Prograde and retrograde precession of a fluid-filled cylinder

We numerically study precession driven flows in a cylindrical container whose nutation angle varies between 60 and 90 degrees for prograde and retrograde precession. For prograde precession we observe sharp transitions between a laminar and a turbulent flow state with low and high geostrophic axisymmetric flow components related with a centrifugal instability, while for retrograde precession a rather smooth transition between a low state and a high state occurs. At the same time prograde and perpendicular precession shows an abrupt breakdown of the flow directly excited by the forcing mechanism, which is not the case for retrograde motion. We characterize the corresponding flow states in terms of the directly driven, non-axisymmetric Kelvin mode, the axisymmetric geostrophic mode, and an axisymmetric poloidal flow which is promising for precession-driven dynamo action. The latter issue is discussed with particular view on an optimal parameter choice for the DRESDYN dynamo project.

Influence of Shock Wave on Loss and Breakdown of Tip-Leakage Vortex in Turbine Rotor with Varying Backpressure

In modern turbine rotors, tip-leakage flow is a common phenomenon that accounts for about 1/3 of the stage loss. Studies show that as the imposed load increases, a shock wave appears in the tip region, which causes a significant interference on the leakage vortex. In the present study, numerical simulations are carried out to investigate the influence of the shock wave on the loss and breakdown of the tip-leakage vortex. The obtained results indicate that with no effective control on the flow, the loss of the leakage vortex has an approximate exponential growth up to about 10 times as the outlet Mach number increases from 0.67 to 1.15 and the corresponding proportion in the total loss increases sharply to 30.2%. It is found that the stagnation position of the breakdown changes with the backpressure and the amplitude of variation along the axial direction is up to 0.13 Cx. It is inferred that the breakdown of the leakage vortex core may be affected by the periodical passing of downstream blade and the induced pressure fluctuation may result in additional vibration in this rotor blade. The leakage vortex is unstable in supersonic flow with a shock wave and it may transfer to a flow with a low-velocity bubble in its core region. It is concluded that the leakage vortex breakdown mainly originates from interferences of the shock wave, while the internal cause of such breakdown is the centrifugal instability of the vortex.

On the settling depth of meltwater escaping from beneath Antarctic ice shelves

Antarctic glacial meltwater is thought to play an important role in determining large-scale Southern Ocean climate trends, yet recent modeling efforts have proceeded without a good understanding of how its vertical distribution in the water column is set. To rectify this, here we conduct new large-eddy simulations of the ascent of a buoyant meltwater plume after its escape from beneath an Antarctic ice shelf. We find that the meltwater’s settling depth is primarily a function of the buoyancy forcing per unit width of the source and the ambient stratification, consistent with the classical theory of turbulent buoyant plumes and in contrast to previous work that suggested an important role for centrifugal instability. Our results further highlight the significant role played by localized variability in stratification; this helps explain observed interannual variability in the vertical meltwater distribution near Pine Island Glacier. Because of the vast heterogeneity in mass loss rates and ambient conditions at different Antarctic ice shelves, a dynamic parameterization of meltwater settling depth may be crucial for accurately simulating high-latitude climate in a warming world; we discuss how this may be developed following this work, and where the remaining challenges lie.

A computational modeling on transient heat and fluid flow through a curved duct of large aspect ratio with centrifugal instability

Due to remarkable applications of the curved ducts in engineering fields, scientists have paid much attention to invent new characteristics of curved-duct flow in mechanical systems. In the ongoing study, a computational modeling of fluid flow and energy distribution through a curved rectangular duct of large aspect ratio is presented. Governing equations are enumerated by using a spectral-based numerical technique together with the function expansion and collocation method. The main purpose of the paper is to analyze the effect of centrifugal force in the flow transition as well as heat transfer in the fluid. The investigations are performed for the aspect ratio, Ar = 4; the curvature ratio, $$\delta = 0.5$$ δ = 0.5 ; the Grashof number, $${\text{Gr}} = 1000$$ Gr = 1000 ; and varying the Dean number, $$0 < {\text{Dn}} \le 1000.$$ 0 < Dn ≤ 1000 . It is found that various types of flow regimes including steady-state and irregular oscillations occur as Dn is increased. To well understand the characteristics of the flow phase spaces and power spectrum of the solutions are performed. Next, pattern variations of axial and secondary flow velocity with isotherms are illustrated for different Dn’s. It is revealed that the flow velocity and the isotherms are significantly influenced by the duct curvature and the aspect ratio. Convective heat transfer and temperature gradients are calculated which explores that the fluids are diversified due to centrifugal instability, and as a consequence the overall heat transfer is enhanced significantly in the curved duct.

Magnetic inhibition of the recollimation instability in relativistic jets

ABSTRACT In this paper, we describe the results of three-dimensional relativistic magnetohydrodynamic simulations aimed at probing the role of regular magnetic field on the development of the instability that accompanies recollimation of relativistic jets. In particular, we studied the recollimation driven by the reconfinement of jets from active galactic nuclei (AGN) by the thermal pressure of galactic coronas. We find that a relatively weak azimuthal magnetic field can completely suppress the recollimation instability in such jets, with the critical magnetization parameter σcr &lt; 0.01. We argue that the recollimation instability is a variant of the centrifugal instability (CFI) and show that our results are consistent with the predictions based on the study of magnetic CFI in rotating fluids. The results are discussed in the context of AGN jets in general and the nature of the Fanaroff–Riley morphological division of extragalactic radio sources in particular.

Centrifugal Instability of a Geostrophic Jet

&lt;p&gt;Oceanic and Atmospheric jets with sufficiently strong anticyclonic vorticity are subject to centrifugal instabilities. This mechanism is relatively fast in comparison to barotropic and baroclinic instabilities and require non-conservative forces that mix the fluid properties. In this work, we present a novel approach to compute the linear stability characteristics of both barotropic and baroclinic jets. This enables us to compute the growth rates and spatial structures very accurately and efficiently. Subsequently, by integrating the fully nonlinear, non-hydrostatic dynamics using the spectrally accurate numerical model SPINS, we validate the predictions of the linear theory and then investigate the nonlinear equilibration that results. Depending on the Reynolds number of the flows, there are instances where a secondary instability occurs that eventually produces vortical structures, some of which are themselves subject to centrifugal instabilities. This idealized investigation quantifies the effects of centrifugal instabilities as an initial step to determine how to parameterize them.&lt;/p&gt;&lt;p&gt;&amp;#160;&lt;/p&gt;

Effect of Pressure Gradient on the Development of Görtler Vortices

Boundary layers over concave surfaces may become unstable due to centrifugal instability that manifests itself as stationary streamwise counter rotating vortices. The centrifugal instability mechanism in boundary layers has been extensively studied and there is a large number of publications addressing different aspects of this problem. The results on the effect of pressure gradient show that favorable pressure gradients are stabilizing and adverse pressure gradient enhances the instability. The objective of the present investigation is to complement those works, looking particularly at the effect of pressure gradient on the stability diagram and on the determination of the spanwise wave number corresponding to the fastest growth. This study is based on the classic linear stability theory, where the parallel boundary layer approximation is assumed. Therefore, results are valid for Görtler numbers above 7, the lower limit where local mode linear stability analysis was identified in the literature as valid. For the base flow given by the Falkner-Skan solution, the linear stability equations are solved by a shooting method where the eigenvalues are the Görtler number, the spanwise wavenumber and the growth rate. The results show stabilization due to favorable pressure gradient as the constant amplification rate curves are displaced to higher Görtler numbers, with the opposite effect for adverse pressure gradient. Results previously unavailable in the literature identifying the fastest growing mode spanwise wavelength for a range of Falkner-Skan acceleration parameters are presented.

Propagation, cocoon formation, and resultant destabilization of relativistic jets

ABSTRACT A cocoon is a by-product of a propagating jet that results from shock heating at the jet head. Herein, considering simultaneous cocoon formation, we study the stability of relativistic jets propagating through the uniform ambient medium. Using a simple analytic argument, we demonstrate that independent from the jet launching condition, the effective inertia of the jet is larger than that of the cocoon when the fully relativistic jet oscillates radially owing to the pressure mismatch between jet and cocoon. In such situations, it is expected that the onset condition for the oscillation-induced Rayleigh–Taylor instability is satisfied at the jet interface, resulting in the destabilization of the relativistic jet during its propagation. We have quantitatively verified and confirmed our prior expectation by performing relativistic hydrodynamic simulations in three dimensions. The possible occurrences of the Richtmyer–Meshkov instability, oscillation-induced centrifugal instability, and Kelvin–Helmholtz instability are also discussed.