Hydrodynamic Framework Research Articles

An Improved Direct Forcing Immersed Boundary Method With Integrated Mooring Algorithm for Floating Offshore Wind Turbines

Abstract An upgraded direct forcing immersed boundary method is implemented in the open-source hydrodynamic framework REEF3D::CFD for simulating the six-degrees-of-freedom (6DOF) motions of a floating offshore wind turbine (FOWT) based on the OC5 semi-submersible design. The direct forcing method is enhanced with a new density interpolation method across the fluid-structure interface that removes unphysical spurious phenomena and ensures stable and accurate wave load calculations on floating objects. A quasi-static algorithm is used for modeling the mooring system of the OC5 platform and restraining its motions in waves. The Navier-Stokes equations are solved on a staggered structured rectilinear grid for the hydrodynamic simulations. The level-set method is used to capture the free surface of the ocean waves. A ray-casting algorithm is employed to get inside-outside information near the fluid-solid interface while maintaining the underlying Cartesian grid in the hydrodynamic domain. The performance and accuracy of the mooring algorithm are compared to the widely-used mooring model MoorDyn, which is coupled to the hydrodynamic solver in REEF3D::CFD. The study demonstrates that the enhanced direct forcing method with the integrated quasi-static mooring algorithm in REEF3D::CFD provides a robust and accurate tool, suitable for the numerical analysis of the state-of-the-art FOWT in ocean waves.

Geological and hydrological controls on the pressure regime of coalbed methane reservoir in the Yanchuannan field: Implications for deep coalbed methane exploitation in the eastern Ordos Basin, China

The pressure regimes of the No. 2 coalbed methane (CBM) reservoir in the Yanchuannan field located in the southeastern Ordos Basin are highly variable and divided into overpressured (pressure gradient >9.80 kPa/m), slightly underpressured (pressure gradient of 8–9.80 kPa/m), and moderately underpressured (pressure gradient of 5–8 kPa/m). The controlling factors for the variable pressure regimes were investigated through the analysis of geological and hydrological characteristics. The pressure regimes are controlled by different mechanisms in different hydrodynamic environments. In the closed hydrodynamic environment characterized by TDS > 10,000 mg/L and NaCl type of groundwater, the pressure regime is dominated by overpressured to slightly underpressured and is controlled by CBM migration. Overpressure was developed by thermogenic CBM generation during the coalification process and is maintained by thermogenic CBM migration from the extended northwestward and deeply buried CBM reservoir during tectonic uplift. The transition from overpressure to slight underpressure and then to moderate underpressure towards the southeast is the result of the progressively weakened migrated thermogenic CBM with increasing migration distance. In the open hydrodynamic environment characterized by TDS < 10,000 mg/L and NaHCO3 type of groundwater, the pressure regime is dominated by slightly to moderately underpressured and is governed by hydrodynamics. Groundwater is fed by meteoric recharge along the structurally upturned basin margin and creates the hydrodynamic framework during tectonic uplift. The transition from moderate to slight underpressure towards the southwest is associated with the minor decrease range in ground elevation from basin margin to basin interior and the gradually weakened runoff intensity of groundwater with increasing distance to meteoric recharge. The idealized models for the pressure regimes are established, which can provide guidance to deep CBM sweet spot identification in CBM fields in the eastern Ordos Basin and elsewhere.

Hydrodynamization and resummed viscous hydrodynamics

In this paper, I review our current understanding of the applicability of hydrodynamics to modeling the quark–gluon plasma (QGP), focusing on the question of hydrodynamization/thermalization of the QGP and the anisotropic hydrodynamics (aHydro) far-from-equilibrium hydrodynamic framework. I discuss the existence of far-from-equilibrium hydrodynamic attractors and methods for determining attractors within different hydrodynamical frameworks. I also discuss the determination of attractors from exact solutions to the Boltzmann equation in relaxation time approximation and effective kinetic field theory applied to quantum chromodynamics. I then present comparisons of the kinetic attractors with the attractors obtained in standard second-viscous hydrodynamics frameworks and aHydro. I demonstrate that, due to the resummation of terms to all orders in the inverse Reynolds number, the aHydro framework can describe both the weak- and strong-interaction limits. I then review the phenomenological application of aHydro to relativistic heavy-ion collisions using both quasiparticle aHydro and second-order viscous aHydro. The phenomenological results indicate that aHydro provides a controlled extension of dissipative relativistic hydrodynamics to the early-time far-from-equilibrium stage of heavy-ion collisions. This allows one to better describe the data and to extract the temperature dependence of transport coefficients at much higher temperatures than linearized second-order viscous hydrodynamics.

A dispersion analysis of dust Coulomb waves in complex astroclouds

A semi-analytical fugacity-based model formalism to investigate the normal instability modes excitable in strongly correlated self-gravitating dust molecular clouds (DMCs) on the Jeans spatiotemporal scales has recently been reported. It is based on a viscoelastic magnetized complex plasma with charge-fluctuating heavier dust grains with non-thermal ( κ -distributed) lighter electrons and ions in an astrophysically relevant generalized hydrodynamic (GH) framework. In this continued study, the dispersive properties of the dust Coulomb waves (DCWs) in the high-fugacity regime (HFR) of the constitutive massive, charged dust component are extensively investigated in new multiparametric windows previously remaining unexplored. It is particularly seen that the equilibrium electronic concentration, dust charge number, and azimuthal magnetic field act as DCW accelerating stabilizing agents against the ionic concentration. It is illustratively found further that equilibrium electronic concentration, dust charge number, and azimuthal magnetic field (ionic concentration) interestingly act as normal (anomalous) dispersive factors. The real astronomic relevancy of our investigated results is summarily highlighted in light of the RCW 38 regions of the dark DMCs leading to gravitationally condensed astrostructure formation and evolution.

Dissipative fracton superfluids

We present a comprehensive study of hydrodynamic theories for superfluids with dipole symmetry. Taking diffusion as an example, we systematically construct a hydrodynamic framework that incorporates an intrinsic dipole degree of freedom in analogy to spin density in micropolar (spinful) fluids. Subsequently, we study a dipole condensed phase and propose a model that captures the spontaneous breaking of the U(1) charge. The theory explains the role of the inverse Higgs constraint for this class of theories, and naturally generates the gapless field. Next, we introduce finite temperature theory using the Hamiltonian formalism and study the hydrodynamics of ideal fracton superfluids. Finally, we postulate a derivative counting scheme and incorporate dissipative effects using the method of irreversible thermodynamics. We verify the consistency of the dispersion relations and argue that our counting is systematic.

Assessment of flood risk in a coastal city considering multiple socio-economic vulnerability scenarios

Abstract. The Intergovernmental Panel on Climate Change stresses the importance of vulnerability and exposure along with hazard in defining flood risk. Therefore, a novel approach for flood risk quantification is proposed that evaluates the impact of various realistic socio-economic scenarios on risk reduction. The flood hazard is derived from a hydrodynamic flood modelling framework over Mumbai, India's highly flood-prone coastal megacity. The socio-economic vulnerability is assessed by a multivariate approach based on principal component analysis and data envelopment analysis. Finally, the flood risk is quantified and mapped by aggregating hazard and vulnerability for different socio-economic scenarios, also key indicators contributing to a significant reduction in vulnerability and risk are identified. This non-structural long-term flood risk management approach will benefit densely populated urban areas, especially in developing, and underdeveloped countries.

Turbulent Gas-rich Disks at High Redshift: Bars and Bulges in a Radial Shear Flow

Recent observations of high-redshift galaxies (z ≲ 7) reveal that a substantial fraction have turbulent, gas-rich disks with well-ordered rotation and elevated levels of star formation. In some instances, disks show evidence of spiral arms, with bar-like structures. These remarkable observations have encouraged us to explore a new class of dynamically self-consistent models using our agama/Ramses hydrodynamic N-body simulation framework that mimic a plausible progenitor of the Milky Way at high redshift. We explore disk gas fractions of f gas = 0%, 20%, 40%, 60%, 80%, and 100% and track the creation of stars and metals. The high gas surface densities encourage vigorous star formation, which in turn couples with the gas to drive turbulence. We explore three distinct histories: (i) there is no ongoing accretion and the gas is used up by the star formation, (ii) the star-forming gas is replenished by cooling in the hot halo gas, and (iii) in a companion paper, we revisit these models in the presence of a strong perturbing force. At low f disk (≲0.3), where f disk is the baryon mass fraction of the disk relative to dark matter within 2.2 R disk, a bar does not form in a stellar disk; this remains true even when gas dominates the inner disk potential. For a dominant baryon disk (f disk ≳ 0.5) at all gas fractions, the turbulent gas forms a strong radial shear flow that leads to an intermittent star-forming bar within about 500 Myr; turbulent gas speeds up the formation of bars compared to gas-free models. For f gas ≲ 60%, all bars survive, but for higher gas fractions, the bar devolves into a central bulge after 1 Gyr. The star-forming bars are reminiscent of recent discoveries in high-redshift Atacama Large Millimeter/submillimeter Array observations of gaseous disks.

Extrapolation of Hydrodynamic Pressure in Lubricated Contacts: A Novel Multi-Case Physics-Informed Neural Network Framework

In many technical applications, understanding the behavior of tribological contacts is pivotal for enhancing efficiency and lifetime. Traditional experimental investigations into tribology are often both costly and time-consuming. A more profound insight can be achieved through elastohydrodynamic lubrication (EHL) simulation models, such as the ifas-DDS, which determines precise friction calculations in reciprocating pneumatic seals. Similar to other distributed parameter simulations, EHL simulations require a labor-intensive resolution process. Physics-informed neural networks (PINNs) offer an innovative method to expedite the computation of such complex simulations by incorporating the underlying physical equations into the neural network’s parameter optimization process. A hydrodynamic PINN framework has been developed and validated for a variant of the Reynolds equation. This paper elucidates the framework’s capacity to handle multi-case scenarios—utilizing one PINN for various simulations—and its ability to extrapolate solutions beyond a limited training domain. The outcomes demonstrate that PINNs can overcome the typical limitation of neural networks in extrapolating the solution space, showcasing a significant advancement in computational efficiency and model adaptability.

Dispersion and fate of methane emissions from cold seeps on Hikurangi Margin, New Zealand

The influence of cold seep methane on the surrounding benthos is well-documented but the fate of dissolved methane and its impact on water column biogeochemistry remains less understood. To address this, the distribution of dissolved methane was determined around three seeps on the south-east Hikurangi Margin, south-east of New Zealand, by combining data from discrete water column sampling and a towed methane sensor. Integrating this with bottom water current flow data in a dynamic Gerris model determined an annual methane flux of 3 x 105 kg at the main seep. This source was then applied in a Regional Ocean Modelling System (ROMS) simulation to visualize lateral transport of the dissolved methane plume, which dispersed over ∼100 km in bottom water within 1 year. Extrapolation of this approach to four other regional seeps identified a combined plume volume of 3,500 km3 and annual methane emission of 0.4–3.2 x 106 kg CH4 y-1. This suggests a regional methane flux of 1.1–10.9 x 107 kg CH4 y-1 for the entire Hikurangi Margin, which is lower than previous hydroacoustic estimates. Carbon stable isotope values in dissolved methane indicated that lateral mixing was the primary determinant of methane in bottom water, with potential methane oxidation rates orders of magnitude lower than the dilution rate. Calculations indicate that oxidation of the annual total methane emitted from the five seeps would not significantly alter bottom water dissolved carbon dioxide, oxygen or pH; however, superimposition of methane plumes from different seeps, which was evident in the ROMS simulation, may have localized impacts. These findings highlight the value of characterizing methane release from multiple seeps within a hydrodynamic model framework to determine the biogeochemical impact, climate feedbacks and connectivity of cold seeps on continental shelf margins.

Quantum-to-Classical Coexistence: Wavefunction Decay Kinetics, Photon Entanglement, and Q-Bits

By utilizing a generalized version of the Madelung quantum hydrodynamic framework that incorporates noise, we derive a solution using the path integral method to investigate how a quantum superposition of states evolves over time. This exploration seeks to comprehend the process through which a stable quantum state emerges when fluctuations induced by the noisy gravitational background are present. The model defines the conditions that give rise to a limited range of interactions for the quantum potential, allowing for the existence of coarse-grained classical descriptions at a macroscopic level. The theory uncovers the smallest attainable level of uncertainty in an open quantum system and examines its consistency with the localized behavior observed in large-scale classical systems. The research delves into connections and similarities alongside other theories such as decoherence and the Copenhagen foundation of quantum mechanics. Additionally, it assesses the potential consequences of wave function decay on the measurement of photon entanglement. To validate the proposed theory, an experiment involving entangled photons transmitted between detectors on the moon and Mars is discussed. Finally, the findings of the theory are applied to the creation of larger Q-bit systems at room temperatures.

Unraveling the 2021 Central Tennessee flood event using a hierarchical multi-model inundation modeling framework

Flood prediction systems need hierarchical atmospheric, hydrologic, and hydraulic models to predict rainfall, runoff, streamflow, and floodplain inundation. The accuracy of such systems depends on the error propagation through the modeling chain, sensitivity to input data, and choice of models. In this study, we used multiple precipitation forcings (hindcast and forecast) to drive hydrologic and hydrodynamic models to analyze the impacts of various drivers on the estimates of flood inundation depth and extent. We implement this framework to unravel the August 2021 extreme flooding event that occurred in Central Tennessee, USA. We used two radar-based quantitative precipitation estimates (STAGE4 and MRMS) as well as quantitative precipitation forecasts (QPF) from the National Weather Service Weather Prediction Center (WPC) to drive a series of models in the hierarchical framework, including the Variable Infiltration Capacity (VIC) land surface model, the Routing Application for Parallel Computation of Discharge (RAPID) river routing model, and the AutoRoute and TRITON inundation models. An evaluation with observed high-water marks demonstrates that the framework can reasonably simulate flood inundation. Despite the complex error propagation mechanism of the modeling chain, we show that inundation estimates are most sensitive to rainfall estimates. Most notably, QPF significantly underestimates flood magnitudes and inundations leading to unanticipated severe flooding for all stakeholders involved in the event. Finally, we discuss the implications of the hydrodynamic modeling framework for real-time flood forecasting.

A spatially distributed hydrodynamic model framework for urban flood hydrological and hydraulic processes involving drainage flow quantification

Two-dimensional hydrodynamic models are increasingly used to predict overland surface water flooding in urban catchments. The complexity of urban surfaces and subsurface drainage systems poses great challenges to modelling urban rainfall-runoff and flood hydraulics. This work develops a spatially distributed hydrodynamic model framework incorporating both hydrological and hydraulic processes of surface and subsurface drainage processes during urban flooding. The model is built upon 2D full shallow water equations solved by a Godunov-type finite volume method with robust treatments of the bed source term. To properly involve drainage flow effects, we present three methods to quantify the drainage flow discharge and its delay time which affect both urban hydrology and surface inundation. Besides, a simple OpenMPI-based parallel algorithm is applied to accelerate the model and ensure computational efficiency when applied to real-world events. The model framework is justified through the validations with five benchmark cases. Benchmark results indicate that the well-balanced treatment of bed source term ensures the model applicability in irregular urban surfaces, the model can predict both urban surface inundation and flood hydrograph, and the proposed drainage flow treatments can well reproduce drainage flow hydrograph. The model framework is successfully applied to simulate rainstorm-induced flood events in a rural–urban catchment, the upper Shenzhen River catchment. Results further demonstrate the robust capability of the model in the quantification of flow exchange between surface and subsurface systems to some extent even in the absence of drainage information. Our framework provides a practical solution for urban flood simulation even when pipe data are scarce.

A Novel Response Priority Framework for an Urban Coastal Catchment Using Global Weather Forecasts‐Based Improved Flood Risk Estimates

AbstractA novel flood risk forecasting‐based response priority framework is proposed in this study, which will facilitate efficient decision‐making ahead of an extreme precipitation event. This study is demonstrated over a highly flood‐prone and geomorphologically diverse coastal catchment in Mumbai city, the financial capital of India, and is subjected to high spatio‐temporal variability of precipitation. A regional precipitation forecast model is developed, where a quantile regression (QR)‐based statistical approach is applied to the global weather forecasts for improvement in finer resolution extreme precipitation estimates. A QR is performed between the observed synoptic‐scale predictors obtained from ERA‐Interim Reanalysis data set and the observed subdaily precipitation within the study area. Subsequently, a set of reliably well‐simulated forecasted predictors obtained from the ensemble members of the Global Ensemble Forecast System are used in the established relationship to obtain extreme precipitation forecasts for higher quantile levels. The forecasted precipitation data serves as an essential input to a comprehensive hydrodynamic flood modeling framework. The flood inundation maps corresponding to different quantiles of forecasted precipitation are quantified to identify the flood hotspots. The set of flood inundations maps developed for different quantiles are utilized to demarcate the areas based on critical response time, that is, the time required by each cell within the study area to be inundated to a certain threshold depth, and the response priority levels for each cell are determined. This information is combined with socioeconomic vulnerability (SEV), a critical component of flood risk, to derive conjugated SEV‐based response priority maps.

Regional assessment of extreme sea levels and associated coastal flooding along the German Baltic Sea coast

Abstract. Among the Baltic Sea littoral states, Germany is anticipated to endure considerable damage as a result of increased coastal flooding due to sea-level rise (SLR). Consequently, there is a growing demand for flood risk assessments, particularly at regional scales, which will improve the understanding of the impacts of SLR and assist adaptation planning. Existing studies on coastal flooding along the German Baltic Sea coast either use state-of-the-art hydrodynamic models but cover only a small fraction of the study region or assess potential flood extents for the entire region but rely on global topographic data sources and apply the simplified bathtub approach. In addition, the validation of produced flood extents is often not provided. Here we apply a fully validated hydrodynamic modelling framework covering the German Baltic Sea coast that includes the height of natural and anthropogenic coastal protection structures in the study region. Using this modelling framework, we extrapolate spatially explicit 200-year return water levels, which align with the design standard of state embankments in the region, and simulate associated coastal flooding. Specifically, we explore (1) how flood extents may change until 2100 if dike heights are not upgraded, by applying two high-end SLR scenarios (1 and 1.5 m); (2) hotspots of coastal flooding; and (3) the use of SAR imagery for validating the simulated flood extents. Our results confirm that the German Baltic coast is exposed to coastal flooding, with flood extent varying between 217 and 1016 km2 for the 200-year event and a 200-year event with 1.5 m SLR, respectively. Most of the flooding occurs in the federal state of Mecklenburg-Western Pomerania, while extreme water levels are generally higher in Schleswig-Holstein. Our results emphasise the importance of current plans to update coastal protection schemes along the German Baltic Sea coast over the 21st century in order to prevent large-scale damage in the future.

Transverse expansion of Bjorken flow in (1+1D) relativistic ideal-magnetohydrodynamics with magnetization

We study the evolution of magnetized quark gluon plasma (QGP) in the magneto hydrodynamic (MHD) framework. The fluid under investigation has a non-zero magnetization with infinite electrical conductivity. We solve the coupled Maxwell and conservation equations in (1+1D) transverse flow. We assume that the motion of fluid is longitudinally boost-invariant along beam line.In this study, we consider two different scenarios. First, we consider an ideal relativistic plasma with massless particles and infinite electrical conductivity with a constant magnetic susceptibility (χm). Thus, we solve the coupled Maxwell and conservation equations, and obtain the transverse fluid velocity, the energy density and the magnetic field as functions of both space and time. We investigate the effects of magnetic susceptibility (χm) on the evolution of thermodynamic quantities. Then, we solve the coupled Maxwell and conservation equations with a temperature-dependent magnetic susceptibility and a realistic equation of state given by lattice-QCD data [43,44]. We find the evaluation of temperature, energy density, the magnetic field, and the transverse fluid velocity. We improve our previous study [21] to include a nonzero magnetization, the transverse relativistic velocity ux2≠0, and a realistic equation of state.We realize the effects of non-zero magnetization on the fluid quantities are rather small. Besides, our work shows a fluid with a realistic equation and a temperature-dependent magnetic susceptibility behaves like a conformal fluid with a small constant magnetic susceptibility.

Active learning-based hydrodynamic shape optimization and numerical simulation of auxiliary structures for circular bridge piers

Cylinders as a common form of bridge piers are widely used in engineering practices, yet the hydrodynamic forces and local scouring of the cylinder due to the fluid flow cause significant concern about the functionality of circular bridge piers. In this paper, two novel auxiliary structural types are proposed for passive control of flow around bridge piers, and their optimal structural parameters are determined efficiently using a surrogate model-based hydrodynamic shape optimization framework. Specifically, a Kriging-based active learning algorithm is proposed for hydrodynamic shape optimization of auxiliary structures, which are placed at the rear and both the front and rear of a cylinder. The hydrodynamic performance of the circular bridge pier with the optimized auxiliary structures (F3 and F6) is investigated through 2D and 3D numerical simulations. The effectiveness of the optimized auxiliary structures in mitigating the adverse effect of local scouring around a cylinder is also revealed through a case study. Results indicate that the optimized auxiliary structures F3 and F6 can dramatically reduce the drag coefficient compared with the bare cylinder, i.e., with a reduction rate of 69.8% and 77.2%, respectively; and the reduction rate is more pronounced for the lift coefficient, i.e., with a reduction rate higher than 90% for both F3 and F6. The reduction of drag and lift coefficients is mainly attributed to the positive effects of the optimized auxiliary structures for adjusting the pressure distribution around the cylinder, elongating the free shear layer, improving the wake stability etc. Interestingly, the auxiliary structure F6 also exhibits a high potential to mitigate the scouring effect of fluid flow around a cylinder by decreasing the flow velocity and bed shear stress around the cylinder. However, it should be noted that placing the auxiliary structure at the rear of a cylinder (such as the auxiliary structure type F3) could introduce an adverse effect on reducing local scouring. This study provides valuable guidance for designing effective auxiliary structures for passive control of fluid flow around cylinders.

Production and anisotropic flow of thermal photons in collisions of α -clustered carbon with heavy nuclei at relativistic energies

The presence of $\ensuremath{\alpha}$-clustered structure in the light nuclei produces different exotic shapes in nuclear structure studies at low energies. Recent phenomenological studies suggest that collision of heavy nuclei with $\ensuremath{\alpha}$-clustered carbon ($^{12}\mathrm{C}$) at relativistic energies can lead to large initial state anisotropies. This is expected to impact the final momentum anisotropies of the produced particles significantly. The emission of electromagnetic radiations is considered to be more sensitive to the initial state compared to hadronic observables and thus photon observables are expected to be affected by the initial clustered structure profoundly. In this work we estimate the production and anisotropic flow of photons from most-central collisions of triangular $\ensuremath{\alpha}$-clustered carbon and gold at $\sqrt{{s}_{NN}}=200$ GeV using an event-by-event hydrodynamic framework and compare the results with those obtained from unclustered carbon and gold collisions. We show that the thermal photon ${v}_{3}$ for most central collisions is significantly large for the clustered case compared to the case with unclustered carbon, whereas the elliptic flow parameter does not show much difference for the two cases. In addition, the ratio of anisotropic flow coefficients is found to be a potential observable to constrain the initial state produced in relativistic heavy-ion collisions and also to know more about the $\ensuremath{\alpha}$-clustered structure in carbon nucleus.

Hydrodynamics of plastic deformations in electronic crystals

We construct a new hydrodynamic framework describing plastic deformations in electronic crystals. The framework accounts for pinning, phase, and momentum relaxation effects due to translational disorder, diffusion due to the presence of interstitials and vacancies, and strain relaxation due to plasticity and dislocations. We obtain the hydrodynamic mode spectrum and correlation functions in various regimes in order to identify the signatures of plasticity in electronic crystal phases. In particular, we show that proliferation of dislocations de-pins the spatially resolved conductivity until the crystal melts, after which point a new phase of a pinned electronic liquid emerges. In addition, the mode spectrum exhibits a competition between pinning and plasticity effects, with the damping rate of some modes being controlled by pinning-induced phase relaxation and some by plasticity-induced strain relaxation. We find that the recently discovered damping-attenuation relation continues to hold for pinned-induced phase relaxation even in the presence of plasticity and dislocations. We also comment on various experimental setups that could probe the effects of plasticity. The framework developed here is applicable to a large class of physical systems including electronic Wigner crystals, multicomponent charge density waves, and ordinary crystals.

Generating tensor polarization from shear stress

We derive an expression for the tensor polarization of a system of massive spin-1 particles in a hydrodynamic framework. Starting from quantum kinetic theory based on the Wigner-function formalism, we employ a modified method of moments which also takes into account all spin degrees of freedom. It is shown that the tensor polarization of an uncharged fluid is determined by the shear-stress tensor. In order to quantify this novel polarization effect, we provide a formula which can be used for numerical calculations of vector-meson spin alignment in relativistic heavy-ion collisions.

Equatorial waves in rotating bubble-trapped superfluids

As the Earth rotates, the Coriolis force causes several oceanic and atmospheric waves to be trapped along the equator, including Kelvin, Yanai, Rossby, and Poincar\'e modes. It has been demonstrated that the mathematical origin of these waves is related to the nontrivial topology of the underlying hydrodynamic equations. Inspired by recent observations of Bose-Einstein condensation (BEC) in bubble-shaped traps in microgravity ultracold quantum gas experiments, we show that equatorial modes are supported by a rapidly rotating condensate in a spherical geometry. Based on a zero-temperature coarse-grained hydrodynamic framework, we reformulate the coupled oscillations of the superfluid and the Abrikosov vortex lattice resulting from rotation by a Schr\"odinger-like eigenvalue problem. The obtained non-Hermitian Hamiltonian is topologically nontrivial. Furthermore, we solve the hydrodynamic equations for a spherical geometry and find that the rotating superfluid hosts Kelvin, Yanai, and Poincar\'e equatorial modes, but not the Rossby mode. Our predictions can be tested with state-of-the-art bubble-shaped trapped BEC experiments.