Search Results (304)

This paper focuses on the variable coefficients geophysical KdV (VCGKdV) equation, which involves time-dependent perturbation, nonlinearity and dispersion parameters. It is a more realistic model than its constant coefficient counterpart and can be useful to, for instance, investigate the Coriolis effect on oceanic flows. Firstly, we analyzed this model using three strong methods that allow the investigation of its integrability: the Lie symmetry approach, Painlevé property and Hirota formalism. The general constraints between the involved parameters under which the complete integrability in Lie, Painlevé or Hirota sense exists, as well as the largest class of this type of equations, which admits the same class of imposed symmetries are generated. Then, some new specific families of solutions for the model endowed with either Lie symmetry properties, Lie and Painlevé constraints or with Lie, Painlevé and Hirota constraints were generated and compared with solutions derived with other techniques. By numerical simulations, the dynamical behaviors of some Lie invariant solutions and nonautonomous multiple solitons are depicted. Full article

The mechanisms by which rotation influences zonal flows (ZFs) in plasma are incompletely understood, presenting a significant challenge in the study of plasma dynamics. This research addresses this gap by investigating the role of non-inertial effects—specifically centrifugal and Coriolis forces—on Geodesic Acoustic Modes (GAMs) and ZFs in rotating tokamak plasmas. While previous studies have linked centrifugal convection to plasma toroidal rotation, they often overlook the Coriolis effects or inconsistently incorporate non-inertial terms into magneto-hydrodynamic (MHD) equations. In this work, we derive self-consistent drift-ordered two-fluid equations from the collisional Vlasov equation in a non-inertial frame, and we modify the Hermes cold ion code to simulate the impact of rotation on GAMs and ZFs. Our simulations reveal that toroidal rotation enhances ZF amplitude and GAM frequency, with Coriolis convection playing a critical role in GAM propagation and the global structure of ZFs. Analysis of simulation outcomes indicates that centrifugal drift drives parallel velocity growth, while Coriolis drift facilitates radial propagation of GAMs. This work may provide valuable insights into momentum transport and flow shear dynamics in tokamaks, with implications for turbulence suppression and confinement optimization. Full article

In a large deep lake, the generation of internal Kelvin waves and internal Poincaré waves due to wind stress on the lake surface is a significant phenomenon. These internal waves play a crucial role in material transport within the lake and have profound effects on its ecosystem and environment. Our study, which investigated the modes of internal waves in Lake Biwa using the vertical temperature distribution from field observations, has yielded important findings. We have demonstrated the applicability of the frequency equation solutions, considering the Coriolis force. The period of the internal Poincaré waves, as observed in the field, was found to match the solutions of the frequency equation. For example, observational data collected in late October revealed excellent agreement with the theoretical solutions derived from the frequency equation, showing periods of 14.7 h, 11.8 h, 8.2 h, and 6.3 h compared to the theoretical values of 14.4 h, 11.7 h, 8.5 h, and 6.1 h, respectively. However, the periods of the internal Kelvin waves in the field observation results were longer than those of the theoretical solutions. The Modified Mathew function uses a series expansion around $q_i=0$, making it difficult to estimate the periods of internal Kelvin waves under conditions where $\left|q_i\right|>1.0$. Furthermore, in lakes with an elliptical shape, such as Lake Biwa, the elliptical cylinder showed better reproducibility than the circular cylinder. These findings have significant implications for the rapid estimation of internal wave periods using the frequency equation. Full article

A FEM model of Shallow Wave Equations (SWE-FEM) is studied, taking into account the variable bathymetry of semi-enclosed sea basins. The model, with a spatially varying Coriolis term, is implemented for the description of combined refraction–diffraction effects, from which the eigenperiods and eigenmodes of extended geographical sea areas are calculated by means of a low-order FEM scheme. The model is applied to the western Mediterranean basin, illustrating its versatility to easily include the effects of geographical characteristics like islands and other coastal features. The calculated resonant frequencies and modes depend on the domain size and characteristics as well as the location of the open sea boundary, and it is shown to provide results compatible with tide measurements at several stations in the coastal region of France. The calculation of the natural oscillation modes in the western Mediterranean basin, bounded by open boundaries at the Strait of Gibraltar and the Strait of Sicily, reveals a natural period of around 6 h corresponding to the quarter-diurnal tidal components, which are stationary and of roughly constant amplitude on the northern coast of the basin and on the west coast of Corsica (France). On the east coast of Corsica, on the other hand, these components are of very low amplitude and in phase opposition. The semi-diurnal tidal components observed on the same tide gauges north of the basin and west of Corsica are also quasi-stationary although they are not resonant. Resonant oscillations are also observed at lower periods, especially at a period of around 3 h at the Sète station. This period corresponds to a higher-order natural mode of the western Mediterranean basin, but this resonance seems to be essentially linked to the presence of the Gulf of Lion, whose shallowness and the width of the shelf at this point induce a resonance. Other oscillations are also observed at lower periods (T = 1.5 h at station Fos-sur-Mer, T = 45 min in the Toulon harbour station), due to more local forcing. Full article

Geophysical flows are characterized by rapid rotation. Simulating these flows requires small timesteps to achieve stability and accuracy. Numerical stability can be greatly improved by the implicit integration of the terms that are most responsible for destabilizing the numerical scheme. We have implemented an implicit treatment of the Coriolis force in a rotating spherical shell driven by a radial thermal gradient. We modified the resulting timestepping code to carry out steady-state solving via Newton’s method, which has no timestepping error. The implicit terms have the effect of preconditioning the linear systems, which can then be rapidly solved by a matrix-free Krylov method. We computed the branches of rotating waves with azimuthal wavenumbers ranging from 4 to 12. As the Ekman number (the non-dimensionalized inverse rotation rate) decreases, the flows are increasingly axially independent and localized near the inner cylinder, in keeping with well-known theoretical predictions and previous experimental and numerical results. The advantage of the implicit over the explicit treatment also increases dramatically with decreasing $\mathrm{Ek}$, reducing the cost of computation by as much as a factor of 20 for Ekman numbers of order of ${10}^{-5}$. We carried out continuation for both the Rayleigh and Ekman numbers and obtained interesting branches in which the drift velocity remained unchanged between pairs of saddle–node bifurcations. Full article

As the core components of geophysical dynamic system, oceans and atmospheres are dominated by the Coriolis force, which governs complex dynamic phenomena such as internal waves, gravity currents, vortices, and others involving multi-scale spatiotemporal coupling. Due to the limitations of in situ observations, large-scale rotating tanks have emerged as critical experimental platforms for simulating Earth’s rotational effects. This review summarizes recent advancements in rotating tank applications for studying oceanic flow phenomena, including mesoscale eddies, internal waves, Ekman flows, Rossby waves, gravity currents, and bottom boundary layer dynamics. Advanced measurement techniques, such as particle image velocimetry (PIV) and planar laser-induced fluorescence (PLIF), have enabled quantitative analyses of internal wave breaking-induced mixing and refined investigations of vortex merging dynamics. The findings demonstrate that large-scale rotating tanks provide a controllable experimental framework for unraveling the physical essence of geophysical fluid motions. Such laboratory experimental endeavors in a rotating tank can be applied to more extensive scientific topics, in which the rotation and stratification play important roles, offering crucial support for climate model parameterization and coupled ocean–land–atmosphere mechanisms. Full article

In this paper, we investigated a three-dimensional incompressible fractional rotating magnetohydrodynamic (FrMHD) system by reformulating the Cauchy problem into its equivalent mild formulation and working in critical homogeneous Sobolev spaces. For this, we first established the existence and uniqueness of a global mild solution for small and divergence-free initial data. Moreover, our approach is based on proving sharp bilinear convolution estimates in critical Sobolev norms, which in turn guarantee the uniform analyticity of both the velocity and magnetic fields with respect to time. Furthermore, leveraging the decay properties of the associated fractional heat semigroup and a bootstrap argument, we derived algebraic decay rates and established the long-time dissipative behavior of FrMHD solutions. These results extended the existing literature on fractional Navier–Stokes equations by fully incorporating magnetic coupling and Coriolis effects within a unified fractional-dissipation framework. Full article

The development of coal–water slurry (CWS), a new type of coal-based chemical product in China, has garnered increasing attention as a potential substitute for petroleum resources. The Coriolis mass flow meter is widely used in industrial measurement due to its low uncertainty and its ability to simultaneously measure fluid density and mass flow rate, with a single-phase measurement error as low as 0.1%. However, significant errors still exist in multiphase flow measurement scenarios. To address this issue, we designed and constructed a CWS liquid–solid two-phase flow measurement platform to investigate the flow measurement errors of CWS in Coriolis mass flow meters under various conditions. A deep learning correction framework was developed to mitigate the significant measurement errors in liquid–solid two-phase flow. Based on the theoretical support provided by repeatability experiments, two correction models were established: (1) An error correction model based on a BP neural network was developed, which provided corrections for the measurement errors of CWS liquid–solid two-phase flow. The first correction results showed that the corrected error of the predictive model was 3.98%, a significant improvement compared to the 5.11% error measured by the X company’s meter. (2) Building on this, a second correction model was established through algorithm optimization, successfully reducing the corrected error of the predictive model to 1.01%. Through this study, we aim at providing a new technical approach for Coriolis mass flow meters in the field of liquid–solid two-phase flow measurement, enhancing measurement accuracy, reducing costs, and offering more reliable data support for industrial process control and scientific research. Full article

Rotational spectra for hexafluoroacetone imine, the singly substituted ¹³C isotopologues, and the ¹⁵N isotopologue, have been recorded using both cavity and chirped pulse Fourier transform microwave spectrometers. The spectra observed present as being doubled with separations between each pair of transitions being on the order of a few tens of kilohertz which is consistent with a large amplitude motion producing two torsional substates. The observed splitting is most likely due to the combined motions of the CF3 groups, for which the calculated barrier is small. However, no transitions between states could be observed and, similarly, no Coriolis coupling parameters were required to achieve a satisfactory fit for the transition frequencies. Hence, and somewhat curiously, the two states have been fit independently of each other such that the two states may simply be considered near-equivalent conformers. The structural properties of hexafluoroacetone imine are compared with two isoelectronic molecules hexafluoroisobutene and hexafluoroacetone. Rotational constants, quartic centrifugal distortion constants, and the ¹⁴N nuclear electric quadrupole coupling tensor have been determined and are presented together with supporting quantum chemical calculations. Full article

In previous studies, a valveless piezoelectric pump with arc-shaped tubes (VPPAST) based on the Coriolis Effect was proposed. To promote the application of VPPAST in the field of navigation and guidance, it is vital to further explore the influences of the layout and structural parameters of arc-shaped tubes on the flow rate. Accordingly, in this study, the analysis of flow characteristics of fluid in arc-shaped tubes was conducted, and the velocity difference between the clockwise and counterclockwise flow of the liquid was reduced. Eventually, the flow equations of three layout modes of arc-shaped tubes were established. VPPAST with anomalous-direction arc-shaped tubes, single-arc-shaped tube, and same-direction arc-shaped tubes were produced using 3D printing technology. In addition, the valveless piezoelectric pump with the anomalous-direction arc-shaped tubes (VLPPADA) with different parameter flow tubes were also fabricated. Based on the resultant flow rates of each piezoelectric pump, it was demonstrated that the flow rate of the VLPPADA was the highest under the same driving conditions, and the flow rate can be determined as 1.72 mL/min when the driving voltage was set as 160 V at 14 Hz. It indicated that the pump flow rate of VLPPADA was directly proportional to the base radius and width of the arc-shaped tube. Full article

Ehlers’ Frame Theory is a class of geometric theories parameterized by $\lambda :=1/c^2$ and identical to the General Theory of Relativity for $\lambda \ne 0$. The limit $\lambda \to 0$ does not recover Newtonian gravity, as one might expect, but yields the so-called Newton–Cartan theory of gravity, which is characterized by a second gravitational field $\mathit{\omega }$, called the Coriolis field. Such a field encodes at a non-relativistic level the dragging feature of general spacetimes, as we show explicitly for the case of the $(\eta ,H)$ geometries. Taking advantage of the Coriolis field, we apply Ehlers’ theory to an axially symmetric distribution of matter, mimicking, for example, a disc galaxy, and show how its dynamics might reproduce a flattish rotation curve. In the same setting, we further exploit the formal simplicity of Ehlers’ formalism in addressing non-stationary cases, which are remarkably difficult to treat with the General Theory of Relativity. We show that the time derivative of the Coriolis field gives rise to a tangential acceleration which allows for studying a possible formation in time of the rotation curve’s flattish feature. Full article

This paper investigates the effect of electrostatic nonlinearity on the rate-sensing performance of imperfect ring-based Coriolis Vibrating Gyroscopes (CVGs) for devices having 8 and 16 evenly distributed electrodes. Mathematical models are developed for CVGs operating in (i) an open loop for a linear electrostatically trimmed device, (ii) a closed loop where a sense force balancing is applied to negate the sense quadrature response, and the effects of electrostatic nonlinearity are investigated for increasing drive amplitudes. The modeling indicates the nonlinear responses for 8- and 16-electrode arrangements are quite different, and this can be attributed to the nonlinear frequency imbalance, which depends on the drive and sense frequency softening as well as the presence of self-induced parametric excitation in the sense response. In open loop the 16-electrode arrangement exhibits much weaker levels of nonlinearity than the 8-electrode arrangement because the nonlinear frequency imbalance is less sensitive to drive amplitude. For devices operating in closed-loop with sense force balancing to ensure the drive and sense responses are in-phase/anti-phase, it is shown that ideal rate-sensing performance is achieved at large drive amplitudes for both 8- and 16-electrode arrangements. Using sense force balancing, rate sensing can be achieved using either the sense response or the required balancing voltage. For the latter, large nonlinear frequency imbalances and low damping levels enhance rate-sensing performance. Full article

Molds are frequent indoor contaminants, where they can colonize many materials. The subsequent aerosolization of fungal spores from moldy surfaces can strongly impact indoor air quality and the health of occupants. The investigation of fungal contamination of habitations is a key point in evaluating sanitary risks and understanding the relationship that may exist between the fungal presence on surfaces and air contamination. However, to date there is no “gold standard” of sampling indoor air for such investigations. Among various air sampling methods, impingement can be used for capturing fungal spores, as it enables real-time sampling and preserves analytical follow-up. Its efficiency varies depending on several factors, such as spore hydrophobicity, sampling conditions, etc. Sampling devices may also impact the results, with recovery rates sometimes lower than filtration-based methods. The Coriolis µ air sampler, an impingement-based device, utilizes centrifugal force to concentrate airborne particles into a liquid medium, offering flexibility for molecular analysis. Several studies have used this device for air sampling, demonstrating its application in detecting pollen, fungal spores, bacteria, and viruses, but it is most often used in laboratory conditions. The present case study, conducted in a moldy house, aims to investigate the efficiency of this device in sampling fungal spores for DNA analysis in indoor environments. The results obtained suggest that the use of this device requires an optimized methodology to enhance its efficiency and reliability in bioaerosol research. Full article

A GPU-accelerated shallow water model with a local time-step (LTS) is employed in this work to examine how the Coriolis forces affect the tidal level difference and, consequently, the water–sediment exchange between Hangzhou Bay (HZB) and the Yangtze River Estuary. The model is applied to both idealized and realistic estuary configurations to analyze tidal level gradients between the two neighboring estuaries under different flow conditions and with and without the Coriolis force condition. The model’s accuracy in predicting tidal levels and currents was validated against field data. It is shown that the tidal level gradient is negative during flood tide, indicating a mass transfer trend from south to north, whereas the tidal level gradient is positive during ebb tide, indicating a north-to-south mass transfer. Considering sediment originates mainly from the riverine side, the sediment mass transfer may occur mainly during ebb tide, and the direction is from the Yangtze River to the HZB. This finding provides numerical evidence for previous recognition that sediment in HZB mainly comes from the Yangtze River Estuary. A comparison of the idealized and realistic estuary configurations further indicates that the contrasting bed topography enhances tidal level gradients. The findings show that by causing tidal phase changes and asymmetric tidal range modifications, the Coriolis force increases lateral water level gradients (up to 0.7 m) between the Yangtze Estuary and Hangzhou Bay. Idealized modeling further demonstrates that higher Coriolis coefficients promote sediment exchange and exacerbate water level fluctuations across estuaries. Without the Coriolis effect, the tide level distribution in adjacent estuaries is symmetrical. In the Northern and Southern Hemispheres, the tide level distribution in adjacent estuaries is the opposite. In addition, this study has shown that changes in river flow have a limited effect on water levels at stations farther from the estuary’s flow intake and therefore have a negligible effect on the water level gradient in adjacent estuaries farther away. However, topography differences have a significant effect on water level gradients in neighboring estuaries. These studies emphasize the significance of the Coriolis force in regulating sediment transport pathways in estuaries. Full article

Power generation is an important part of air vehicle energy management when developing long-endurance and reusable hypersonic aircraft. In order to utilize an air turbine power generation system on board, fuel-based rotating cooling has been researched to cool the turbine’s rotor blades. For fuel-cooling air turbines, each blade corresponds to a separate cooling channel. All the separate cooling channels cross together and form a distributary cavity and a confluence cavity in the center of the disk. In order to determine the flow characteristics in the distributary and confluence cavities, computational fluid dynamics (CFD) simulations using the shear–stress–transport turbulence model were carried out under the conditions of different rotating speeds and different mass flow rates. The results showed great differences between non-rotating flow and rotating flow conditions in the distributary and confluence cavities. The flow in the distributary and confluence cavities has rotational velocity, with obvious layering distribution regularity. Moreover, a high-speed rotational flow surface is formed in the confluence cavity of the original structure, due to the combined functions of centrifugal force, inertia, and the Coriolis force. Great pressure loss occurs when fluid passes through the high-speed rotational flow surface. This pressure loss increases with the increase in rotating speed and mass flow rate. Finally, four structures were compared, and an optimal structure with a separated outlet channel was identified as the best structure to eliminate this great pressure loss. Full article