Flow around a Rectangular Cylinder Placed in a Channel with a High Blockage Ratio under a Subcritical Reynolds Number

With the depletion of fossil energy sources, clean energy has become a growing concern for scholars. Vortex-Induced Vibration Aquatic Clean Energy (VIVACE), a device that uses water flow energy to generate electricity, has attracted much attention for its broad applicability and other advantages. Particle Image Velocimetry (PIV) experiments were conducted to improve the efficiency of the VIVACE device in low-velocity areas. The present study investigated the effects of the Blockage ratio (Br), Reynolds number (Re = ρU0D/μ), and Aspect ratio (Ar = B/D, width-to-height) of rectangular cylinders on flow characteristics. The influence of the Ar, Br, and Re on the flow field structure was systematically analyzed in terms of the time-averaged flow field, Reynolds shear stress, space–time correlation, vorticity field, and water pressure characteristics. The vorticity field was deconstructed by Proper Orthogonal Decomposition (POD). The results show that the first two orders of POD modal energy accounted for 75% of the total energy, indicating that the first two modes can be used to identify the large-scale vortex structure. The main water pressure frequency and vortex shedding frequency (f) had a high degree of consistency. Thus, vortex shedding was the main cause of wall water pressure fluctuations. Given the blockage effect, the shear layer’s development spanwise was restricted. Moreover, the blockage effect increased the local flow velocity and accelerated the vortex shedding. The dimensionless time-averaged flow velocity U/U0 increased to 1.5, and the frequency of vortex shedding increased by approximately 25% when the Br increased from 0.067 to 0.25. The frequency increased by 25% when the Ar decreased from 0.5 to 0.2. The experimental results also provide a new idea for optimizing the VIVACE device.

Description of Nonlinear Vortical Flows of Incompressible Fluid in Terms of a Quasi-Potential

As it was shown earlier, a wide class of nonlinear 3-dimensional (3D) fluid flows of incompressible viscous fluid can be described by only one scalar function dubbed the quasi-potential. This class of fluid flows is characterized by a three-component velocity field having a two-component vorticity field. Both these fields may, in general, depend on all three spatial variables and time. In this paper, the governing equations for the quasi-potential are derived and simple illustrative examples of 3D flows in the Cartesian coordinates are presented. The generalisation of the developed approach to the fluid flows in the cylindrical and spherical coordinate frames represents a nontrivial problem that has not been solved yet. In this paper, this gap is filled and the concept of a quasi-potential to the cylindrical and spherical coordinate frames is further developed. A few illustrative examples are presented which can be of interest for practical applications.

The generation of matter–antimatter asymmetries and hypermagnetic fields by the chiral vortical effect of transient fluctuations

We study the contribution of the temperature-dependent chiral vortical effect to the generation and evolution of hypermagnetic fields and matter-antimatter asymmetries, in the symmetric phase of the early Universe, in the temperature range 100 GeV $$\le T \le $$ ≤ T ≤ 10 TeV. Our most important result is that, due to the chiral vortical effect, small overlapping transient fluctuations in the vorticity field in the plasma and temperature of matter degrees of freedom can lead to the generation of strong hypermagnetic fields and matter-antimatter asymmetries, all starting from zero initial values. We show that, either an increase in the amplitudes of the fluctuations of vorticity or temperature, or a decrease in their widths, leads to the production of stronger hypermagnetic fields, and therefore, larger matter-antimatter asymmetries. We have the interesting result that fluctuating vorticity fields are more productive, by many orders of magnitude, as compared to vorticities that are constant in time.

Energy Structure Analysis of Vorticity Driven by Thermal Gradient in Developing Cumulonimbus Clouds and Application to Data Assimilation

<p> It is an essential problem for forecasting Mesoscale Convection Systems to understand the mechanism of interaction between atmospheric flow and vortices with the development of cumulonimbus clouds using a numerical weather model. In this research, potential temperature gradient based vorticity which is the expression of baroclinic is obtained to analyze the energy structure of the vorticity field in developing cumulonimbus. First, applying the variational method enables us to obtain a diagnostic equation in which the equation of motion, conservation law of mass, and entropy are considered as constraints. Second, Fourier analysis was performed on the vorticity field in the cross-section of the convective core in the isolated cumulonimbus simulation. The temporal change of the spectrum of the vorticity field indicates that the rotational intensity of potential temperature gradient based vorticity increases at the same time as the degree of baroclinicity increases. It was also found that the same tendency can be seen in the analysis of the vorticity field of developing clouds using the environment of the heavy rainfall event in the Kuma River basin that occurred on July 4, 2020. We are planning to analyze the vorticity field in the cluster of cumulonimbus clouds and consider the difference in the energy structure of the vorticity field due to the difference in model resolution. Third, we conducted the data assimilation experiment assuming the use of vertical vorticity estimated by doppler radar observation. As a result, the change in the potential temperature and vertical wind through the error covariance matrix generates coherent convection in the computations.</p>

2D Euler Equations with Stratonovich Transport Noise as a Large-Scale Stochastic Model Reduction

The limit from an Euler-type system to the 2D Euler equations with Stratonovich transport noise is investigated. A weak convergence result for the vorticity field and a strong convergence result for the velocity field are proved. Our results aim to provide a stochastic reduction of fluid-dynamics models with three different time scales.

The Godbillon-Vey invariant as topological vorticity compression and obstruction to steady flow in ideal fluids

If the vorticity field of an ideal fluid is tangent to a foliation, additional conservation laws arise. For a class of zero-helicity vorticity fields, the Godbillon-Vey (GV) invariant of foliations is defined and is shown to be an invariant purely of the vorticity, becoming a higher-order helicity-type invariant of the flow. GV ≠ 0 gives both a global topological obstruction to steady flow and, in a particular form, a local obstruction. GV is interpreted as helical compression and stretching of vortex lines. Examples are given where the value of GV is determined by a set of distinguished closed vortex lines.