scholarly journals Horizontal shear instabilities in rotating stellar radiation zones

2020 ◽  
Vol 635 ◽  
pp. A133 ◽  
Author(s):  
J. Park ◽  
V. Prat ◽  
S. Mathis
Keyword(s):  
Growth Rate ◽  
Thermal Diffusion ◽  
Turbulent Transport ◽  
Stable Stratification ◽  
Shear Instability ◽  
Inviscid Limit ◽  
Horizontal Shear ◽  
Wide Range ◽  
Inertial Instability ◽  
Shear Instabilities

Context. Rotational mixing transports angular momentum and chemical elements in stellar radiative zones. It is one of the key processes for modern stellar evolution. In the past two decades, an emphasis has been placed on the turbulent transport induced by the vertical shear instability. However, instabilities arising from horizontal shear and the strength of the anisotropic turbulent transport that they may trigger remain relatively unexplored. The weakest point of this hydrodynamical theory of rotational mixing is the assumption that anisotropic turbulent transport is stronger in horizontal directions than in the vertical one. Aims. This paper investigates the combined effects of stable stratification, rotation, and thermal diffusion on the horizontal shear instabilities that are obtained and discussed in the context of stellar radiative zones. Methods. The eigenvalue problem describing linear instabilities of a flow with a hyperbolic-tangent horizontal shear profile was solved numerically for a wide range of parameters. When possible, the Wentzel–Kramers–Brillouin–Jeffreys (WKBJ) approximation was applied to provide analytical asymptotic dispersion relations in both the nondiffusive and highly diffusive limits. As a first step, we consider a polar f-plane where the gravity and rotation vector are aligned. Results. Two types of instabilities are identified: the inflectional and inertial instabilities. The inflectional instability that arises from the inflection point (i.e., the zero second derivative of the shear flow) is the most unstable when at a zero vertical wavenumber and a finite wavenumber in the streamwise direction along the imposed-flow direction. While the maximum two-dimensional growth rate is independent of the stratification, rotation rate, and thermal diffusivity, the three-dimensional inflectional instability is destabilized by stable stratification, while it is stabilized by thermal diffusion. The inertial instability is rotationally driven, and a WKBJ analysis reveals that its growth rate reaches the maximum value of √f(1 − f) in the inviscid limit as the vertical wavenumber goes to infinity, where f is the dimensionless Coriolis parameter. The inertial instability for a finite vertical wavenumber is stabilized as the stratification increases, whereas it is destabilized by the thermal diffusion. Furthermore, we found a selfsimilarity in both the inflectional and inertial instabilities based on the rescaled parameter PeN2 with the Péclet number Pe and the Brunt–Väisälä frequency N.

scholarly journals Numerical Study of Horizontal Shear Instability Waves along Narrow Cold Frontal Rainbands

2011 ◽  
Vol 68 (4) ◽  
pp. 878-903 ◽  
Author(s):  
Masayuki Kawashima
Keyword(s):  
Numerical Study ◽  
Leading Edge ◽  
Shear Instability ◽  
Vertical Shear ◽  
Horizontal Shear ◽  
Edge Waves ◽  
Instability Waves ◽  
Low Level ◽  
Wide Range ◽  
The Mean

Abstract The effects of variations in low-level ambient vertical shear and horizontal shear on the alongfront variability of narrow cold frontal rainbands (NCFRs) that propagate into neutral and slightly unstable environments are investigated through a series of idealized cloud-resolving simulations. In cases initialized with slightly unstable sounding and weak ambient cross-frontal vertical shears, core-gap structures of precipitation along NCFRs occur that are associated with wavelike disturbances that derive their kinetic energy mainly from the mean local vertical shear and buoyancy. However, over a wide range of environmental conditions, core-gap structures of precipitation occur because of the development of a horizontal shear instability (HSI) wave along the NCFRs. The growth rate and amplitude of the HSI wave decrease significantly as the vertical shear of the ambient cross-front wind is reduced. These decreases are a consequence of the enhancement of the low-level local vertical shear immediately behind the leading edge. The strong local vertical shear acts to damp the vorticity edge wave on the cold air side of the shear zone, thereby suppressing the growth of the HSI wave through the interaction of the two vorticity edge waves. It is also noted that the initial wavelength of the HSI wave increases markedly with increasing horizontal shear. The local vertical shear around the leading edge is shown to damp long HSI waves more strongly than short waves, and the horizontal shear dependency of the wavelength is explained by the decrease in the magnitude of the vertical shear relative to that of the horizontal shear.

Inertial instability in rotating and stratified fluids: barotropic vortices

2007 ◽  
Vol 583 ◽  
pp. 379-412 ◽  
Author(s):  
R. C. KLOOSTERZIEL ◽  
G. F. CARNEVALE ◽  
P. ORLANDI
Keyword(s):  
Reynolds Number ◽  
Angular Momentum ◽  
Velocity Profile ◽  
Vortex Dynamics ◽  
Horizontal Shear ◽  
Numerical Studies ◽  
Inertial Instability ◽  
Equilibration Process ◽  
Shear Instabilities ◽  
Number Form

The unfolding of inertial instability in intially barotropic vortices in a uniformly rotating and stratified fluid is studied through numerical simulations. The vortex dynamics during the instability is examined in detail. We demonstrate that the instability is stabilized via redistribution of angular momentum in a way that produces a new equilibrated barotropic vortex with a stable velocity profile. Based on extrapolations from the results of a series of simulations in which the Reynolds number and strength of stratification are varied, we arrive at a construction based on angular momentum mixing that predicts the infinite-Reynolds-number form of the equilibrated vortex toward which inertial instability drives an unstable vortex. The essential constraint is conservation of total absolute angular momentum. The construction can be used to predict the total energy loss during the equilibration process. It also shows that the equilibration process can result in anticyclones that are more susceptible to horizontal shear instabilities than they were initially, a phenomenon previously observed in laboratory and numerical studies.

scholarly journals Layer formation in horizontally forced stratified turbulence: connecting exact coherent structures to linear instabilities

2017 ◽  
Vol 832 ◽  
pp. 409-437 ◽  
Author(s):  
Dan Lucas ◽  
C. P. Caulfield ◽  
Rich R. Kerswell
Keyword(s):  
Coherent Structures ◽  
Stable Stratification ◽  
Finite Amplitude ◽  
Shear Instability ◽  
Stratified Turbulence ◽  
Layer Formation ◽  
Horizontal Shear ◽  
Chaotic Flow ◽  
Background Shear ◽  
First Time

We consider turbulence in a stratified ‘Kolmogorov’ flow, driven by horizontal shear in the form of sinusoidal body forcing in the presence of an imposed background linear stable stratification in the third direction. This flow configuration allows the controlled investigation of the formation of coherent structures, which here organise the flow into horizontal layers by inclining the background shear as the strength of the stratification is increased. By numerically converging exact steady states from direct numerical simulations of chaotic flow, we show, for the first time, a robust connection between linear theory predicting instabilities from infinitesimal perturbations to the robust finite-amplitude nonlinear layered state observed in the turbulence. We investigate how the observed vertical length scales are related to the primary linear instabilities and compare to previously considered examples of shear instability leading to layer formation in other horizontally sheared flows.

scholarly journals Vertical shear mixing in stellar radiative zones

2019 ◽  
Vol 82 ◽  
pp. 167-173
Author(s):  
V. Prat ◽  
J. Guilet ◽  
M. Vialler ◽  
E. Müller
Keyword(s):  
Numerical Simulations ◽  
Thermal Diffusion ◽  
Stellar Evolution ◽  
Turbulent Transport ◽  
Shear Instability ◽  
Vertical Shear ◽  
Jean Paul ◽  
Chemical Stratification ◽  
Shear Mixing

Jean-Paul Zahn’s formalism for vertical shear mixing is used in several stellar evolution codes, but the physics of the shear instability in stellar radiative zones is still not completely understood. Over the last few years, numerical simulations have provided new constraints on the shear instability, including the effect of thermal diffusion and chemical stratification. We present here new simulations that show the effect of viscosity on the vertical turbulent transport due to the shear instability.

Effects of Schmidt number on the short-wavelength instabilities in stratified vortices

2019 ◽  
Vol 867 ◽  
pp. 765-803
Author(s):  
Suraj Singh ◽  
Manikandan Mathur
Keyword(s):  
Growth Rate ◽  
Stagnation Point ◽  
Short Wavelength ◽  
Schmidt Number ◽  
Maximum Growth ◽  
Stable Stratification ◽  
Oscillatory Instability ◽  
Inviscid Limit ◽  
Small Diffusion ◽  
Axisymmetric Vortex

We present a local stability analysis to investigate the effects of differential diffusion between momentum and density (quantified by the Schmidt number $Sc$) on the three-dimensional, short-wavelength instabilities in planar vortices with a uniform stable stratification along the vorticity axis. Assuming small diffusion in both momentum and density, but arbitrary values for $Sc$, we present a detailed analytical/numerical analysis for three different classes of base flows: (i) an axisymmetric vortex, (ii) an elliptical vortex and (iii) the flow in the neighbourhood of a hyperbolic stagnation point. While a centrifugally stable axisymmetric vortex remains stable for any $Sc$, it is shown that $Sc$ can have significant effects in a centrifugally unstable axisymmetric vortex: the range of unstable perturbations increases when $Sc$ is taken away from unity, with the extent of increase being larger for $Sc\ll 1$ than for $Sc\gg 1$. Additionally, for $Sc>1$, we report the possibility of oscillatory instability. In an elliptical vortex with a stable stratification, $Sc\neq 1$ is shown to non-trivially influence the three different inviscid instabilities (subharmonic, fundamental and superharmonic) that have been previously reported, and also introduce a new branch of oscillatory instability that is not present at $Sc=1$. The unstable parameter space for the subharmonic (instability IA) and fundamental (instability IB) inviscid instabilities are shown to be significantly increased for $Sc<1$ and $Sc>1$, respectively. Importantly, for sufficiently small and large $Sc$, respectively, the maximum growth rate for instabilities IA and IB occurs away from the inviscid limit. The new oscillatory instability (instability III) is shown to occur only for sufficiently small $Sc<1$, the signature of which is nevertheless present with zero growth rate in the inviscid limit. The Schmidt number is then shown to play no role in the evolution of transverse perturbations on the flow around a hyperbolic stagnation point with a stable stratification. We conclude by discussing the physical length scales associated with the $Sc\neq 1$ instabilities, and their potential relevance in various realistic settings.

Instabilities of Jets and Fronts and their Nonlinear Evolution

2018 ◽  
Author(s):  
Vladimir Zeitlin
Keyword(s):  
Nonlinear Evolution ◽  
Baroclinic Instability ◽  
Trapped Modes ◽  
Nonlinear Saturation ◽  
Parallel Flows ◽  
Inertial Instability ◽  
Shear Instabilities ◽  
Linear And Nonlinear ◽  
Flow Configurations ◽  
Characteristic Features

Notions of linear and nonlinear hydrodynamic (in)stability are explained and criteria of instability of plane-parallel flows are presented. Instabilities of jets are investigated by direct pseudospectral collocation method in various flow configurations, starting from the classical barotropic and baroclinic instabilities. Characteristic features of instabilities are displayed, as well as typical patterns of their nonlinear saturation. It is shown that in the Phillips model of Chapter 5, new ageostrophic Rossby–Kelvin and shear instabilities appear at finite Rossby numbers. These instabilities are interpreted in terms of resonances among waves counter-propagating in the flow. It is demonstrated that the classical inertial instability is a specific case of ageostrophic baroclinic instability. At the equator it appears also in the barotropic configuration, and is related to resonances of Yanai waves. The nature of the inertial instability in terms of trapped modes is established. A variety of instabilities of density fronts is displayed.

Frontogenesis and frontal arrest of a dense filament in the oceanic surface boundary layer

2017 ◽  
Vol 837 ◽  
pp. 341-380 ◽  
Author(s):  
Peter P. Sullivan ◽  
James C. McWilliams
Keyword(s):  
Boundary Layer ◽  
Turbulent Mixing ◽  
Shear Instability ◽  
Upper Ocean ◽  
Surface Boundary ◽  
Horizontal Shear ◽  
Boundary Layer Turbulence ◽  
Filament Axis ◽  
Small Width ◽  
The Cross

The evolution of upper ocean currents involves a set of complex, poorly understood interactions between submesoscale turbulence (e.g. density fronts and filaments and coherent vortices) and smaller-scale boundary-layer turbulence. Here we simulate the lifecycle of a cold (dense) filament undergoing frontogenesis in the presence of turbulence generated by surface stress and/or buoyancy loss. This phenomenon is examined in large-eddy simulations with resolved turbulent motions in large horizontal domains using${\sim}10^{10}$grid points. Steady winds are oriented in directions perpendicular or parallel to the filament axis. Due to turbulent vertical momentum mixing, cold filaments generate a potent two-celled secondary circulation in the cross-filament plane that is frontogenetic, sharpens the cross-filament buoyancy and horizontal velocity gradients and blocks Ekman buoyancy flux across the cold filament core towards the warm filament edge. Within less than a day, the frontogenesis is arrested at a small width,${\approx}100~\text{m}$, primarily by an enhancement of the turbulence through a small submesoscale, horizontal shear instability of the sharpened filament, followed by a subsequent slow decay of the filament by further turbulent mixing. The boundary-layer turbulence is inhomogeneous and non-stationary in relation to the evolving submesoscale currents and density stratification. The occurrence of frontogenesis and arrest are qualitatively similar with varying stress direction or with convective cooling, but the detailed evolution and flow structure differ among the cases. Thus submesoscale filament frontogenesis caused by boundary-layer turbulence, frontal arrest by frontal instability and frontal decay by forward energy cascade, and turbulent mixing are generic processes in the upper ocean.

scholarly journals Aircraft measurements of gravity waves in the upper troposphere and lower stratosphere during the START08 field experiment

2015 ◽  
Vol 15 (13) ◽  
pp. 7667-7684 ◽  
Author(s):  
Fuqing Zhang ◽  
Junhong Wei ◽  
Meng Zhang ◽  
K. P. Bowman ◽  
L. L. Pan ◽  
...  
Keyword(s):  
Power Law ◽  
Gravity Waves ◽  
Lower Stratosphere ◽  
Potential Temperature ◽  
Shear Instability ◽  
Aircraft Measurements ◽  
Upper Troposphere ◽  
Airborne Measurements ◽  
Wide Range

Abstract. This study analyzes in situ airborne measurements from the 2008 Stratosphere–Troposphere Analyses of Regional Transport (START08) experiment to characterize gravity waves in the extratropical upper troposphere and lower stratosphere (ExUTLS). The focus is on the second research flight (RF02), which took place on 21–22 April 2008. This was the first airborne mission dedicated to probing gravity waves associated with strong upper-tropospheric jet–front systems. Based on spectral and wavelet analyses of the in situ observations, along with a diagnosis of the polarization relationships, clear signals of mesoscale variations with wavelengths ~ 50–500 km are found in almost every segment of the 8 h flight, which took place mostly in the lower stratosphere. The aircraft sampled a wide range of background conditions including the region near the jet core, the jet exit and over the Rocky Mountains with clear evidence of vertically propagating gravity waves of along-track wavelength between 100 and 120 km. The power spectra of the horizontal velocity components and potential temperature for the scale approximately between ~ 8 and ~ 256 km display an approximate −5/3 power law in agreement with past studies on aircraft measurements, while the fluctuations roll over to a −3 power law for the scale approximately between ~ 0.5 and ~ 8 km (except when this part of the spectrum is activated, as recorded clearly by one of the flight segments). However, at least part of the high-frequency signals with sampled periods of ~ 20–~ 60 s and wavelengths of ~ 5–~ 15 km might be due to intrinsic observational errors in the aircraft measurements, even though the possibilities that these fluctuations may be due to other physical phenomena (e.g., nonlinear dynamics, shear instability and/or turbulence) cannot be completely ruled out.

Influence of Turbulent Flow Characteristics and Coherent Vortices on the Pressure Recovery of Annular Diffusers: Part A — Experimental Results

2015 ◽  
Author(s):  
Marcus Kuschel ◽  
Bastian Drechsel ◽  
David Kluß ◽  
Joerg R. Seume
Keyword(s):  
Boundary Layer ◽  
High Pressure ◽  
Static Pressure ◽  
Turbulent Transport ◽  
Axial Flow ◽  
Pressure Recovery ◽  
Turbulence Structure ◽  
Reynolds Stresses ◽  
Wide Range ◽  
Operating Points

Exhaust diffusers downstream of turbines are used to transform the kinetic energy of the flow into static pressure. The static pressure at the turbine outlet is thus decreased by the diffuser, which in turn increases the technical work as well as the efficiency of the turbine significantly. Consequently, diffuser designs aim to achieve high pressure recovery at a wide range of operating points. Current diffuser design is based on conservative design charts, developed for laminar, uniform, axial flow. However, several previous investigations have shown that the aerodynamic loading and the pressure recovery of diffusers can be increased significantly if the turbine outflow is taken into consideration. Although it is known that the turbine outflow can reduce boundary layer separations in the diffuser, less information is available regarding the physical mechanisms that are responsible for the stabilization of the diffuser flow. An analysis using the Lumley invariance charts shows that high pressure recovery is only achieved for those operating points in which the near-shroud turbulence structure is axi-symmetric with a major radial turbulent transport component. This turbulent transport originates mainly from the wake and the tip vortices of the upstream rotor. These structures energize the boundary layer and thus suppress separation. A logarithmic function is shown that correlates empirically the pressure recovery vs. the relevant Reynolds stresses. The present results suggest that an improved prediction of diffuser performance requires modeling approaches that account for the anisotropy of turbulence.

Dependence of Microstructures and Mechanical Properties on the Growth Rate and Composition in Directionally Solidified Mg-Gd Alloys

2022 ◽  
Vol 327 ◽  
pp. 82-97
Author(s):  
He Qin ◽  
Guang Yu Yang ◽  
Shi Feng Luo ◽  
Tong Bai ◽  
Wan Qi Jie
Keyword(s):  
Mechanical Properties ◽  
Growth Rate ◽  
Tensile Strength ◽  
Ultimate Tensile Strength ◽  
Dendritic Structure ◽  
Directionally Solidified ◽  
Dendrite Morphology ◽  
Microstructural Parameters ◽  
Wide Range ◽  
Microstructures And Mechanical Properties

Microstructures and mechanical properties of directionally solidified Mg-xGd (5.21, 7.96 and 9.58 wt.%) alloys were investigated at a wide range of growth rates (V = 10-200 μm/s) under the constant temperature gradient (G = 30 K/mm). The results showed that when the growth rate was 10 μm/s, different interface morphologies were observed in three tested alloys: cellular morphology for Mg-5.21Gd alloy, a mixed morphology of cellular structure and dendritic structure for Mg-7.96Gd alloy and dendrite morphology for Mg-9.58Gd alloy, respectively. Upon further increasing the growth rate, only dendrite morphology was exhibited in all experimental alloys. The microstructural parameters (λ1, λ2) decreased with increasing the growth rate for all the experimental alloy, and the measured λ1 and λ2 values were in good agreement with Trivedi model and Kattamis-Flemings model, respectively. Vickers hardness and the ultimate tensile strength increased with the increase of the growth rate and Gd content, while the elongation decreased gradually. Furthermore, the relationships between the hardness, ultimate tensile strength, the growth rate and the microstructural parameters were discussed and compared with the previous experimental results.

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