Spin-up of a stratified fluid: theory and experiment

Buzyna, George; Veronis, George

doi:10.1017/s0022112071002775

Cited by 52 publications

(30 citation statements)

References 8 publications

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“…Note that in this reference frame, the final state will depend on the final density profile: the curvature of the isotherms near the bottom/top of the insulated walls results in radial diffusive mass transport and the associated SweetEddington azimuthal flow. 15,16 The governing equations that describe the motion of an incompressible flow of density in the rotational ͑noniner-tial͒ reference frame in the Boussinesq limit have the following form: 42,43 ١ · û = 0, ͑1a͒…”

Section: A Governing Equationsmentioning

confidence: 99%

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Numerical simulations of nonlinear thermally stratified spin-up in a circular cylinder

2010

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Formation of organized nanostructures from unstable bilayers of thin metallic liquids Phys. Fluids 23, 122105 (2011) Higher-order (2+4) Korteweg-de Vries-like equation for interfacial waves in a symmetric three-layer fluid Phys. Fluids 23, 116602 (2011) Resonant generation of internal waves by short length scale topography Phys. We present a numerical study of incremental spin-up of a thermally stratified fluid enclosed within a right circular cylinder with rigid bottom and side walls and stress-free upper surface. This investigation reveals a feasibility for transition from an axisymmetric initial circulation to nonaxisymmetric flow patterns, and it is motivated by the desire to compare the spin-up for Dirichlet and Neumann thermal boundary conditions. The numerical simulations demonstrate that the destabilizing mechanism is not purely baroclinic but that vertical and horizontal shears may contribute to the instability. By characterizing the azimuthal instabilities without introducing any simplification, we were able to assess to what extent an insulating boundary condition changes the time-dependent emergence of the instability. Our results agree with previous experimental data and provide a framework for understanding the role played by the baroclinic vorticity in the development of instabilities in thermally stratified incremental spin-up flows.

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Section: A Governing Equationsmentioning

confidence: 99%

“…The final state will depend on the final density profile: the curvature of the isotherms near the bottom/top of the insulated walls results in radial diffusive mass transport and the associated Sweet-Eddington azimuthal flow. 15,16 This is a nonlinear question where the interest is in the state of the transient flow.…”

Section: Introductionmentioning

confidence: 99%

Numerical simulations of nonlinear thermally stratified spin-up in a circular cylinder

2010

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“…Results from these studies agreed qualitatively with linear theory (detailed above) but were of insufficient accuracy for a detailed quantitative comparison. More accurate experimental studies were conducted by Buzyna & Veronis (1971), Saunders & Beardsley (1975), and Lee (1975). Buzyna & Veronis (1971) used a salt-stratified solution and photographed the motion of fluid dye to measure the angular displacement of the fluid, whereas Saunders & Beardsley (1975) used a thermally stratified fluid to measure the temperature field with an array of thermistors.…”

Section: Nonlinear Axisymmetric Spin-upmentioning

confidence: 99%

SPIN-UP OF HOMOGENEOUS AND STRATIFIED FLUIDS

Duck

Foster

2001

Annu. Rev. Fluid Mech.

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Key Words rotating flows, spin-down, spin-over, conical flows s Abstract We consider the manner in which a container filled with viscous fluid adjusts to changes in its rotation rate. We begin with homogeneous flows involving small departures in rotation rate from an initial state of solid-body rotation in an axisymmetric container. This is followed by a summary of other more recent developments, including weakly and fully nonlinear calculations and comparison with experiment and the question of spin-down. The question of "spin-over" is addressed, followed by a brief synopsis of free-surface effects, and a discussion of nonaxisymmetric spin-up. The second part of the review focuses on the effects of stratification on the spin-up process. Linearized (low Rossby number) spin-up within a cylindrical container is described. Thereafter, both experimental and nonlinear computational results are described and compared. The final section focuses on stratified spin-up and spin-down in conical geometries, and a number of comparisons between theory and experiment are given.

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“…Flow dynamics is characterized by an additional parameter, the Burger number, B u = NH/fR. The initial phase of stratified spin-up is similar to that of homogeneous spin-up (Benton and Clark [3], Buzyna and Veronis [4], Holton [5], Pedlosky [6]). Near-bottom heavy fluid is transported radially outward causing a strong deformation of isopycnals (surfaces of constant density) near the outer wall.…”

Section: Introductionmentioning

confidence: 99%

Stability of stratified spin-up flows

Smirnov¹

2007

WIT Transactions on Modelling and Simulation, Vol 46

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The stability of stratified rotating flows is investigated by means of laboratory experiments in axisymmetric cylindrical and annular containers with both horizontal and sloping bottoms. The baroclinic current is initiated via incremental spin-up/down of a linearly stratified fluid by an abrupt change in the rotation rate of the system (from Ω ± ∆Ω to Ω). The flow stability depends on the characteristic values of the Rossby number, ε = ∆Ω/Ω, and the Burger number, B u = NH/fR, where f = 2Ω is the Coriolis parameter, R is the characteristic horizontal length scale of the flow, H is the depth of the fluid layer, and N is the buoyancy frequency. Particular attention is given to the nonlinear flow regime (finite Rossby numbers). It is found that axisymmetric spin-up current loses its azimuthal symmetry when B u < 1, and breaks into a system of large-scale cyclonic and anticyclonic vortices with a predominantly vertical axis of rotation. The eddies always develop at the density fronts formed by the corner regions adjacent to the sidewalls of the container. The corner regions reach a quasi-equilibrium state at the characteristic time scale E -1/2 Ω -1 (where E = ν/ΩH 2 is the Ekman number and ν is the kinematic viscosity), which is also observed for homogenous fluids. It is also shown that the stability of the spin-up flow is affected by the bottom slope. In the presence of the latter the bottom boundary layer experiences a qualitatively different behavior. While the density field demonstrates a smooth monotonic behavior in the case of stratified spin-up at all times, it reveals high-frequency fluctuations in the spin-down case, suggesting the turbulent nature of the bottom boundary layer. The results of observations may be found useful in interpreting in-situ measurements of upwelling-and downwelling-favorable oceanic currents in the littoral zones.

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Spin-up of a stratified fluid: theory and experiment

Cited by 52 publications

References 8 publications

Numerical simulations of nonlinear thermally stratified spin-up in a circular cylinder

Numerical simulations of nonlinear thermally stratified spin-up in a circular cylinder

SPIN-UP OF HOMOGENEOUS AND STRATIFIED FLUIDS

Stability of stratified spin-up flows

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