the analytical model to including a two-layer quasi-geostrophic baroclinic atmospheric model and then identifies the roles of vertical distributions of atmospheric TEDF and diabatic heating in midlatitude unstable air–sea interaction. It is found that midlatitude air–sea coupling with more realistic vertical profiles of atmospheric TEDF and diabatic heating destabilizes oceanic Rossby wave modes over the entire range of zonal wavelengths, in which the most unstable coupled mode features an equivalent barotropic atmospheric low (high) pressure over a cold (warm) oceanic surface. Spatial structure and period of the most unstable mode are more consistent with the observation than those from in previous model. Although either TEDF or diabatic heating alone can lead to a destabilized coupled mode, the former makes a dominant contribution to the instability. The increase of low-layer TEDF stimulates the instability more effectively if the TEDF in upper layer is larger than in lower layer, while the TEDF in either high or low layers can individually cause the instability. The surface heating always destabilizes the air–sea interaction, while the mid-level heating always decays the coupled mode. The results of this study further confirm the TEDF-driven positive feedback mechanism in midlatitude air–sea interaction proposed by recent observational and numerical experiment studies.

Interannual Variability of Stratospheric Final Warming in the Southern Hemisphere and Its Tropospheric Origin

AbstractThe relation between interannual variability of stratospheric final warming (SFW) and tropospheric circulation in the Southern Hemisphere (SH) is explored using reanalysis data and a linear barotropic model. The analysis is focused on quasi-stationary waves with zonal wavenumber 1 (s = 1 QSWs; s is zonal wavenumber), which are the dominant component of the SH extratropical planetary waves. First, interannual variability of SFW is investigated in terms of amplitudes of stratospheric and tropospheric s = 1 QSWs, and wave transmission properties of the mean flow from the late austral winter to spring. Upward Eliassen–Palm flux due to s = 1 QSWs is larger from the stratosphere down to the middle troposphere in early-SFW years than late-SFW years. More favorable conditions for propagation of s = 1 stationary waves into the stratosphere are identified in early-SFW years. These results indicate that the amplification of tropospheric s = 1 QSWs and the favorable conditions for their propagation into the stratosphere lead to the amplification of stratospheric s = 1 QSWs and hence earlier SFWs. Next, numerical calculations using a linear barotropic model are performed to explore how tropospheric s = 1 QSWs at high latitudes amplifies in early-SFW years. By using tropical Rossby wave source and horizontal winds in the reanalysis data as a source and background field, respectively, differences in s = 1 steady responses between early- and late-SFWs are examined at high latitudes. It is suggested that the larger amplitudes of tropospheric s = 1 QSWs in early-SFW years are attributed to differences in wave propagation characteristics associated with structure of the midlatitude jets in austral spring.

Optimisation of Parameters in a German Bight Circulation Model by 4DVAR Assimilation of Current and Water Level Observations

Uncertain parameters in a 3D barotropic circulation model of the German Bight are estimated with a variational optimisation approach. Surface current measurements from a high frequency (HF) radar are used in combination with acoustic Doppler current profiler (ADCP) and tide gauge observations as input for a 4DVAR assimilation scheme. The required cost function gradients are estimated using an adjoint model code. The focus of the study is on systematic errors of the model with the control vector including parameters of the bathymetry, bottom roughness, open boundary forcing, meteorological forcing as well as the turbulence model. The model uses the same bathymetry, open boundary forcing, and metereological forcing as the operational model run at the Federal Maritime and Hydrographic Agency (BSH). The baroclinic BSH model is used as a reference to put the performance of the optimised model into perspective. It is shown that the optimised model has better agreement with HF radar data and tide gauge observations both within the fortnight training period and the test period 1 month later. Current profile measurements taken at two platforms indicate that both models have comparable error magnitudes at those locations. The optimised model was also compared with independent drifter data. In this case, drifter simulations based on the BSH model and the respective operational drift model including some surface wave effects were used as a reference. Again, these comparison showed very similar results overall, with some larger errors of the tuned model in very shallow areas, where no observations were used for the tuning and surface wave effects, which are only explicitly considered in the BSH model, play a more important role. The tuned model seems to be slightly more dissipative than the BSH model with more energy entering through the western boundary and less energy leaving toward the north. It also became evident that the 4DVAR cost function minimisation process is complicated by momentum advection, which leads to non-differentiable dependencies of the model with respect to the control vector. It turned out that the omission of momentum advection in the adjoint code still leads to robust estimates of descent directions.

Near-Coast Tide Model Validation Using GNSS Unmanned Surface Vehicle (USV), a Case Study in the Pertuis Charentais (France)

Nowadays, uncertainties related to the determination of ocean tides remain a major issue for the exploitation of altimetry data in coastal areas. Using Sea Surface Height (SSH) observations from a new GNSS-based system mounted on an Unmanned Surface Vehicle (USV), we develop a crossover methodology to assess tide models under altimetry tracks. To this purpose, we address the Pertuis Charentais area, a semi enclosed sea located in the centre of the Bay of Biscay (France), as a field and modelling case study. We have developed a barotropic model configuration, based on SCHISM platform, using tidal elevations of an up-to-date regional atlas as boundary conditions. To test the impact of boundary conditions, we propose a second configuration where we applied uniform empirical biases in phases and amplitudes on M3 and MN4 constituents. In addition, the survey was designed to highlight the contribution of third and fourth-diurnal waves that are strongly amplified on the shelf and is used to assess model performances under the pass 216 of Sentinel-3A. Our results show that the second configuration reduces the Root-Mean-Square Error (RMSE) of the survey crossover residuals by more than 60%, leading to half of the residuals below 2.5 cm. This improved solution also reduces by 20% the RMSE computed with data from tide gauges located in the inner part of the Pertuis Charentais. Therefore, our study reinforces the importance for coastal tide modelling of an accurate tidal forcing, especially for shallow water waves. We finally discuss the impact of the remaining M4 error on crossover residual heights. By introducing an empirical correction term based on M4 observations at tide gauges, we further reduce the RMSE of crossover residuals by 15–25%. With this innovative study, we demonstrate the interest of combining crossover validation methods and USV systems to spatially extend our understanding of coastal areas dynamics. This will be crucial in the scope of the future SWOT mission, for which the tide correction accuracy must be assessed over the large-extent areas covered by swaths observations.