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This study focuses on changes in the Tibetan Plateau vortices (TPVs) by using ERA5 reanalysis, covering the summers from 1979 to 2022 within the Tibetan Plateau (TP) region. These TPVs were identified using a geopotential height analysis. We discovered that the central-western TP had the most TPV activity and observed a clear decreasing trend in both the intensity and frequency of the TPVs in this region. This decrease was also accompanied by a decline in the strength of the associated vertical upward motion. To better understand this change, we employed the quasi-geostrophic omega equation. This allowed us to examine the dynamic, diabatic, and topographic factors contributing to the vertical motion during different phases of TPV activity in this region. Our results indicate that the main reason behind the weakened TPVs is the diminishing upper-level jet stream, which exerts dynamic forcing on the system. In the later stage, we observed that intensive moisture transport induces heightened diabatic vertical motion. However, this effect is not potent enough to counterbalance the diminishing dynamic influence. Therefore, our findings suggest a significant shift in TPV activity, transitioning from a dynamic-dominated regime to a latent heating-dominated diabatic regime. This new insight enhances our understanding of the complex mechanisms that influence TPV behavior.

The response of global atmospheric vertical motion to climate change has important impacts on the hydrological cycle and extreme rainfall. However, limited research has discussed the long-term change of vertical motion, and its corresponding impacts on precipitation are seldom studied in a global aspect. Here we find that the spatial distribution of global daily vertical motion has become more asymmetric since 1979, and both vertical motion and rainfall have coherently become more extreme on both ends of the spectrum under the recent climate change background. Specifically, both the global extreme upward and downward motions have been strengthening, resulting from the intensifying tropical Walker circulation and Hadley cell, while the intensity of weak updrafts has been weakening. Meanwhile, the proportions of global updraft and downdraft areas have correspondingly been contracting and expanding, respectively. Such asymmetrical changes consequently affect the global precipitation by intensifying extreme rainfall, enlarging heavy-rain and dry areas, but narrowing light-rain areas. This study demonstrates that the long-term global-scaled change of atmospheric vertical motion, a fundamental dynamical factor of precipitation, under the recent climate change background coheres with that of rainfall, providing an observational reference for future research on the dynamical mechanism of precipitation change under climate change.

The severe vertical motion of high-speed multihull vessels significantly impairs their seakeeping performance, making the design of effective anti-motion controllers crucial. However, existing controllers, predominantly designed based on deterministic dynamic models, suffer from limitations such as insufficient robustness, reliance on empirical knowledge, structural complexity, and suboptimal performance, which hinder their practical applicability. To address this, this paper proposes a robust decoupled vertical motion controller based on the step response inversion method and incorporating an Extended State Observer (ESO) uncertainty compensation term. The control algorithm is designed leveraging the equivalent noise bandwidth theory to account for the stochastic characteristics of pitch/heave motion, with ESO compensation introduced to enhance robustness. The stability of the closed loop system is rigorously proven through theoretical analysis. Simulation results demonstrate that the proposed algorithm significantly suppresses the amplitudes of both pitch and heave motions.

Research on vertical motion in mesoscale systems is an extraordinarily challenging effort. Allowing for fewer assumptions, a new form of generalized vertical motion equation and a generalized Omega equation are derived in the Cartesian coordinate system (nonhydrostatic equilibrium) and the isobaric coordinate system (hydrostatic equilibrium), respectively. The terms on the right-hand side of the equations, which comprise the Q vector, are composed of three factors: dynamic, thermodynamic, and mass. A heavy rain event that occurred from 18 to 19 July 2021 in southern Xinjiang was selected to analyze the characteristics of the diagnostic variable in the generalized vertical motion equation ( Q z ) and the diagnostic variable in the generalized Omega equation ( Q p ) using high-resolution model data. The results show that the horizontal distribution of the Q z -vector divergence at 5.5 km is roughly similar to the distribution of the Q p -vector divergence at 500 hPa, and that both relate well to the composite radar reflectivity, vertical motion, and hourly accumulated precipitation. The Q z -vector divergence is more effective in indicating weak precipitation. In vertical cross sections, regions with alternating positive and negative large values that match the precipitation are mainly concentrated in the middle levels for both forms of Q vectors. The temporal evolutions of vertically integrated Q z -vector divergence and Q p -vector divergence are generally similar. Both perform better than the classical quasigeostrophic Q vector and nongeostrophic Q vector in indicating the development of the precipitation system.

This study proposes a new simplified Ground Motion Model (GMM) for vertical spectra by combining comprehensive datasets from the NESS and NGA-West2 databases. The proposed Artificial Neural Network (ANN) architecture-based model requires only 288 unknowns to predict spectral accelerations (Sa) at 33 distinct periods ranging from 0 to 4 s. Notably, this model inherently captures known physical phenomena with reduced variability using a minimum number of unknowns compared to the GMMs existing literature, thus offering a valuable addition to current hazard estimation frameworks. Furthermore, recognizing the necessity for physics-based simulations in vertical ground motion analysis, we introduce a physics-based broadband model for vertical spectra using ANN methodology. The proposed broadband model exhibits better robustness due to the comprehensiveness of the dataset utilized and the inclusion of source path and site characteristics at the input layer. Additionally, the model effectively captures the physical trends with minimal deviation. Further, we verified the predictive ability of the developed models through a comprehensive case study of the 2008 Iwate–Miyagi earthquake. The proposed models serve as essential tools for physics-based broadband simulations and hazard assessments in active shallow crustal regions.

A disc-type underwater glider (DTUG) is characterized by full-wing body shape, omnidirectional characteristics, and high maneuverability. To further reveal the differences between DTUGs and hybrid-driven underwater gliders (HUGs), the vertical motion of a DTUG with zero pitch angle is simulated. Based on the structural characteristics of DTUGs, the motion control equations with control inputs are derived and solved by the fourth-order Runge–Kutta method. The DTUG’s vertical velocity, fixed-depth motion, vertical motion with external disturbance, and stability are mainly analyzed and compared with those of an HUG. The results show that the DTUG’s full-wing body shape increases its vertical resistance so that the vertical steady motion velocity is low, which is advantageous for vertical depth control but disadvantageous for fast vertical motion; furthermore, fixed-depth motion control can be easily realized in limited space. The DTUG’s vertical motion with external disturbances can quickly return to a stable state within a smaller vertical distance than that of the HUG, which is beneficial for assisting the DTUG in returning to the target position and will improve its movement efficiency in a small body of water with limited depth. The stability analysis shows the DTUG can remain stable within the range of control parameter.

T-foils with active control systems can adjust their attack angle according to the movement of the ship in real time, providing higher lift force and improving the seakeeping performance of a ship. The optimization of the control signal and that of the control method have an important influence on the effect of active T-foils. In this paper, the control method of the T-foil’s swinging angle is established and optimized on the basis of model testing in order to increase the effect of the T-foil. First, the governing equation is introduced by establishing the proportional relationship between the angular motion of the hull and the lift moment of the T-foil. On the basis of the model of the T-foil’s lift force, the governing equation of the T-foil’s swinging angle is deduced and simplified using the test results of the ship model with a passive T-foil and without a T-foil. Then, the active T-foil control system is established by comparing the effects of T-foils with different control signals. Finally, the efficacies of the passive and active T-foil are reported and discussed. It is found that the pitch angular velocity is a more appropriate signal than the pitch angle and pitch angular acceleration. T-foils with pitch angular velocity control can decrease the vertical motion response in the resonance region of a ship’s encounter frequency by more than about 20% compared to the case of the bare ship model, while also increasing the anti-bow acceleration effect by more than 15% compared to the case of passive control. The results obtained by model testing have a certain guiding significance for specific engineering practices.

Dynamic topography is a well-established consequence of global geodynamic models of mantle convection with horizontal dimensions of >1000 km and amplitudes up to 2 km. Such physical models guide the interpretation of geological records on equal dimensions. Continent-scale geological maps therefore serve as reference frames of choice to visualize erosion/non-deposition as a proxy for long-wavelength, low-amplitude vertical surface motion. At a resolution of systems or series, such maps display conformable and unconformable time boundaries traceable over hundreds to thousands of kilometres. Unconformable contact surfaces define the shape and size of time gap (hiatus) in millions of years based on the duration of time represented by the missing systems or series. Hiatus for a single system or series base datum diminishes laterally to locations (anchor points) where it is conformable at the mapped resolution; it is highly dependent upon scale. A comparison of hiatus area between two successive system or series boundaries yields changes in location, shape, size and duration, indicative of the transient nature of vertical surface motion. As a single-step technique, it serves as a quantitative proxy for palaeotopography that can be calibrated using other geological data. The tool magnifies the need for geological mapping at the temporal resolution of stages, matching process rates. The method has no resolving power within conformable regions (basins) but connects around them. When applied to marine seismic sections that relate to rock record, not to time, biostratigraphic and radiometric data from deep wells are needed before hiatus areas – that relate to time – can be mapped.

In this paper, some real world modeling problems: vertical motion of a falling body problem in a resistant medium, and the Malthusian growth equation, are considered by the newly defined Liouville–Caputo fractional conformable derivative and the modified form of this new definition. We utilize the σ auxiliary parameter for preserving the dimension of physical quantities for newly defined fractional conformable vertical motion of a falling body problem in a resistant medium. The analytical solutions are obtained by iterating this new fractional integral and results are illustrated under different orders by comparison with the Liouville–Caputo fractional operator.

The major focus in earthquake analysis is typically on the excitation caused by two in-plane horizontal components. However, the direction of vertical ground motion (VGM) is a critical aspect of an earthquake’s inherent nature that has received less attention in recent research. Accordingly’, the present study investigates the effects of VGM direction on the responses of a multi-span continuous concrete bridge pier seismically isolated with a friction pendulum system (FPS). The friction-based isolator is chosen because vertical force influences the coefficient of friction through variations in the normal force. To precisely assess the impact of vertical ground motion, a coefficient is proposed based on the ratio of the peak ground acceleration (PGA) of the vertical component in the upward and downward directions. The incremental dynamic analysis approach for the vertical component of an earthquake (IDA-V) is introduced and applied using a set of ground motion records. These records are categorized by their predominant vertical acceleration direction to emphasize the vertical impacts of inertia forces on the overall bridge responses. Fragility curves for substructure components are then developed. The results indicate that when the predominant direction of VGM is upward, it can cause compression-based damage in structural components, such as column compression failure and increased displacement of the friction pendulum systems (FPS). Conversely, when the predominant direction of VGM is downward, it can lead to tension-based damage, including tensile forces along the columns and a higher probability of isolator uplift. In general, incorporating the effects of VGM in the analysis increases the probability of failure across all structural components and damage states. Additionally, accounting for the upward or downward direction of VGM results in distinct types of damage.