Symmetric Stability of Zonal Flow under Full-Component Coriolis Force —Effect of the Horizontal Component of the Planetary Vorticity—

2009 ◽  
Vol 87 (4) ◽  
pp. 747-753 ◽  
Author(s):  
Toshihisa ITANO ◽  
Kiyoshi MARUYAMA
Keyword(s):  
Coriolis Force ◽  
Zonal Flow ◽  
Horizontal Component ◽  
Force Effect ◽  
Symmetric Stability

Flows in a rotating spherical shell: the equatorial case

1994 ◽  
Vol 276 ◽  
pp. 233-260 ◽  
Author(s):  
A. Colin de Verdière ◽  
R. Schopp
Keyword(s):  
Angular Momentum ◽  
Rotation Axis ◽  
Dynamic Pressure ◽  
Vertical Component ◽  
Low Frequency ◽  
Zonal Flow ◽  
Horizontal Component ◽  
Meridional Plane ◽  
Earth’S Rotation ◽  
Earth's Rotation

It is well known that the widely used powerful geostrophic equations that single out the vertical component of the Earth's rotation cease to be valid near the equator. Through a vorticity and an angular momentum analysis on the sphere, we show that if the flow varies on a horizontal scale L smaller than (Ha)1/2 (where H is a vertical scale of motion and a the Earth's radius), then equatorial dynamics must include the effect of the horizontal component of the Earth's rotation. In equatorial regions, where the horizontal plane aligns with the Earth's rotation axis, latitudinal variations of planetary angular momentum over such scales become small and approach the magnitude of its radial variations proscribing, therefore, vertical displacements to be freed from rotational constraints. When the zonal flow is strong compared to the meridional one, we show that the zonal component of the vorticity equation becomes (2Ω.Δ)u1 = g/ρ0)(∂ρ/a∂θ). This equation, where θ is latitude, expresses a balance between the buoyancy torque and the twisting of the full Earth's vorticity by the zonal flow u1. This generalization of the mid-latitude thermal wind relation to the equatorial case shows that u1 may be obtained up to a constant by integrating the ‘observed’ density field along the Earth's rotation axis and not along gravity as in common mid-latitude practice. The simplicity of this result valid in the finite-amplitude regime is not shared however by the other velocity components.Vorticity and momentum equations appropriate to low frequency and predominantly zonal flows are given on the equatorial β-plane. These equatorial results and the mid-latitude geostrophic approximation are shown to stem from an exact generalized relation that relates the variation of dynamic pressure along absolute vortex lines to the buoyancy field. The usual hydrostatic equation follows when the aspect ratio δ = H/L is such that tan θ/δ is much larger than one. Within a boundary-layer region of width (Ha)1/2 and centred at the equator, the analysis shows that the usually neglected Coriolis terms associated with the horizontal component of the Earth's rotation must be kept.Finally, some solutions of zonally homogeneous steady equatorial inertial jets are presented in which the Earth's vorticity is easily turned upside down by the shear flow and the correct angular momentum ‘Ωr2cos2(θ)+u1rCos(θ)’ contour lines close in the vertical–meridional plane.

Parallel rotation for negating Coriolis force effect on heat transfer

2020 ◽  
Vol 124 (1274) ◽  
pp. 581-596
Author(s):  
A. Sarja ◽  
P. Singh ◽  
S.V. Ekkad
Keyword(s):  
Heat Transfer ◽  
Fluid Flow ◽  
Coriolis Force ◽  
Turbine Blades ◽  
Vortex Pair ◽  
Internal Cooling ◽  
Interesting Phenomenon ◽  
Steady State Condition ◽  
Force Effect ◽  
Cooling Channels

ABSTRACTGas turbine blades feature multi-pass internal cooling channels, through which relatively colder air bled from the compressor is routed to cool internal walls. Under rotation, due to the influence of Coriolis force and centrifugal buoyancy, heat transfer at the trailing side enhances and that at the leading side reduces, for a radially outward flow. This non-uniform temperature distribution results in increased thermal stress, which is detrimental to blade life. In this study, a rotation configuration is presented which can negate the Coriolis force effect on heat and fluid flow, thereby maintaining uniform heat transfer on leading and trailing walls. A straight, smooth duct of unit aspect ratio is considered to demonstrate the concept and understand the fluid flow within the channel and its interaction with the walls. The new design is compared against the conventional rotation design. Numerical simulations under steady-state condition were carried out at a Reynolds number of 25000, where the Rotation numbers were varied as 0, 0.1, 0.15, 0.2, 0.25. Realisable version of k-$\varepsilon$ model was used for turbulence modelling. It was observed that new rotation (parallel) configuration’s heat transfer on leading and trailing sides were near similar, and trailing side was marginally higher compared to leading side. An interesting phenomenon of secondary Coriolis effect is reported which accounts for the minor differences in heat transfer augmentation between leading and trailing walls. Due to centrifugal buoyancy, the fluid is pushed towards the radially outward wall, resulting in a counter-rotating vortex pair, which also enhances the heat transfer on leading and trailing walls when compared to stationary case.

Effect of Top and Bottom Boundary Conditions on Symmetric Instability under Full-Component Coriolis Force

2011 ◽  
Vol 68 (11) ◽  
pp. 2771-2782 ◽  
Author(s):  
Toshihisa Itano ◽  
Akira Kasahara
Keyword(s):  
Boundary Conditions ◽  
Coriolis Force ◽  
Unbounded Domain ◽  
Plane Waves ◽  
Low Frequency ◽  
Zonal Flow ◽  
Internal Gravity Waves ◽  
Bottom Boundary ◽  
Stable Conditions ◽  
Symmetric Instability

Abstract The linear stability of a zonal flow confined in a domain within horizontal top and bottom boundaries is examined under full consideration of the Coriolis force. The basic zonal flow is assumed to be in thermal wind balance with the density field and to be sheared in both vertical and horizontal directions under statically and inertially stable conditions. By imposing top and bottom boundary conditions in this framework, the number of wave modes increases to four, instead of two in an unbounded domain, as already reported in studies on internal gravity waves. The four modes are classified into two pairs of high- and low-frequency modes: the high modes are superinertial and the low modes are subinertial. The discriminant of symmetric instability is nevertheless determined by the sign of the potential vorticity of the basic zonal flow, as in the case of an unbounded domain. The solutions satisfying the top and bottom boundary conditions are interpreted as the superposition of incident and reflected waves, revealing that the neutral solutions consist of two neutral plane waves with oppositely directed vertical group velocities. This may explain why the properties of wave behavior, such as the instability criteria, remain the same in both the bounded and unbounded domains, although the manifestation of wave activity, such as the order of dispersion relation, is quite different in the two cases. Furthermore, the slope of the constant momentum surface, the slope of the isopycnic surface including the nontraditional effect of the Coriolis force, and the ratio between the frequencies of gravity and inertial waves form an essential set of parameters for symmetric motion. The combination of these dimensionless quantities determines the fundamental nature of symmetric motions, such as stability, regardless of boundary conditions with and without the horizontal component of the planetary vorticity.

The Coriolis force effect on molten silicon convection in a rotating crucible

1992 ◽  
Vol 35 (10) ◽  
pp. 2551-2555 ◽  
Author(s):  
Kakimoto Koichi ◽  
Watanabe Masahito ◽  
Eguchi Minoru ◽  
Hibiya Taketoshi
Keyword(s):  
Coriolis Force ◽  
Molten Silicon ◽  
Force Effect

scholarly journals Symmetric Stability of Compressible Zonal Flows on a Generalized Equatorial β Plane

2008 ◽  
Vol 65 (6) ◽  
pp. 1927-1940 ◽  
Author(s):  
Mark D. Fruman ◽  
Theodore G. Shepherd
Keyword(s):  
Angular Momentum ◽  
Linear Stability ◽  
Euler Equations ◽  
Coriolis Force ◽  
Sufficient Conditions ◽  
Zonal Flow ◽  
Positive Definiteness ◽  
Planetary Rotation ◽  
The Stability ◽  
Invariant Functional

Abstract Sufficient conditions are derived for the linear stability with respect to zonally symmetric perturbations of a steady zonal solution to the nonhydrostatic compressible Euler equations on an equatorial β plane, including a leading order representation of the Coriolis force terms due to the poleward component of the planetary rotation vector. A version of the energy–Casimir method of stability proof is applied: an invariant functional of the Euler equations linearized about the equilibrium zonal flow is found, and positive definiteness of the functional is shown to imply linear stability of the equilibrium. It is shown that an equilibrium is stable if the potential vorticity has the same sign as latitude and the Rayleigh centrifugal stability condition that absolute angular momentum increase toward the equator on surfaces of constant pressure is satisfied. The result generalizes earlier results for hydrostatic and incompressible systems and for systems that do not account for the nontraditional Coriolis force terms. The stability of particular equilibrium zonal velocity, entropy, and density fields is assessed. A notable case in which the effect of the nontraditional Coriolis force is decisive is the instability of an angular momentum profile that decreases away from the equator but is flatter than quadratic in latitude, despite its satisfying both the centrifugal and convective stability conditions.

Effects of Coriolis force on flow in rotating diffusers

AIAA Journal ◽  
1997 ◽  
Vol 35 ◽  
pp. 1164-1170
Author(s):  
Hide S. Koyama ◽  
Kuniharu Uchikawa ◽  
Hani H. Nigim
Keyword(s):  
Coriolis Force
Sign in / Sign up

Export Citation Format

Share Document