Stability Of Stratified Spin-up Flows
Author(s)
S. A. Smirnov
Abstract
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, Bu = NH/fR, where f = 2 Ω 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 Bu < 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/ ΩH2
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.
Keywords: geophysical systems, rotating stratified flows, spin-up, flow
instability.
Keywords
geophysical systems, rotating stratified flows, spin-up, flow
instability.
Related Book
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