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The article discusses various aspects of the interaction of vortices with the barotropic flow. Vortex interaction with a flow results in rotation variants, nutational oscillations, and unlimited stretching of its core. The vortex remains in a localized formation, with the semi-axes of the ellipse experiencing fluctuations near an average value in the first two cases. In the third case, the vortex is significantly elongated, and its shape in the horizontal plane changes as follows: one axis of the ellipse increases, and the other decreases. In this case, the vortex, when viewed from above, stretches into a thread, while remaining ellipsoidal. These vortex formations are called filaments. The latter arise from initially almost circular vortices in the horizontal plane and represent structures with non-zero vorticity elongated in one direction. Here, we aim to study the energy transformation of a vortex during its evolution process, mainly due to changes in its shape by stretching. The energy evolution of a mesoscale vortex located in the Norwegian Sea is analyzed using GLORYS12V1 ocean reanalysis data to verify the theoretical conclusions. During the evolution, the vortex is found to transform from a round shape and becomes elongated, and after three weeks its longitudinal scale becomes 4 times larger than the transverse one. During the transformation of a vortex, the kinetic energy and available potential energy decrease respectively by 3 times and 1.7 times. Concurrently, the total energy of the vortex is found to decrease by 2.3 times. We argue that the stretching of vortices results in a loss of energy as well as its redistribution from mesoscale to submesoscale. The lost part of the energy returns to the flow and results in the occurrence of the reverse energy cascade phenomenon. [ABSTRACT FROM AUTHOR]

The runaway condition is unsteady and is of significant importance in pump turbines. In this research, the shear-stress transport (SST) k - ω turbulence model is used to simulate the unsteady flow in the vaneless region and the runner of a prototype pump turbine. The characteristics of pressure fluctuations, vortex identification based on Q criterion and local entropy generation rate (LEGR) in the pump turbine under runaway condition are studied, and the relationships of these physical quantities in the vaneless region are determined. Internal flow research reveals the motion and transmission characteristics of vortices in the vaneless region and the runner. The results show that the vortices that move clockwise in the vaneless region are responsible for the flow separation, the increase of LEGR, and the generation of the characteristic frequency 1.4 f n of these physical quantities (pressure fluctuations, Q criterion and LEGR). In runner, it is found that the characteristic frequency of pressure fluctuation is 3.6 f n , which satisfies a linear relationship with the characteristic frequency 1.4 f n in the vaneless region. The vortices, moving in the vaneless and runner region, interact with the blades of runner and mainly contribute to the pressure fluctuation characteristic frequency in the runner. • Unsteady flow and fluctuations of a pump turbine under runaway condition are studied. • Flow separation and vortices cause energy dissipation in vaneless region and runner. • Vortex motion greatly affects pressure fluctuation in vaneless region. • Interaction between blade and vortex causes pressure fluctuation frequency in runner. [ABSTRACT FROM AUTHOR]

The accuracy, robustness, dissipation characteristics and efficiency of several structured and unstructured grid methods are investigated with reference to the low Mach double vortex pairing flow problem. The aim of the study is to shed light into the numerical advantages and disadvantages of different numerical discretizations, principally designed for shock-capturing, in low Mach vortical flows. The methods include structured and unstructured finite volume and Lagrange-Remap methods, with accuracy ranging from 2nd to 9th-order, with and without applying low-Mach corrections. Comparison of the schemes is presented for the vortex evolution, momentum thickness, as well as for their numerical dissipation versus the viscous and total dissipation. The study shows that the momentum thickness and large scale features of a basic vortical structure are well resolved even at the lowest grid resolution of 32×32 provided that the numerical schemes are of a high-order of accuracy or the numerical framework is sufficiently non-dissipative. The implementation of the finite volume methods in unstructured triangular meshes provides the best results even without low Mach number corrections provided that a higher-order advective discretization for the advective fluxes is employed. The compressible Lagrange-Remap framework is computationally the fastest one, although the numerical error for the momentum thickness does not reduce as fast as for other numerical schemes and computational frameworks, e.g., when higher-order schemes are utilized. It is also shown that the low-Mach number correction has a lesser effect on the results as the order of the spatial accuracy increases. [ABSTRACT FROM AUTHOR]