The stability chart of parallel shear flows with double-diffusive processes ? general properties

1985 ◽  
Vol 19 (3) ◽  
pp. 175-187 ◽  
Author(s):  
M. Magen ◽  
D. Pnueli ◽  
Y. Zvirin
Keyword(s):  
Shear Flows ◽  
General Properties ◽  
Stability Chart ◽  
Parallel Shear Flows ◽  
The Stability ◽  
Diffusive Processes ◽  
Double Diffusive

scholarly journals A General Numerical Method for Analyzing the Linear Stability of Stratified Parallel Shear Flows

2014 ◽  
Vol 31 (12) ◽  
pp. 2795-2808 ◽  
Author(s):  
Tim Rees ◽  
Adam Monahan
Keyword(s):  
Stability Analysis ◽  
Numerical Method ◽  
Shear Flows ◽  
Numerical Solutions ◽  
Analytical Approximations ◽  
Onset Of Turbulence ◽  
Parallel Shear Flows ◽  
Critical Layers ◽  
The Stability ◽  
Stability Results

Abstract The stability analysis of stratified parallel shear flows is fundamental to investigations of the onset of turbulence in atmospheric and oceanic datasets. The stability analysis is performed by considering the behavior of small-amplitude waves, which is governed by the Taylor–Goldstein (TG) equation. The TG equation is a singular second-order eigenvalue problem, whose solutions, for all but the simplest background stratification and shear profiles, must be computed numerically. Accurate numerical solutions require that particular care be taken in the vicinity of critical layers resulting from the singular nature of the equation. Here a numerical method is presented for finding unstable modes of the TG equation, which calculates eigenvalues by combining numerical solutions with analytical approximations across critical layers. The accuracy of this method is assessed by comparison to the small number of stratification and shear profiles for which analytical solutions exist. New stability results from perturbations to some of these profiles are also obtained.

On the stability of parallel shear flows with embedded swirl

2021 ◽  
Vol 150 (4) ◽  
pp. A177-A177
Author(s):  
Lu Zhao ◽  
Saeed Farokhi ◽  
Ray Taghavi
Keyword(s):  
Shear Flows ◽  
Parallel Shear Flows ◽  
The Stability

On the Stability of Parallel Shear Flows with Embedded Swirl

2022 ◽  
Author(s):  
Lu Zhao ◽  
Saeed Farokhi ◽  
Ray Taghavi
Keyword(s):  
Shear Flows ◽  
Parallel Shear Flows ◽  
The Stability

scholarly journals Double-diffusive mixing makes a small contribution to the global ocean circulation

2021 ◽  
Vol 2 (1) ◽  
Author(s):  
Carine G. van der Boog ◽  
Henk A. Dijkstra ◽  
Julie D. Pietrzak ◽  
Caroline A. Katsman
Keyword(s):  
Ocean Circulation ◽  
Mechanical Energy ◽  
Global Ocean ◽  
Small Contribution ◽  
Global Ocean Circulation ◽  
Diffusive Fluxes ◽  
Diffusive Mixing ◽  
Diffusive Processes ◽  
Flowing Waters ◽  
Double Diffusive

AbstractDouble-diffusive processes enhance diapycnal mixing of heat and salt in the open ocean. However, observationally based evidence of the effects of double-diffusive mixing on the global ocean circulation is lacking. Here we analyze the occurrence of double-diffusive thermohaline staircases in a dataset containing over 480,000 temperature and salinity profiles from Argo floats and Ice-Tethered Profilers. We show that about 14% of all profiles contains thermohaline staircases that appear clustered in specific regions, with one hitherto unknown cluster overlying the westward flowing waters of the Tasman Leakage. We estimate the combined contribution of double-diffusive fluxes in all thermohaline staircases to the global ocean’s mechanical energy budget as 7.5 GW [0.1 GW; 32.8 GW]. This is small compared to the estimated energy required to maintain the observed ocean stratification of roughly 2 TW. Nevertheless, we suggest that the regional effects, for example near Australia, could be pronounced.

Stability of a Rigid Body With an Oscillating Particle: An Application of MACSYMA

1985 ◽  
Vol 52 (3) ◽  
pp. 686-692 ◽  
Author(s):  
L. A. Month ◽  
R. H. Rand
Keyword(s):  
Angular Velocity ◽  
Rigid Body ◽  
Classical Problem ◽  
Moment Of Inertia ◽  
Model Parameters ◽  
Stability Chart ◽  
The Stability ◽  
Transition Curves ◽  
Minimum Moment ◽  
Small Angular Velocity

This problem is a generalization of the classical problem of the stability of a spinning rigid body. We obtain the stability chart by using: (i) the computer algebra system MACSYMA in conjunction with a perturbation method, and (ii) numerical integration based on Floquet theory. We show that the form of the stability chart is different for each of the three cases in which the spin axis is the minimum, maximum, or middle principal moment of inertia axis. In particular, a rotation with arbitrarily small angular velocity about the maximum moment of inertia axis can be made unstable by appropriately choosing the model parameters. In contrast, a rotation about the minimum moment of inertia axis is always stable for a sufficiently small angular velocity. The MACSYMA program, which we used to obtain the transition curves, is included in the Appendix.

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