Nonlinear asymptotic stability and transition threshold for 2D Taylor-Couette flows in Sobolev spaces

In this paper, we investigate the stability of the 2-dimensional (2D) Taylor-Couette (TC) flow for the incompressible Navier-Stokes equations. The explicit form of velocity for 2D TC flow is given by $u=(Ar+\frac{B}{r})(-\sin \theta, \cos \theta)^T$ with $(r, \theta)\in [1, R]\times \mathbb{S}^1$ being an annulus and $A, B$ being constants. Here, $A, B$ encode the rotational effect and $R$ is the ratio of the outer and inner radii of the annular region. Our focus is the long-term behavior of solutions around the steady 2D TC flow. While the laminar solution is known to be a global attractor for 2D channel flows and plane flows, it is unclear whether this is still true for rotating flows with curved geometries. In this article, we prove that the 2D Taylor-Couette flow is asymptotically stable, even at high Reynolds number ($Re\sim \nu^{-1}$), with a sharp exponential decay rate of $\exp(-\nu^{\frac13}|B|^{\frac23}R^{-2}t)$ as long as the initial perturbation is less than or equal to $\nu^\frac12 |B|^{\frac12}R^{-2}$ in Sobolev space. The powers of $\nu$ and $B$ in this decay estimate are optimal. It is derived using the method of resolvent estimates and is commonly recognized as the enhanced dissipative effect. Compared to the Couette flow, the enhanced dissipation of the rotating Taylor-Couette flow not only depends on the Reynolds number but also reflects the rotational aspect via the rotational coefficient $B$. The larger the $|B|$, the faster the long-time dissipation takes effect. We also conduct space-time estimates describing inviscid-damping mechanism in our proof. To obtain these inviscid-damping estimates, we find and construct a new set of explicit orthonormal basis of the weighted eigenfunctions for the Laplace operators corresponding to the circular flows. These provide new insights into the mathematical understanding of the 2D Taylor-Couette flows.Comment: 50 page

Hydrodynamic coefficients of oscillating flat plates at 0.15 ⩽ KC⩽ 3.15

This article presents an experimental investigation on the hydrodynamic coefficients of oscillating flat plates. The plates are forced to oscillate harmonically in still water. The range of Keulegan–Carpenter number (KC= 2 πa/ D, where a is the single amplitude of oscillation and D is the equivalent diameter of the plate) is 0.15 ⩽ KC⩽ 3.15. The hydrodynamic forces acting on the plates are measured and the hydrodynamic coefficients including added mass and damping coefficients are calculated using the Morison’s equation. The influences of the thickness ratio, shape, edge corner radius, perforation ratio and hole size on the hydrodynamic coefficients of a single plate are analyzed and presented. For the twin- and triplet-plate configurations, the spacing effects are also evaluated

Assessing the eco-efficiency of cruise tourism at the national level: Determinants, challenges, and opportunities for sustainable development

In the face of the cruise industry\u27s rapid global expansion and its significant interplay with national tourism, economic growth, and environmental conservation, a notable gap exists in comprehensively evaluating its eco-efficiency. This study aims to fill this gap by implementing a novel analytical framework, merging the undesirable slack-based measure (SBM) model with fraction regression model (FRM) analysis. This approach is designed to dissect the complex relationship between economic development, environmental impact, and resource consumption in the context of cruise tourism. The study applies this integrated methodology to data from 11 countries, spanning from 2010 to 2018. The findings reveal marked differences in eco-efficiency across nations, with Australia and Japan standing out for their exemplary practices in natural ecology management and balanced cruise ship development. On the other hand, nations like Italy and Singapore, while supportive of the cruise industry, exhibit areas for improvement in market expansion and leveraging regional advantages. The research also brings to light the dual challenge for developing countries, such as China and Brazil, in balancing economic gains from cruise tourism with environmental concerns. A significant revelation of this study is the substantial influence of a nation\u27s per capita GDP and the rigor of environmental regulations on eco-efficiency in cruise tourism. This highlights the critical role of economic stability and policy frameworks in steering the industry towards sustainability. Interestingly, factors like foreign trade, industrial structure, and R&D investments appear to have a less pronounced impact on eco-efficiency. Moreover, the study presents a structured approach to enhance sustainability in the cruise industry, categorizing countries by eco-efficiency and returns to scale. This categorization leads to tailored recommendations for each group, focusing on the unique challenges and strengths of different nations, thus promoting effective, targeted strategies for sustainable development. Overall, the study provides a comprehensive framework for evaluating and enhancing sustainability practices in this rapidly growing industry. It also outlines potential areas for future research, considering the limitations of the current approach, thereby paving the way for further exploration into the sustainable evolution of cruise tourism

Data Envelopment Analysis for Relative Efficiency Measurement of Chinese Hospitals: A Systematic Review

The purpose was to explore the gap between China and the international world in efficiency measurement of hospitals with Data Envelopment Analysis, and to improve the standardization of healthcare efficiency measurement in China. A systematic review was conducted using appropriate search strategies. Studies were included containing DEA approaches regarding general hospital efficiency, published in international literature and in both Chinese and English about Chinese hospitals from January 2004 to October 2014. The results showed that statistical significances were found in indicators such as number of DMUs, percentage of allocative efficiency studies, ratio of studies with multiple years, number of studies with monetary indicators in input and output sets, etc. The statistical insignificance in some indicators such as the number of input and output indicators were also found among China, Europe, USA and others. Some problems were found in current DEA-based hospital efficiency studies in China, such as inappropriate selection of input-output indicators, no bias-correction on efficiency scores, etc. The standardization of DEA methods applied in China’s hospital efficiency research needs to be improved. Chinese researchers should pay more attention to latest international research findings, so as to keep pace with the cutting edge hospital efficiency research

Direct numerical simulation of compressible turbulence accelerated by graphics processing unit. Part 1: An open-source high accuracy accelerated computational fluid dynamic software

This paper introduces open-source computational fluid dynamics software named open computational fluid dynamic code for scientific computation with graphics processing unit (GPU) system (OpenCFD-SCU), developed by the authors for direct numerical simulation (DNS) of compressible wall-bounded turbulence. This software is based on the finite difference method and is accelerated by the use of a GPU, which provides an acceleration by a factor of more than 200 compared with central processing unit (CPU) software based on the same algorithm and number of message passing interface (MPI) processes, and the running speed of OpenCFD-SCU with just 512 GPUs exceed that of CPU software with 130\,000 CPUs. GPU-Stream technology is used to implement overlap of computing and communication, achieving 98.7\% parallel weak scalability with 24\,576 GPUs. The software includes a variety of high-precision finite difference schemes, and supports a hybrid finite difference scheme, enabling it to provide both robustness and high precision when simulating complex supersonic and hypersonic flows. When used with the wide range of supercomputers currently available, the software should able to improve the performance of large-scale simulations by up to two orders on the computational scale. Then, OpenCFD-SCU is applied to a validation and verification case of a Mach 2.9 compression ramp with mesh numbers up to 31.2 billion. More challenging cases using hybrid finite schemes are shown in Part 2(Dang, Li et al. 2022). The code is available and supported at \url{http://developer.hpccube.com/codes/danggl/opencfd-scu.git}.Comment: 23 pages, 25 figure

Inverse Kinematic Analysis and Evaluation of a Robot for Nondestructive Testing Application

The robot system has been utilized in the nondestructive testing field in recent years. However, only a few studies have focused on the application of ultrasonic testing for complex work pieces with the robot system. The inverse kinematics problem of the 6-DOF robot should be resolved before the ultrasonic testing task. A new effective solution for curved-surface scanning with a 6-DOF robot system is proposed in this study. A new arm-wrist separateness method is adopted to solve the inverse problem of the robot system. Eight solutions of the joint angles can be acquired with the proposed inverse kinematics method. The shortest distance rule is adopted to optimize the inverse kinematics solutions. The best joint-angle solution is identified. Furthermore, a 3D-application software is developed to simulate ultrasonic trajectory planning for complex-shape work pieces with a 6-DOF robot. Finally, the validity of the scanning method is verified based on the C-scan results of a work piece with a curved surface. The developed robot ultrasonic testing system is validated. The proposed method provides an effective solution to this problem and would greatly benefit the development of industrial nondestructive testing