Advances in Rapid Distortion Theory: From Rotating Shear Flows to the Baroclinic Instability

2003 ◽  
Author(s):  
Claude Cambon ◽  
Aziz Salhi
Keyword(s):  
Shear Flows ◽  
Single Point ◽  
Baroclinic Instability ◽  
Vertical Direction ◽  
Rotating Flows ◽  
Vertical Shear ◽  
Stratified Medium ◽  
Rapid Distortion Theory ◽  
System Rotation ◽  
Rotating Shear Flows

The essentials of Rapid Distortion Theory (RDT) are recalled for homogeneous turbulence subjected to rotational mean flows, including its linkage to stability analysis. The latter ‘linkage’ is of particular importance from our viewpoint, since it also attracted the attention of Charles Speziale, resulting in at least two papers (Speziale et al., 1996; Salhi et al., 1997) with particular emphasis on rotating flows. New analytical solutions and related RDT results are presented for shear flows possibly including buoyancy forces, with system rotation or mean density stratification. Finally, combining shear, rotation and stratification, RDT is shown to be pertinent to revisiting the baroclinic instability. This instability results from the tilting of mean isopycnal surfaces under combined effects of vertical shear and system rotation, in a vertically (stably) stratified medium rotating around the vertical direction. In conclusion, the challenge of reproducing RDT dynamics in single-point closure models is briefly discussed, from the viewpoint of structure-based modeling (Cambon et al., 1992; Kassinos et al., 2000).

Advances in Rapid Distortion Theory: From Rotating Shear Flows to the Baroclinic Instability

2005 ◽  
Vol 73 (3) ◽  
pp. 449-460 ◽  
Author(s):  
Aziz Salhi ◽  
Claude Cambon
Keyword(s):  
Stability Analysis ◽  
Reynolds Stress ◽  
Shear Flows ◽  
Baroclinic Instability ◽  
Vertical Direction ◽  
Vertical Shear ◽  
Stratified Medium ◽  
Turbulence Structure ◽  
Rapid Distortion Theory ◽  
System Rotation

The essentials of rapid distortion theory (RDT) are briefly recalled for homogeneous turbulence subjected to rotational mean flows, including its linkage to stability analysis. The latter “linkage” is of particular importance from our viewpoint, since it also attracted the attention of Charles Speziale, resulting in at least two papers [Speziale, C. G., Abid, R., and Blaisdell, G. A., 1996, “On the Consistency of Reynolds Stress Turbulence Closures With Hydrodynamic Stability Theory,” Phys. Fluids, 8, pp. 781–788 and Salhi, A., Cambon, C., and Speziale, C. G., 1997, “Linear Stability Analysis of Plane Quadratic Flows in a Rotating Frame,” Phys. Fluids, 9(8), pp. 2300–2309] with particular emphasis on rotating flows. New analytical solutions and related RDT results are presented for shear flows including buoyancy forces, with system rotation or mean density stratification. Finally, combining shear, rotation and stratification, RDT is shown to be pertinent to revisiting the baroclinic instability. This instability results from the tilting of mean isopycnal surfaces under combined effects of vertical shear and system rotation, in a vertically (stably) stratified medium rotating around the vertical direction. In addition, the challenge of reproducing RDT dynamics in single-point closure models is briefly discussed, from the viewpoint of structure-based modeling [Cambon C., Jacquin, L., and Lubrano, J.-L., 1992, “Towards a New Reynolds Stress Model for Rotating Turbulent Flows,” Phys. Fluids A, 4, pp. 812–824 and Kassinos, S. C., Reynolds, W. C., and Rogers, M. M., 2000, “One-Point Turbulence Structure Tensors,” J. Fluid Mech., 428, pp. 213–248.

scholarly journals Stability Analysis of the Labrador Current

2014 ◽  
Vol 44 (2) ◽  
pp. 445-463 ◽  
Author(s):  
Sören Thomsen ◽  
Carsten Eden ◽  
Lars Czeschel
Keyword(s):  
Stability Analysis ◽  
Growth Rates ◽  
Baroclinic Instability ◽  
Cross Flow ◽  
Vertical Shear ◽  
Maximal Growth ◽  
Phase Velocities ◽  
Labrador Current ◽  
Lateral Mixing ◽  
Weak Stratification

Abstract Mooring observations and model simulations point to an instability of the Labrador Current (LC) during winter, with enhanced eddy kinetic energy (EKE) at periods between 2 and 5 days and much less EKE during other seasons. Linear stability analysis using vertical shear and stratification from the model reveals three dominant modes of instability in the LC: 1) a balanced interior mode with along-flow wavelengths of about 30–45 km, phase velocities of 0.3 m s−1, maximal growth rates of 1 day−1, and surface-intensified but deep-reaching amplitudes; 2) a balanced shallow mode with along-flow wavelengths of about 0.3–1.5 km, phase velocities of 0.55 m s−1, about 3 times larger growth rates, but amplitudes confined to the mixed layer (ML); and 3) an unbalanced symmetric mode with the largest growth rates, vanishing phase speeds, and along-flow structure, and very small cross-flow wavelengths, also confined to the ML. Both balanced modes are akin to baroclinic instability but operate at moderate-to-small Richardson numbers Ri with much larger growth rates as for the quasigeostrophic limit of Ri ≫ 1. The interior mode is found to be responsible for the instability of the LC during winter. Weak stratification and enhanced vertical shear due to local buoyancy loss and the advection of convective water masses from the interior result in small Ri within the LC and up to 3 times larger growth rates of the interior mode in March compared to summer and fall conditions. Both the shallow and the symmetric modes are not resolved by the model, but it is suggested that they might also play an important role for the instability in the LC and for lateral mixing.

Time Domain Simulations on a Single Point Moored Submerged Sphere of Variable Radius

2005 ◽  
Author(s):  
Joa˜o M. B. P. Cruz ◽  
Anto´nio J. N. A. Sarmento
Keyword(s):  
Wave Propagation ◽  
Time Domain ◽  
Physical Phenomenon ◽  
Single Point ◽  
Vertical Direction ◽  
Equation Of Motion ◽  
Hydrodynamic Coefficients ◽  
Energy Converter ◽  
Submerged Sphere ◽  
The Time Domain

This paper presents a different approach to the work developed by Cruz and Sarmento (2005), where the same problem was studied in the frequency domain. It concerns the same sphere, connected to the seabed by a tension line (single point moored), that oscillates with respect to the vertical direction in the plane of wave propagation. The pulsating nature of the sphere is the basic physical phenomenon that allows the use of this model as a simulation of a floating wave energy converter. The hydrodynamic coefficients and diffraction forces presented in Linton (1991) and Lopes and Sarmento (2002) for a submerged sphere are used. The equation of motion in the angular direction is solved in the time domain without any assumption about its output, allowing comparisons with the previously obtained results.

Development of Magnetic Field-Assisted Single-Point Incremental Forming

2021 ◽  
Vol 883 ◽  
pp. 189-194
Author(s):  
Marco Gucciardi ◽  
Derrick Benson ◽  
Livan Fratini ◽  
Gianluca Buffa ◽  
Hitomi Yamaguchi
Keyword(s):  
Magnetic Field ◽  
Magnetic Force ◽  
Incremental Forming ◽  
Single Point ◽  
Vertical Direction ◽  
Aluminum Sheet ◽  
Single Point Incremental Forming ◽  
Vertical Load ◽  
Localized Deformation ◽  
Physical Interference

Single Point Incremental Forming (SPIF) has recently introduced the concept of material formability enhancement through localized deformation. Since material is processed by means of a pin tool attached to spindle, physical interference (especially in vertical direction) limits attainable shapes with the conventional process. The aim of the following work is to increase the variety of achievable geometries with SPIF through in-process magnetic field assistance. An innovative configuration managing SPIF tool movement using magnetic force is proposed. With this in mind, a magnet configuration was designed to generate a vertical load able to plastically deform a 0.5 mm thick AA1100 aluminum sheet. Experiments were carried out to prove the concept by manufacturing a truncated cone; the results demonstrated the feasibility of Magnetic Field-Assisted SPIF.

scholarly journals Instabilities of continuously stratified zonal equatorial jets in a periodic channel model

2002 ◽  
Vol 20 (5) ◽  
pp. 729-740 ◽  
Author(s):  
S. Masina
Keyword(s):  
Channel Model ◽  
Baroclinic Instability ◽  
Phase Speed ◽  
Maximum Velocity ◽  
Equatorial Region ◽  
Eastern Pacific ◽  
Vertical Shear ◽  
Coriolis Parameter ◽  
Vertical Scale ◽  
Surface Jet

Abstract. Several numerical experiments are performed in a nonlinear, multi-level periodic channel model centered on the equator with different zonally uniform background flows which resemble the South Equatorial Current (SEC). Analysis of the simulations focuses on identifying stability criteria for a continuously stratified fluid near the equator. A 90 m deep frontal layer is required to destabilize a zonally uniform, 10° wide, westward surface jet that is symmetric about the equator and has a maximum velocity of 100 cm/s. In this case, the phase velocity of the excited unstable waves is very similar to the phase speed of the Tropical Instability Waves (TIWs) observed in the eastern Pacific Ocean. The vertical scale of the baroclinic waves corresponds to the frontal layer depth and their phase speed increases as the vertical shear of the jet is doubled. When the westward surface parabolic jet is made asymmetric about the equator, in order to simulate more realistically the structure of the SEC in the eastern Pacific, two kinds of instability are generated. The oscillations that grow north of the equator have a baroclinic nature, while those generated on and very close to the equator have a barotropic nature.  This study shows that the potential for baroclinic instability in the equatorial region can be as large as at mid-latitudes, if the tendency of isotherms to have a smaller slope for a given zonal velocity, when the Coriolis parameter vanishes, is compensated for by the wind effect.Key words. Oceanography: general (equatorial oceanography; numerical modeling) – Oceanography: physics (fronts and jets)

Interannual Variability of the North Pacific Subtropical Countercurrent and Its Associated Mesoscale Eddy Field

2010 ◽  
Vol 40 (1) ◽  
pp. 213-225 ◽  
Author(s):  
Bo Qiu ◽  
Shuiming Chen
Keyword(s):  
North Pacific ◽  
Southern Oscillation ◽  
North Pacific Ocean ◽  
Baroclinic Instability ◽  
Mesoscale Eddy ◽  
Vertical Shear ◽  
North Equatorial Current ◽  
Altimeter Data ◽  
Subtropical Countercurrent ◽  
Eddy Field

Abstract Interannual changes in the mesoscale eddy field along the Subtropical Countercurrent (STCC) band of 18°–25°N in the western North Pacific Ocean are investigated with 16 yr of satellite altimeter data. Enhanced eddy activities were observed in 1996–98 and 2003–08, whereas the eddy activities were below average in 1993–95 and 1999–2002. Analysis of repeat hydrographic data along 137°E reveals that the vertical shear between the surface eastward-flowing STCC and the subsurface westward-flowing North Equatorial Current (NEC) was larger in the eddy-rich years than in the eddy-weak years. By adopting a 2½-layer reduced-gravity model, it is shown that the increased eddy kinetic energy level in 1996–98 and 2003–08 is because of enhanced baroclinic instability resulting from the larger vertical shear in the STCC–NEC’s background flow. The cause for the STCC–NEC’s interannually varying vertical shear can be sought in the forcing by surface Ekman temperature gradient convergence within the STCC band. Rather than El Niño–Southern Oscillation signals as previously hypothesized, interannual changes in this Ekman forcing field, and hence the STCC–NEC’s vertical shear, are more related to the negative western Pacific index signals.

scholarly journals Ageostrophic instability in rotating, stratified interior vertical shear flows

2014 ◽  
Vol 755 ◽  
pp. 397-428 ◽  
Author(s):  
Peng Wang ◽  
James C. McWilliams ◽  
Claire Ménesguen
Keyword(s):  
Energy Source ◽  
Kinetic Energy ◽  
Potential Energy ◽  
Gravity Waves ◽  
Shear Flows ◽  
Vertical Shear ◽  
Mean Flow ◽  
Efficient Energy Transfer ◽  
The Mean ◽  
Inertia Gravity Waves

AbstractThe linear instability of several rotating, stably stratified, interior vertical shear flows $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\overline{U}(z)$ is calculated in Boussinesq equations. Two types of baroclinic, ageostrophic instability, AI1 and AI2, are found in odd-symmetric $\overline{U}(z)$ for intermediate Rossby number ($\mathit{Ro}$). AI1 has zero frequency; it appears in a continuous transformation of the unstable mode properties between classic baroclinic instability (BCI) and centrifugal instability (CI). It begins to occur at intermediate $\mathit{Ro}$ values and horizontal wavenumbers ($k,l$) that are far from $l= 0$ or $k = 0$, where the growth rate of BCI or CI is the strongest. AI1 grows by drawing kinetic energy from the mean flow, and the perturbation converts kinetic energy to potential energy. The instability AI2 has inertia critical layers (ICL); hence it is associated with inertia-gravity waves. For an unstable AI2 mode, the coupling is either between an interior balanced shear wave and an inertia-gravity wave (BG), or between two inertia-gravity waves (GG). The main energy source for an unstable BG mode is the mean kinetic energy, while the main energy source for an unstable GG mode is the mean available potential energy. AI1 and BG type AI2 occur in the neighbourhood of $A-S= 0$ (a sign change in the difference between absolute vertical vorticity and horizontal strain rate in isentropic coordinates; see McWilliams et al., Phys. Fluids, vol. 10, 1998, pp. 3178–3184), while GG type AI2 arises beyond this condition. Both AI1 and AI2 are unbalanced instabilities; they serve as an initiation of a possible local route for the loss of balance in 3D interior flows, leading to an efficient energy transfer to small scales.

scholarly journals Maintenance of mid-latitude oceanic fronts by mesoscale eddies

2020 ◽  
Vol 6 (31) ◽  
pp. eaba7880 ◽  
Author(s):  
Zhao Jing ◽  
Shengpeng Wang ◽  
Lixin Wu ◽  
Ping Chang ◽  
Qiuying Zhang ◽  
...  
Keyword(s):  
Heat Transport ◽  
Baroclinic Instability ◽  
Mesoscale Eddies ◽  
Vertical Shear ◽  
Western Boundary ◽  
Boundary Current ◽  
Surface Cooling ◽  
Surface Ocean ◽  
Oceanic Fronts ◽  
Ocean Carbon

Oceanic fronts associated with strong western boundary current extensions vent a vast amount of heat into the atmosphere, anchoring mid-latitude storm tracks and facilitating ocean carbon sequestration. However, it remains unclear how the surface heat reservoir is replenished by ocean processes to sustain the atmospheric heat uptake. Using high-resolution climate simulations, we find that the vertical heat transport by ocean mesoscale eddies acts as an important heat supplier to the surface ocean in frontal regions. This vertical eddy heat transport is not accounted for by the prevailing inviscid and adiabatic ocean dynamical theories such as baroclinic instability and frontogenesis but is tightly related to the atmospheric forcing. Strong surface cooling associated with intense winds in winter promotes turbulent mixing in the mixed layer, destructing the vertical shear of mesoscale eddies. The restoring of vertical shear induces an ageostrophic secondary circulation transporting heat from the subsurface to surface ocean.

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