Spin Up And Spin Down Experiments In A Closed Basin

Spin up and Spin down Experiments in a closed Basin Moutushi Tanjia Zakir Arizona State University

Outline • • • • • • • •

Introduction Background Theoretical analysis Physical system and Parameters Experimental facilities and Techniques Experimental Results. Conclusion Future work

Introduction • Laboratory Experiments are carried out for the flow of homogenous fluids along a bottom topography in the presence of background rotation. • Laboratory experiments are concerned with the development of motion fields initiated by impulsively establishing up-welling (spin down) or down-welling (spin up) favorable flows along a conical shape bottom topography. •

Our primary objective is to obtain both qualitative observations and quantitative data of the resulting motion field of impulsively started spin up and spin down favorable oceanic flows.

Background •

It is widely recognized that the dynamical characteristics of oceanic bottom boundary layer are important in considering such matters as sediment transport , turbulent mixing of the oceanic interior, suitability as a habitat for aquatic biota and the specification of boundary conditions for coastal general circulation.

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Experiments are being conducted at the Laboratoire des Ecoulements Geophysiques et industriels( LEGI), Grenoble, France in an effort to better parameterize bottom boundary layers in a large scale oceanic flows over slopping surfaces.

Background(continued) •

A series of laboratory experiments were conducted in Coriolis lab, Grenoble concerning the flow of homogeneous and linearly stratified fluids along a continuous shelf slope system in the presence of background rotation.

•

The continuous shelf slope topography used in Grenoble

Background( continued) •

•

•

Experiments in Grenoble for turbulent and transitional flows have shown the difference in flow between spin up and spin down. Those experiments has led to investigate the flow for spin and spin down over slopping surfaces in the presence of background rotation. Bottom topography used in ASU tank

Theoretical Analysis • A theory is developed in Grenoble in order to relate the shear stress at the bottom of the tank to the velocity of the fluid within it. • The equation for evolution of azimuthal velocity was addressed using integral angular momentum balance and employing conservation of mass. • The equation for evolution of azimuthal velocity : 2 ∂u u∗ r 2 − = hr 2 θ I + cos β ∂t

hB + h

∫

hB

∂ 2 (r ur uθ )dz ∂r

2 ∂u u∗ r 2 − = hr 2 θ I + cos β ∂t

Where

hB + h

∫

hB

∂ 2 (r u r uθ )dz ∂r

u∗

is the shear stress velocity

uθ I

Is the azimuthal velocity of the fluid in the bulk of the flow

uθ , u r

Are azimuthal and radial velocity components ( for boundary layer and bulk of the flow)

h = h(r )

β hB = hB (r )

Is the local height of the fluid column Is the local slope of the bottom topography Is the height of the bottom topography

Theoretical analysis ( continued) • Vishal Vasan has addressed the theory related to the flow for laminar case. • Using the concept of integral momentum balance and conservation of mass he developed the equation for evolution of azimuthal velocity for the laminar flow. ∂uθ I ∂ r 2uθ I hδ E cos β r 2uθ I 3 2 hr + ( ) = −δ E Ωhr uθ I − (5δ E sin β − hKδ E tan β ) ∂t ∂r 8 8 2 2

2

2 2

δE =

ν Ω cos β

Experimental Facility Physical Parameters: Diameter of the tank: d=178 cm. Maximum depth of the water: H= 15.7cm. Angle of the slope: 100  d H

100

Experimental technique : PIV Average Maximum radius of laser sheet: 65.5 cm.

Camera Laser

Maximum radius of the water level: 71.5 cm.

Tank

Water level

Height of the water level: 12.7 cm. Fig: Schematic diagram of the experimental setup for PIV

Experimental technique Flow Visualization by electrolytic Dye production The working fluid is the aqueous solution of thymol blue( pH indicator) The solution was made acidic ( orange color) close to the point of becoming basic Thin straight platinum wire was used as negative electrode (cathode). Two platinum wire was placed perpendicular to the main flow direction.  dc voltage is applied to produce blue dye around the cathode wire

Anode  wire

Power supply

Platinum  cathode wire

Top view of the tank

Governing Parameters

Experimental procedure First a background rotation of a fixed Coriolis parameter(Ω)is applied to the homogeneous fluid in the tank. • When there is a zero relative motion (Solid body rotation), Flows are driven impulsively by changing the turntable rotation rate. • If the rotation of the tank is increased then the fluid has to Spin Up to the new rotation rate. • If the rotation of the tank is reduced then the fluid has to Spin down to the new rotation rate. • The ratio of the change in the rotation rate (ΔΩ) to the final rotation rate (Ω) tells us how strong the motion of the fluid is relative to the rotating tank. For geophysical applications we like to keep this ratio •

small.

Flow visualization

Spin Up: Ro # 0.4 ( Experiments with lid)

Flow visualization

Spin Up: Ro # 0.4 ( Experiments without lid)

Flow visualization

Spin Up: Ro # 0.15 ( Experiments with lid)

Flow visualization

Spin Up: Ro #0.15 ( Experiments without lid)

Flow visualization

Spin Down: Ro # 0.15 ( Experiments with lid)

Flow visualization

Spin Down : Ro # 0.15 ( Experiments without lid)

Flow visualization

Spin down: Ro # 0.4 ( Without lid) 

Conclusion