Barotropic Model Research Articles

Simultaneous Estimation of Ocean Tides and Underwater Topography in the Weddell Sea

AbstractA new model for the M2, S2, K1, and O1 tides in the Weddell Sea is developed by assimilating CryoSat‐2 data into a barotropic tide model. A variational approach is used, which explicitly allows for errors in the water depth, that is, the bottom topography in open water and the water column thickness under floating ice shelves, so that an optimized estimate of the topography is obtained together with the tidal fields. In preparation for assimilation, the sensitivity of the tidal elevation to the interfacial drag at the sea floor and the ice‐water interface (under the floating ice shelves) is investigated; this motivates the development of a new drag parameterization which is more accurate and physically plausible in comparison with the interfacial drag alone. The assimilation of CryoSat‐2 data into the model results in tidal elevations with essentially the same accuracy as previous estimates, which is demonstrated by comparisons with independent in situ data and withheld CryoSat‐2 data. The novelty of the present tidal estimates is that they are consistent with well‐defined dynamics based on the Laplace Tidal Equations—augmented with the new parameterization of drag—and modifications of the prior estimate of underwater topography and water column thickness. Analysis of the sensitivity to the topography finds that, at this level of precision, the topography is not uniquely determined by the observed data.

Relaxation and simulation of a barotropic three-phase flow model

We focus here on a three-phase flow model in order to represent complex flows involving liquid metal droplets, liquid water, and its vapour. The governing equations and its main properties are given, and focus is given on the pressure–velocity relaxation process on the one hand, and on the structure of solutions of the one-dimensional Riemann problem associated with pure convective effects. A fractional step method that computes successively the convective part and the relaxation effects is used to obtain approximate solutions on unstructured meshes. Details of algorithms are provided, and it is shown that the numerical method preserves positive values of statistical fractions and partial masses. Verification and validation test cases are presented, and some perspectives are eventually drawn.

Forced summer stationary waves: the opposing effects of direct radiative forcing and sea surface warming

We investigate the opposing effects of direct radiative forcing and sea surface warming on the atmospheric circulation using a hierarchy of models. In large ensembles of three general circulation models, direct hbox {CO}_2 forcing produces a wavenumber 5 stationary wave over the Northern Hemisphere in summer. Sea surface warming produces a similar wave, but with the opposite sign. The waves are also present in the Coupled Model Intercomparison Project phase 5 ensemble with opposite signs due to direct hbox {CO}_2 and sea surface warming. Analyses of tropical precipitation changes and equivalent potential temperature changes and the results from a simple barotropic model show that the wave is forced from the tropics. Key forcing locations are the Western Atlantic, Eastern Atlantic and in the Indian Ocean just off the east coast of Africa. The stationary wave has a significant impact on regional temperature anomalies in the Northern Hemisphere summer, explaining some of the direct effect that hbox {CO}_2 concentration has on temperature extremes. Ultimately, the climate sensitivity and future changes in the land–sea temperature contrast will dictate the balance between the opposing effects on regional changes in mean and extreme temperature and precipitation under climate change.

Individual and Combined Impacts of Two Eurasian Wave Trains on Intraseasonal East Asian Winter Monsoon Variability

AbstractThe present study investigates the intraseasonal wind variations over East Asia during boreal winter. It is shown that the wind variations less than 30 days are the main component of total intraseasonal signal. The intraseasonal variations in this time period are associated with two distinctive wave trains over Eurasia starting from the North Atlantic Ocean. One wave train propagates along the polar front jet eastward over Europe and Siberia and then southeastward after passing the Lake Baikal. The other wave train propagates along the subtropical jet southeastward through the Mediterranean region and the Arabian Peninsula to north India and then eastward to southern China. The East Asian wind and temperature anomalies are determined by the combination of the two wave trains. An anomalous cyclone forms over East Asia with large extent and intensity when the two wave trains work coherently, resulting in strong lower‐level northerly wind anomalies with a large meridional extent. More cold air is transported southward from high latitudes by anomalous northerly winds, causing widespread and large temperature decrease in East Asia. When only a single wave train exists, lower‐level wind and temperature anomalies are reduced. When there is a destructive interference of the two wave trains, the lower‐level wind and temperature anomalies are weak in East Asia. Observational analyses and barotropic model experiments indicate that the formation of the two wave trains may be related to the combination of disturbances at different locations over the North Atlantic Ocean.

3D flow simulation of a circular leading edge hydrofoil and assessment of cavitation erosion by the statistical evaluation of void collapses and cavitation structures

A simplified test case of a centrifugal pump blade, a hydrofoil with circular leading edge, is investigated. Cloud cavitation as a particularly aggressive type of cavitation is studied using a compressible 3D flow solver with barotropic cavitation model. The results are compared to measurement data for different Reynolds and cavitation numbers. The shedding frequency is well predicted. A statistical evaluation of a multitude of single collapsing voids is performed. Collapse frequency and magnitude of the pressure peaks are evaluated to obtain wall load collectives. Material damage on the hydrofoil suction surface obtained in erosion measurements is compared to the local flow aggressiveness distribution in the simulation. Erosion sensitive wall zones are identified in good agreement with measurement data. A relationship between cloud cavitation structures and erosion sensitive wall zones is demonstrated that enables a simple and approximate erosion assessment by 3D flow simulation.

Barotropic Instability across the Moat and Inner Eyewall Dissipation: A Numerical Study of Hurricane Wilma (2005)

Abstract Radar imagery of some double-eyewall tropical cyclones shows that the inner eyewalls become elliptical prior to their dissipation. These elliptical features indicate that the barotropic instability (BI) across the moat (aka, type-2 BI) may play a role in the process. To investigate the mechanism for dissipation, a WRF simulation of Hurricane Wilma (2005) is performed. The results reveal an elliptical elongation of the inner eyewall and a change in the structure of the radial flow from wavenumber (WN) 1 to WN 2 at the lower levels. A linear stability analysis as well as idealized nonlinear experiments using a nondivergent barotropic vorticity model initialized with the vorticity fields before the change in the dominant wavenumber of the radial flow are presented with the results supporting the presence of a type-2 BI at the lower levels. The accompanying WN-2 radial flow is also found to dilute the vorticity within the inner eyewall and the eye. However, this dilution is not seen at higher levels as the type-2 BI becomes weak and short lived at the middle levels and reaches its weakest strength at the upper levels. This phenomenon is traced to the fact that a higher growth rate comes with a narrower moat for type-2 BI. As the outward slope of the outer eyewall is larger than that of the inner eyewall, the moat width increases with height so that the growth rate decreases with height. The results presented here thus highlight the potential role played by the barotropic instability across the moat in inner eyewall dissipation.

Cavitation induction by projectile impacting on a water jet

The present paper focuses on the simulation of the high-velocity impact of a projectile impacting on a water-jet, causing the onset, development and collapse of cavitation. The simulation of the fluid motion is carried out using an explicit, compressible, density-based solver developed by the authors using the OpenFOAM library. It employs a barotropic two-phase flow model that simulates the phase-change due to cavitation and considers the co-existence of non-condensable and immiscible air. The projectile is considered to be rigid while its motion through the computational domain is modelled through a direct-forcing Immersed Boundary Method. Model validation is performed against the experiments of Field et al. (2012), who visualised cavity formation and shock propagation in liquid impacts at high velocities. Simulations unveil the shock structures and capture the high-speed jetting forming at the impact location, in addition to the subsequent cavitation induction and vapour formation due to refraction waves. Moreover, model predictions provide quantitative information and a better insight on the flow physics that has not been identified from the reported experimental data, such as shock-wave propagation, vapour formation quantity and induced pressures. Furthermore, evidence of the Richtmyer–Meshkov instability developing on the liquid–air interface are predicted when sufficient dense grid resolution is utilised.

Rare Event Algorithm Links Transitions in Turbulent Flows with Activated Nucleations.

Many turbulent flows undergo drastic and abrupt configuration changes with huge impacts. As a paradigmatic example we study the multistability of jet dynamics in a barotropic beta plane model of atmosphere dynamics. It is considered as the Ising model for Jupiter troposphere dynamics. Using the adaptive multilevel splitting, a rare event algorithm, we are able to get a very large statistics of transition paths, the extremely rare transitions from one state of the system to another. This new approach opens the way for addressing a set of questions that are out of reach through direct numerical simulations. We demonstrate for the first time the concentration of transition paths close to instantons, in a numerical simulation of genuine turbulent flows. We show that the transition is a noise-activated nucleation of vorticity bands. We address for the first time the existence of Arrhenius laws in turbulent flows. The methodology we developed shall prove useful to study many other transitions related to drastic changes for the turbulent dynamics of climate, geophysical, astrophysical, and engineering applications. This opens a new range of studies impossible so far, and bring turbulent phenomena in the realm of nonequilibrium statistical mechanics.

Tidal wave propagation along The Mekong deltaic coast

A two-dimensional, barotropic numerical model was employed to investigate the dynamics of tidal wave propagation in the South China Sea with a particular interest for its characteristics along the Mekong deltaic coast. The study indicates that tidal waves propagate from the Pacific Ocean into the South China Sea mainly through the Luzon Strait (LS), where the K1 diurnal tide dominates due to a quarter wavelength resonance in this semi-enclosed basin, and that the incoming tidal waves from the Celebes open boundary play a more important role than those from the Andaman and Flores open boundaries. Previous studies have not explained why both adjacent seas including the South China Sea and the Gulf of Thailand are dominated by a diurnal tide, while a semidiurnal tide dominates along the eastern Mekong deltaic coast. By means of Green's law, continental shelf tidal resonance theory and standing wave theory, this study clarifies that the large amplified M2 semidiurnal amplitude leading to a prevailing mixed semidiurnal tide is caused not only by the shoaling effect and the continental shelf oscillation resonance phenomenon but also by the position on the standing wave anti-node line. Moreover, the finding of radial tidal currents occurring along the southern Mekong estuarine coast has not been revealed in earlier studies. Based on a number of numerical, geometrically schematised experiments, we suggest that the interaction between the large amplified amplitude near the shoreline associated with the adjacent low amplitude band system, causing convex hydraulic gradients of tidal amplitude due to basin geometry as well as sloping topography, is the mechanism for developing these radial tidal current systems. The results reveal that wind monsoon climate could cause either damped or amplified tidal amplitudes around the Mekong deltaic coast of which approximately 2–3 cm is due to the changing atmospheric pressure, the tangential stress of wind over the water surface and wind enhanced bottom friction. Also, this study suggests that the tidal generating forces should be considered to achieve accurate model results depending on the geographical region of interest. Findings achieved from this study contribute to a deeper insight of tidal wave propagation from a deep ocean to a shallow flat basin similar to the South China Sea and its Mekong deltaic coast.

The wind-driven formation of cross-shelf sediment plumes in a large lake.

Wind-driven turbidity plumes frequently occur in the western arm of Lake Superior and may represent a significant cross shelf transport mechanism for sediment, nutrient and biota. Here we characterize a plume that formed in late April 2016 using observations from in situ sensors and remote sensing imagery, and estimate the volume of cross shelf transport using both the observations and an idealized analytical model of plume formation. The steady-state, barotropic model is used to determine a relationship between the intensity and duration of a wind event and the volume of water transported from nearshore to offshore during the event. The model transport is the result of nearshore flow in the direction of the wind and a pressure-gradient-driven counter flow in the deeper offshore waters, consistent with observations. The volume of offshore transport associated with the 2016 plume is estimated by both methods to have been on the order of 1010 m3. Analysis of similar events from 2008-2016 shows a strong relationship between specific wind impulse and plume volume. Differences in the intensity and duration of individual events as well as ice cover, which prevents plume formation, lead to interannual variability of offshore transport ranging over an order of magnitude and illustrates how wind-driven processes may contribute to interannual variability of ecosystem functioning.

Model-independent constraints on dark energy evolution from low-redshift observations

Knowing the late time evolution of the Universe and finding out the causes for this evolution are the important challenges of modern cosmology. In this work, we adopt a model-independent cosmographic approach and approximate the Hubble parameter considering the Pade approximation which works better than the standard Taylor series approximation for $z>1$. With this, we constrain the late time evolution of the Universe considering low-redshift observations coming from SNIa, BAO, $H(z)$, $H_{0}$ , strong-lensing time-delay as well as the Megamaser observations for angular diameter distances. We confirm the tensions with $\Lambda$CDM model for low-redshifts observations. The present value of the equation of state for the dark energy has to be phantom-like and for other redshifts, it has to be either phantom or should have a phantom crossing. For lower values of $\Omega_{m0}$, multiple phantom crossings are expected. This poses serious challenges for single, non-interacting scalar field models for dark energy. We derive constraints on the {\it statefinders} $(r,s)$ and these constraints show that a single dark energy model cannot fit data for the whole redshift range $0\leq z\leq 2$: in other words, we need multiple dark energy behaviors for different redshift ranges. Moreover, the constraint on sound speed for the total fluid of the Universe, and for the dark energy fluid (assuming them being barotropic), rules out the possibility of a barotropic fluid model for unified dark sector and barotropic fluid model for dark energy, as fluctuations in these fluids are unstable as $c_{s}^2 < 0$ due to constraints from low-redshift observations.

Seafloor Crustal Deformation on Ocean Bottom Pressure Records With Nontidal Variability Corrections: Application to Hikurangi Margin, New Zealand

AbstractOcean bottom pressure (OBP) observations are a powerful tool for determining vertical crustal displacements, especially due to earthquakes and slow earthquakes, with centimeter‐level resolution. In these studies, removal of oceanographic noise (tens of centimeters) is required to identify centimeter‐level crustal deformation. We undertake barotropic modeling to remove oceanographic signals from data from an OBP array deployed offshore New Zealand in 2014/2015. We show that removing the nontidal component calculated from a barotropic ocean model reduces the variance in the data by about 66% and provides a feasible means to resolve pressure changes due to crustal deformation during the slow slip events. We also discuss the vertical displacements from slow slip events that occurred in late September to mid‐October 2014, and we outline our procedure for processing OBP data.

Local Finite-Amplitude Wave Activity as a Diagnostic for Rossby Wave Packets

AbstractUpper-tropospheric Rossby wave packets (RWPs) are important dynamical features, because they are often associated with weather systems and sometimes act as precursors to high-impact weather. The present work introduces a novel diagnostic to identify RWPs and to quantify their amplitude. It is based on the local finite-amplitude wave activity (LWA) of Huang and Nakamura, which is generalized to the primitive equations in isentropic coordinates. The new diagnostic is applied to a specific episode containing large-amplitude RWPs and compared with a more traditional diagnostic based on the envelope of the meridional wind. In this case, LWA provides a more coherent picture of the RWPs and their zonal propagation. This difference in performance is demonstrated more explicitly in the framework of an idealized barotropic model simulation, where LWA is able to follow an RWP into its fully nonlinear stage, including cutoff formation and wave breaking, while the envelope diagnostic yields reduced amplitudes in such situations.

Review article: Comparison of local particle filters and new implementations

Abstract. Particle filtering is a generic weighted ensemble data assimilation method based on sequential importance sampling, suited for nonlinear and non-Gaussian filtering problems. Unless the number of ensemble members scales exponentially with the problem size, particle filter (PF) algorithms experience weight degeneracy. This phenomenon is a manifestation of the curse of dimensionality that prevents the use of PF methods for high-dimensional data assimilation. The use of local analyses to counteract the curse of dimensionality was suggested early in the development of PF algorithms. However, implementing localisation in the PF is a challenge, because there is no simple and yet consistent way of gluing together locally updated particles across domains. In this article, we review the ideas related to localisation and the PF in the geosciences. We introduce a generic and theoretical classification of local particle filter (LPF) algorithms, with an emphasis on the advantages and drawbacks of each category. Alongside the classification, we suggest practical solutions to the difficulties of local particle filtering, which lead to new implementations and improvements in the design of LPF algorithms. The LPF algorithms are systematically tested and compared using twin experiments with the one-dimensional Lorenz 40-variables model and with a two-dimensional barotropic vorticity model. The results illustrate the advantages of using the optimal transport theory to design the local analysis. With reasonable ensemble sizes, the best LPF algorithms yield data assimilation scores comparable to those of typical ensemble Kalman filter algorithms, even for a mildly nonlinear system.

Baroclinic Effect on Modeling Deep Flow in Brown Passage, BC, Canada

Brown Passage is a deep (up to 200 m) ocean channel connecting the western offshore waters of Hecate Strait and Dixon Entrance on the Pacific continental shelf with the eastern inland waters of Chatham Sound in Northern British Columbia, Canada. A high-resolution 3D finite difference hydrodynamic model, COastal CIRculation and SEDiment transport Model (COCIRM-SED), was developed in 2010 and 2013 to determine the tidal and wind-driven currents of this area. The barotropic model results for ocean currents were found to be in reasonably good agreement with the historical ocean current observations at near-surface and middle depth available for Brown Passage. Operated from October 2014 to April 2015, the first modern oceanographic measurement program in Brown Passage found surprisingly strong near-bottom currents (the 99th percentile current speed reaches 53 cm/s at 196 m). As a result, the COCIRM-SED model was modified and rerun, with the most important change incorporating water density/salinity fields as modeled variables. This change led to considerable improvements in the ability of the model to generate episodes of relatively strong currents in the bottom layers. The bottom intensification in ocean currents in Brown Passage is shown to be due to semi-diurnal internal tides, which were not previously included in the barotropic version of the 3D model. This finding for the near-bottom flow from the qualitative modeling study is important for applications of the potential sediment deposition and resuspension studies.

The dynamics of weather-band sea level variations in the Red Sea

The variations of sea level over the Red Sea may be divided into three broad categories: tidal, seasonal and weather-band. Our study employs a variety of in situ and satellite-derived data in the first comprehensive examination of the Red Sea water level variations in the weather-band (covering periods of ∼ 4–30 days). In the central Red Sea, the range of the weather-band sea level signal is of order 0.7 m, which exceeds the tidal and seasonal sea level ranges. From EOF and correlation analysis, we find that a large fraction of the weather-band sea level variation is due to a single mode of motion that extends over the entire Red Sea. In this mode, the water level rises and falls in unison with an amplitude that declines going southward over the southern Red Sea. The temporal signal of this mode is highly correlated with the along-axis surface wind stress over the southern Red Sea, and is closely reproduced by a simple one-dimensional barotropic model with forcing by the along-axis wind stress. Although this model does not account for the full suite of dynamics affecting weather-band sea level variations in the Red Sea, it may serve as a useful predictive tool. Sea level changes associated with the development and movement of sub-mesoscale features (e.g., eddies and boundary currents) are also shown to contribute to weather-band sea level motions in the Red Sea.

Models of rotating coronae

Fitting equilibrium dynamical models to observational data is an essential step in understanding the structure of the gaseous hot haloes that surround our own and other galaxies. However, the two main categories of models that are used in the literature are poorly suited for this task: (i) simple barotropic models are analytic and can therefore be adjusted to match the observations, but are clearly unrealistic because the rotational velocity $v_\phi(R,z)$ does not depend on the distance $z$ from the galactic plane, while (ii) models obtained as a result of cosmological galaxy formation simulations are more realistic, but are impractical to fit to observations due to high computational cost. Here we bridge this gap by presenting a general method to construct axisymmetric baroclinic equilibrium models of rotating galactic coronae in arbitrary external potentials. We consider in particular a family of models whose equipressure surfaces in the $(R,z)$ plane are ellipses of varying axis ratio. These models are defined by two one-dimensional functions, the axial ratio of pressure $q_{\rm axis}(z)$ and the value of the pressure $P_{\rm axis}(z)$ along the galaxy's symmetry axis. These models can have a rotation speed $v_\phi(R,z)$ that realistically decreases as one moves away from the galactic plane, and can reproduce the angular momentum distribution found in cosmological simulations. The models are computationally cheap to construct and can thus be used in fitting algorithms. We provide a python code that given $q_{\rm axis}(z)$, $P_{\rm axis}(z)$ and $\Phi(R,z)$ returns $\rho(R,z)$, $T(R,z)$, $P(R,z)$, $v_\phi(R,z)$. We show a few examples of these models using the Milky Way as a case study.

Inter‐annual variation of the spring haze pollution over the North China Plain: Roles of atmospheric circulation and sea surface temperature

Haze pollution is a serious air quality issue in China. Previous studies over the North China Plain (NCP) mainly focused on analysing the haze during boreal winter. However, the variation in haze during spring and the related factors remain unclear. This study investigates inter‐annual variation of the spring haze, which is represented by the humidity‐corrected dry extinction coefficient (DEC) over the NCP. During high DEC years, pronounced positive DEC anomalies appear over the NCP and its surrounding regions. Correspondingly, a notable anticyclonic anomaly is observed over Northeast Asia, inducing significant southeasterly wind anomalies over the NCP. The anomalous southeasterly winds reduce wind speed and increase relative humidity, which provides favourable meteorological conditions for accumulation and growth of aerosol pollutants. Further analysis shows that the North Atlantic Oscillation (NAO) contributes to the formation of anticyclonic anomalies over Northeast Asia via downstream propagating atmospheric wave trains. Additionally, positive sea surface temperature (SST) anomalies over the subtropical northeastern Atlantic Ocean may also impact the DEC variation. The linear barotropic model experiment further confirms the important role of subtropical northeastern Atlantic SST anomalies in contributing to the anomalous anticyclone over Northeast Asia and southerly wind anomalies over the NCP region, which are triggered via eastwards propagating atmospheric wave trains. This study gives support to the idea that the NAO and the North Atlantic SST may be potential predictors for the frequently observed springtime NCP haze variation.

Tidal Current Circulation in Westhern Bali Sea Using a 2-D Hydrodynamic Model

The circulation of tidal currents in the northern part of the Bali Sea was created using two main steps, namely a large model simulation and a small model simulation. The first step, a large model simulation detailing the circulation of tidal currents in the Bali Strait, uses a 2D barotropic hydrodynamic model that utilizes tidal-generating forces and Gebco bathymetry data with a 30-second resolution. In this large model simulation, tidal heights are procured which are then used as data for the small model. The second step, a small model circulation which focuses on the northern part of the Bali Sea, uses a 2D barotropic hydrodynamic model and utilizes tidal-generating forces from the large model and BIG (Geospatial Information Agency) bathymetry data with a 50-meter resolution. This smaller resolution is used to observe the effects of the cape in the northern Bali Sea. The tidal simulation is done for 29 days (May 2016) with inputted data in the form of bathymetry and tidal data at four points with open boundary conditions. The results of the tidal simulation indicate that tidal currents follow the phase of the tides. During high tides, the tidal currents move North and during low tides, the currents move South. Meanwhile, for the area around the Gondol Cape in Northern Bali, an eastward-westward current is observed.

A Barotropic Mechanism for the Response of Jet Stream Variability to Arctic Amplification and Sea Ice Loss

Previous studies have found that the most consistent response of the eddy-driven jet to sea ice loss and Arctic amplification in fully coupled general circulation models (GCMs) is a broad region of anomalous easterlies on the poleward flank. In this study, a similar response is noted in a dry dynamical core GCM with imposed surface heating at the pole, and it is shown that in both a fully coupled GCM’s North Atlantic basin and the dry dynamical core, the anomalous easterlies cause an asymmetrical narrowing of the jet on the poleward flank of the climatological jet. A suite of barotropic model simulations run with polar forcing shows decreased jet positional variability consistent with a narrowing of the jet profile, and it is proposed that this narrowing decreases the distance Rossby waves can propagate away from the jet core, which drives changes in jet variability. Since Rossby wave propagation and dissipation is intrinsic to the development and maintenance of the eddy-driven jet, and is tightly coupled to a jet’s variability, this acts as a meridional constraint on waves’ ability to propagate outside of the jet core, leading to the decreased variability in zonal-mean jet position. The results from all three models demonstrates that this relationship is present across a model hierarchy.