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Spin up and Spin down Experiments in a closed Basin Moutushi Tanjia Zakir Environmental Fluid Dynamics 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.
•
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 with a different bottom topography. 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.
Experimental Results Evolution of azimuthal velocity with time ( Ro # 0.2) r=0.37 0.2
u/U0
0.1
V1 U1 V2 U2 V3 U3 V4 U4
0.1
v/V0
0
0 Time Series Ro=0.2, r=0.37
0.1 U/U0 & V/U0
0.1 0.2 0.3
0.2 0.3
0.5
0.5
0.6
0.6
0.7
2
3
4
5
6 t/T
7
8
Spin up Ro # 0.2
9
10
11
0.4
0.4
0.7 1
r=0.37
0.2
0.8 2
3
4
5
6
t/T
7
Spin up Ro #0.2
8
9
10
11
Evolution of azimuthal velocity with time r=0.5 0.2
u/U0
0.1
0 0.1
0.2
0.2
U/U0 &V/U0
Time Series Ro=0.2, r=0.5
0.1
0.3 0.4
0.3
0.5
0.6
0.6
0.7
0.7 2
3
4
5
6 t/T
7
8
9
10
11
0.4
0.5
0.8 1
V1 U1 V2 U2 V3 U3 V4 U4
0.1
v/V0
0
r=0.5
0.2
0.8 2
Spin Up Ro #0.2
3
4
5
6
t/T
7
8
9
10
11
Evolution of azimuthal velocity with time r=0.65 0.2
u/U0
0.1
Time Series Ro=0.2, r=0.65
0 0.1
0.2
0.2
U/U0 & V/U0
0.1
0.3 0.4
0.3
0.5
0.6
0.6
0.7
0.7 2
3
4
5
6 t/T
7
8
9
10
11
0.4
0.5
0.8 1
V1 U1 V2 U2 V3 U3 V4 U4
0.1
v/V0
0
radius = 0.65
0.2
0.8 2
Spin Up Ro #0.2
3
4
5
6
t/T
7
8
9
10
11
Evolution of azimuthal velocity with time r = 0.77 radius =0.77 0.2
u/U0
0.1
0.2 0.1
v/V0
0
Time Series Ro=0.2, r=0.77
0
0.1
0.2
0.2
U/U0 & V/U0
0.1
0.3
0.3
0.4
0.4 0.5
0.5
0.6
0.6
0.7
0.7
0.8 1
V1 U1 V2 U2 V3 U3 V4 U4
2
3
4
5
6 t/T
7
8
9
10
11
0.8 2
Spin up , Ro # 0.2
3
4
5
6
t/T
7
8
9
10
11
Evolution of Azimuthal velocity with time (Spin Down) r = 0.37 1.2
u/U0
V1 U1 V2 U2 V3 U3 V4 U4
1.2 1
U/U0 & V/U0
0.8 0.6 0.4 0.2
0.8 0.6
0.4 0.2
0 0.2 1
radius =0.37
1.4
v/V0
1 Time Series Ro=0.2, r=0.37
0
2
3
4
5
6 t/T
7
8
9
10
11
0.2 2
3
Spin Down, Ro # 0.2
4
5
6
t/T
7
8
9
10
11
Evolution of Azimuthal velocity with time r = 0.5 1.4
u/U0
1.2
1
1
0.8 0.6 0.4
0.8 0.6
0.4 0.2
0.2
0 0.2
0 0.2 0
V1 U1 V2 U2 V3 U3 V4 U4
1.4
v/V0
U/U0 & V/U0
Time Series Ro=0.2, r=0.5
1.2
radius =0.5
1.6
2
4
6
8
10 t/T
12
14
16
18
20
0.4 2
3
Spin Down, Ro # 0.2
4
5
6
t/T
7
8
9
10
11
Evolution of Azimuthal velocity with time r= 0.65 1.4
u/U0
V1 U1 V2 U2 V3 U3 V4 U4
1.6
v/V0
1
1.4
0.8
1.2
0.6 0.4 0.2
1 0.8
0.6 0.4
0
0.2
0.2 0.4 0
radius = 0.65
1.8
U/U0 & V/U0
Time Series Ro=0.2, r=0.65
1.2
0 2
4
6
8
10 t/T
12
14
16
18
20
0.2 2
3
Spin Down, Ro # 0.2
4
5
6
t/T
7
8
9
10
11
Evolution of Azimuthal velocity with time r= 0.77 1.4
u/U0
radius = 0.77
1.8
V1 U1 V2 U2 V3 U3 V4 U4
1.6
v/V0
1.4
1
1.2
0.8
U/U0 & V/U0
Time Series Ro=0.2, r=0.77
1.2
0.6 0.4
1 0.8
0.6 0.4
0.2
0.2
0 0.2 1
0 2
3
4
5
6 t/T
7
8
9
10
11
0.2 2
3
Spin Down, Ro# o.2
4
5
6
t/T
7
8
9
10
11
Radial velocity profile for azimuthal velocity Radial velocity profile for U, Ro# 0.2
0.1 0
0.5
0.1
0.4
0.3
t/T=2 t/T=5 t/T=8 t/T=10
0.3 U/U0
t/T=2 t/T=5 t/T=8 t/T=10
0.2 U/U0
Radial velocity profile for U, Ro# 0.2
0.6
0.2
0.4 0.1
0.5
0
0.6 0.7 0.35
0.4
0.45
0.5
0.55
0.6 r/R
0.65
0.7
Spin Up , Ro # 0.2
0.75
0.8
0.85
0.1 0.35
0.4
0.45
0.5
0.55
0.6 r/R
0.65
0.7
Spin Down , Ro # 0.2
0.75
0.8
0.85
Radial velocity profile for radial velocity Radial velocity profile for V, Ro# 0.2
0.12
t/T=2 t/T=5 t/T=8 t/T=10
0.1
V/U0
0.08
0
0.06
0.02
0.04
0.04
0.02
V/U0
0.06 0.08
0 0.02 0.35
Radial velocity profile for V, Ro# 0.2
0.02
0.1 0.4
0.45
0.5
0.55
0.6 r/R
0.65
0.7
0.75
0.8
0.85
0.12
t/T=2 t/T=5 t/T=8 t/T=10
0.14
Spin Down, Ro # 0.2
0.16 0.35
0.4
0.45
0.5
0.55
0.6 r/R
0.65
Spin Up, Ro # 0.2
0.7
0.75
0.8
0.85
Radial velocity (U) from four runs :Spin Up Run 1:t/T=5 Run 3:t/T=5 Run 2:t/T=5 Run 4:t/T=5
Radial velocity profiles for U at 2 rotations for four Runs 0
Run 1:t/T=2 Run 2:t/T=2 Run 3:t/T=2 Run 4:t/T=2
0.1
Radial velocity profiles for U at 5 rotations for four Runs
0 0.1 0.2
0.3
0.3
U/U0
U/U0
0.2
0.4
0.4
0.5
0.5
0.6
0.6
0.35
0.4
0.45
0.5
0.55
0.6 r/R
0.65
0.7
0.75
0.8
0.35
0.85
0.4
0.45
2 rotation Run 1:t/T=8 Run 3:t/T=8 Run 2:t/T=8 Run 4:t/T=8
0.55
0.6 r/R
0.65
0.7
0.75
0.8
0.85
5 rotation Run 1:t/T=10 Run 3:t/T=10 Run 2:t/T=10 Run 4:t/T=10
Radial velocity profiles for U at 8 rotations for four Runs
0
Radial velocity profiles for U at 10 rotations for four Runs
0 0.1
0.2
0.2
0.3
0.3
U/U0
U/U0
0.1
0.4
0.4
0.5
0.5
0.6
0.6
0.35
0.5
0.4
0.45
0.5
0.55
0.6 r/R
8 rotation
0.65
0.7
0.75
0.8
0.35
0.85
Ro #0.2
0.4
0.45
0.5
0.55
0.6 r/R
0.65
10 rotation
0.7
0.75
0.8
0.85
Run 1:t/T=2 Run 3:t/T=2 Run 2:t/T=2 Run 4:t/T=2
Radial velocity (U) from four runs :Spin Down Radial velocity profiles for U at 2 rotations for four Runs
Radial velocity profiles for U at 5 rotations for four Runs
0.5 0.5
0.4
0.4
0.1
0.2 0.1
0
0
0.1
0.4
0.45
0.5
0.55
0.6 r/R
0.65
0.7
0.75
0.8
0.85
0.1
0.35
0.4
0.45
0.5
2 rotation Run 1:t/T=8 Run 2:t/T=8 Run 3:t/T=8 Run 4:t/T=8
0.5 0.4
0.6 r/R
0.65
0.7
0.75
0.8
0.85
Radial velocity profiles for U at 10 rotations for four Runs Run 1:t/T=10 Run 2:t/T=10 Run 3:t/T=10 Run 4:t/T=10
0.5 0.4
0.3
0.3
0.2
U/U0
U/U0
0.55
5 rotation
Radial velocity profiles for U at 8 rotations for four Runs
0.1
0.2 0.1
0
0
0.1
0.35
0.3
0.2
U/U0
U/U0
0.3
0.35
Run 1:t/T=5 Run 2:t/T=5 Run 3:t/T=5 Run 4:t/T=5
0.4
0.45
0.5
0.55
0.6 r/R
8 rotation
0.65
0.7
0.75
0.8
0.85
0.1
0.35
Ro #0.2
0.4
0.45
0.5
0.55
0.6 r/R
0.65
10 rotation
0.7
0.75
0.8
0.85
Evolution of azimuthal velocity with time ( Ro # 0.15) r = 0.37 U1 V1 U3 V3 U2 V2 U4 V4 0.2
u/U0
Time Series Ro=0.15, r=0.37
0.1
0.1
v/V0
0
0
0.1 U/ U0 & V/U0
0.1
0.2
0.2
0.3
0.3
0.4
0.4
0.5
0.5
0.6
0.6 1
radius =0.3
0.2
2
3
4
5
6 t/T
7
8
9
10
11
2
Spin Up : Ro # 0.15
3
4
5
6
t/T
7
8
9
10
11
Evolution of azimuthal velocity with time r = 0.5 0.2
u/U0
0.1
V1 U1 V2 U2 V3 U3 V4 U4
0.1
v/V0
0
0.1
0.1 U/U0 & V/U0
Time Series Ro=0.15, r=0.5
0
0.2
0.2
0.3
0.3
0.4
0.4
0.5
0.5
0.6
0.6
0.7 1
radius= 0.5
0.2
2
3
4
5
6 t/T
7
8
9
10
11
0.7 2
3
Spin Up : Ro # 0.15
4
5
6
t/T
7
8
9
10
11
Evolution of azimuthal velocity with time r =0.65 0.2
u/U0
0.1
0.1
0.1 U/U0 & V/U0
0
Time Series Ro=0.15, r=0.65
0.1
v/V0
0
0.2
0.2
0.3
0.3
0.4
0.4
0.5
0.5
0.6 0.7 1
radius =0.65
0.2
0.6 2
3
4
5
6 t/T
7
8
9
10
11
0.7 2
Spin Up : Ro # 0.15
3
4
5
6
t/T
7
8
9
10
V1 U1 V2 U2 V3 U3 V4 U4
11
Evolution of azimuthal velocity with time r = 0.77 0.1
u/U0
0.1
v/V0
0
radius =0.77
0.2
Time Series Ro=0.15, r=0.77
0 0.1
0.1 0.2 0.3
0.3
0.4
0.4
0.5
0.5 0.6 1
V1 U1 V2 U2 V3 U3 V4 U4
U/U0 & V/U0
0.2
0.6
2
3
4
5
6 t/T
7
8
9
10
11
2
3
Spin Up : Ro # 0.15
4
5
6
t/T
7
8
9
10
11
Evolution of Azimuthal velocity with time (Spin Down) r = 0.37 0.4
u/U0
0.2
0.2 0.1 0
0.1
0
0.1
0.1
0.2
0.2 0.3 1
V1 U1 V2 U2 V3 U3 V4 U4
0.3
Ro=0.15, r=0.37
Time Series Ro=0.15, r=0.37
v/V0
0.3
Time series for different Run
0.4
0.3 2
3
4
5
6 t/T
7
8
9
10
11
0.4 2
3
4
Spin Down : Ro # 0.15
5
6
t/T
7
8
9
10
11
Evolution of Azimuthal velocity with time r = 0.5 0.5
u/U0
0.3
0.3
0.2
0.2
0.1 0
0
0.1
0.2
0.2 2
3
4
5
6 t/T
7
8
9
10
11
0.1
0.1
0.3 1
V1 U1 V2 U2 V3 U3 V4 U4
0.4
v/V0
Ro=0.15, r=0.5
Time Series Ro=0.15, r=0.5
0.4
Time series for different Run
0.5
0.3 2
3
Spin Down : Ro # 0.15
4
5
6
t/T
7
8
9
10
11
Evolution of Azimuthal velocity with time r = 0.65 0.6
u/U0 v/V0
0.4
0.3
0.3 0.2 0.1
0.2
0
0.1
0.1 2
3
4
5
6 t/T
7
8
9
10
11
0.1
0
0.2 1
V1 U1 V2 U2 V3 U3 V4 U4
0.4
Ro=0.15, r=0.65
Time Series Ro=0.15, r=0.65
0.5
Time series for different Run
0.5
0.2 2
3
Spin Down : Ro # 0.15
4
5
6
t/T
7
8
9
10
11
Evolution of Azimuthal velocity with time r = 0.77 0.6
u/U0
0.4
0.4
0.3
0.3
0.2 0.1
0.1 0
0.1
0.1 2
3
4
5
6 t/T
7
8
9
10
11
0.2
0
0.2 1
V1 U1 V2 U2 V3 U3 V4 U4
0.5
v/V 0
Ro=0.15, r=0.77
Time Series Ro=0.15, r=0.77
0.5
Time series for different Run
0.6
0.2 2
3
Spin Down : Ro # 0.15
4
5
6
t/T
7
8
9
10
11
Radial velocity profile for azimuthal velocity ( Ro # 0.15) Radial velocity profile for U, Ro# 0.15
0
0.5
0.2
0.4
0.3
0.3
t/T=2 t/T=5 t/T=8 t/T=10
U/U0
U/U0
0.1
0.4
0.2
0.5
0.1 t/T=2 t/T=5 t/T=8 t/T=10
0.6 0.7 0.35
Radial velocity profile for U, Ro# 0.15
0.6
0.4
0.45
0.5
0.55
0.6 r/R
0.65
Spin Up
0.7
0.75
0.8
0.85
0 0.1 0.35
0.4
0.45
0.5
0.55
0.6 r/R
0.65
Spin Down
0.7
0.75
0.8
0.85
Radial velocity profile for radial velocity ( Ro # 0.15) Radial velocity profile for V, Ro# 0.15
0.14
t/T=2 t/T=5 t/T=8 t/T=10
0.12 0.1
0.04
0.02 0
0.06 V/V0
V/V0
t/T=2 t/T=5 t/T=8 t/T=10
0.06
0.08
0.04
0.02 0.04
0.02
0.06
0
0.08
0.02 0.04 0.35
Radial velocity profile for V, Ro# 0.15
0.08
0.1 0.4
0.45
0.5
0.55
0.6 r/R
0.65
Spin Up
0.7
0.75
0.8
0.85
0.12 0.35
0.4
0.45
0.5
0.55
0.6 r/R
0.65
Spin Down
0.7
0.75
0.8
0.85
Radial velocity (U) from four runs :Spin Up Radial velocity profiles for U at 2 rotations for four Runs 0
0.1
Radial velocity profiles for U at 5 rotations for four Runs
Run 1:t/T=2 Run 2:t/T=2 Run 3:t/T=2 Run 4:t/T=2
0
Run 1:t/T=5 Run 2:t/T=5 Run 3:t/T=5 Run 4:t/T=5
0.1
0.2
U/U0
0.2
U/U0
0.3
0.3
0.4
0.4
0.5
0.5
0.6 0.6 0.35
0.4
0.45
0.5
0.55
0.6 r/R
0.65
0.7
0.75
0.8
0.35
0.85
0.4
0.45
0.5
2 Rotation
0.6 r/R
0.65
0.7
Radial velocity profiles for U at 8 rotations for four Runs Run 1:t/T=8 Run 2:t/T=8 Run 3:t/T=8 Run 4:t/T=8
0.1
Run 1:t/T=10 Run 2:t/T=10 Run 3:t/T=10 Run 4:t/T=10
U/U0
U/U0
0.3
0.4
0.4
0.5
0.5
0.6
0.6 0.55
0.6 r/R
0.65
8 Rotation
0.7
0.75
0.8
0.1
0.3
0.5
0.85
0
0.2
0.45
0.8
Radial velocity profiles for U at 10 rotations for four Runs
0.2
0.4
0.75
5 Rotation
0
0.35
0.55
0.35
0.85
Ro # 0.15
0.4
0.45
0.5
0.55
0.6 r/R
0.65
10 Rotation
0.7
0.75
0.8
0.85
Radial velocity (U) from four runs :Spin Down Radial velocity profiles for U at 2 rotations for four Runs
0.6
Run 1:t/T=2 Run 2:t/T=2 Run 3:t/T=2 Run 4:t/T=2
0.5 0.4
Run 1:t/T=5 Run 2:t/T=5 Run 3:t/T=5 Run 4:t/T=5
0.5 0.4 0.3 U/U0
0.3 U/U0
Radial velocity profiles for U at 5 rotations for four Runs
0.6
0.2
0.2
0.1
0.1
0
0
0.1
0.1
0.2 0.35
0.4
0.45
0.5
0.55
0.6 r/R
0.65
0.7
0.75
0.8
0.2 0.35
0.85
0.4
0.45
Radial velocity profiles for U at 8 rotations for four Runs Run 1:t/T=8 Run 2:t/T=8 Run 3:t/T=8 Run 4:t/T=8
0.5 0.4
0.65
0.7
0.75
0.8
0.85
Run 1:t/T=10 Run 2:t/T=10 Run 3:t/T=10 Run 4:t/T=10
0.5 0.4
0.3 U/U0
U/U0
0.6 r/R
Radial velocity profiles for U at 10 rotations for four Runs
0.6
0.3 0.2
0.2
0.1
0.1
0
0
0.1
0.1
0.2 0.35
0.55
5 Rotation
2 Rotation 0.6
0.5
0.4
0.45
0.5
0.55
0.6 r/R
0.65
8 Rotation
0.7
0.75
0.8
0.2 0.35
0.85
Ro # 0.15
0.4
0.45
0.5
0.55
0.6 r/R
10 Rotation
0.65
0.7
0.75
0.8
0.85
Evolution of azimuthal velocity with time ( Ro # 0.4) r =0.37 r =0.5 0.2
V/U0
0.4
U/U0
0.2
Time Series Ro=0.4, r=0.37
0
V/U0
Time Series Ro=0.4, r=0.5
0.2 0.4
U/U0
0
0.2 0.4
0.6
0.6
0.8
0.8
1
1 1.2 0
1
2
3
4
5 t/T
6
7
8
9
10
Spin Up
1.2 0
1
2
3
4
5 t/T
6
7
8
9
10
Evolution of azimuthal velocity with time r= 0.65
r= 0.77
0.4
V/U0
0.4
U/U0
V/U0
0.2
0
Time Series Ro=0.4, r=0.65
Time Series Ro=0.4, r=0.65
0.2
0.2
U/U0
0
0.2
0.4
0.4
0.6
0.6
0.8
0.8
1 1.2 0
1 1
2
3
4
5 t/T
6
7
8
9
10
1.2 0
1
2
Spin Up ( Ro #0.4)
3
4
5 t/T
6
7
8
9
10
Evolution of Azimuthal velocity with time (Spin Down) r = 0.37
r = 0.5
0.8
V/U0
0.7
1.2
U/U0
0.6
V/U0 U/U0
Time Series Ro=0.4, r=0.37
1
0.5 Time Series Ro=0.4, r=0.5
0.8
0.4 0.3
0.6
0.2
0.4
0.1 0
0.2
0.1 0.2 0
0 2
4
6
8
t/T
10
12
14
16
18
0.2 0
Ro # 0.4
2
4
6
8
t/T
10
12
14
16
18
Evolution of Azimuthal velocity with time r = 0.65
r = 0.77
1
V/U0 U/U0
V/U0
0.8
U/U0
0.6
0.6
0.4
0.4
0.2
0.2 0
0
0.2
0.2 0.4 0
1
Time Series Ro=0.4, r=0.65
0.8 Time Series Ro=0.4, r=0.65
2
4
6
8
t/T
10
12
14
16
18
0.4 0
2
Spin Down ( Ro #0.4)
4
6
8
t/T
10
12
14
16
18
Radial velocity profile for azimuthal velocity ( Ro # 0.4) Radial velocity profile for U,Ro #0.4
0.2 0
Radial velocity profile for U,Ro #0.4
0.9
t/T=2 t/T=5 t/T=8 t/T=10
t/T=2 t/T=5 t/T=8 t/T=10
0.8 0.7
0.6
0.2
0.5
U/U0
U/U0
0.4 0.6
0.4 0.3 0.2
0.8
0.1 1 1.2 0.35
0
0.4
0.45
0.5
0.55
0.6 r/R
Spin Up
0.65
0.7
0.75
0.8
0.85
0.1 0.35
0.4
0.45
0.5
0.55
0.6 r/R
Spin Down
0.65
0.7
0.75
0.8
0.85
Radial velocity profile for radial velocity ( Ro # 0.4) Radial velocity profile for V,Ro #0.4
0.3
t/T=2 t/T=5 t/T=8 t/T=10
0.25
Radial velocity profile for V,Ro #0.4
0
t/T=2 t/T=5 t/T=8 t/T=10
0.02 0.04
0.2
0.06
V/U0
V/U0
0.15 0.1
0.08 0.1 0.12
0.05
0.14
0 0.05 0.35
0.16
0.4
0.45
0.5
0.55
0.6 r/R
0.65
Spin Up
0.7
0.75
0.8
0.85
0.18 0.35
0.4
0.45
0.5
0.55
0.6 r/R
0.65
0.7
Spin Down
0.75
0.8
0.85
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 • Flows in the shallow water spin up and spin down faster then the flow in the deep water. • There is a evidence of periodic flow blocking for spin up at high Rossby number. • High Rossby number can make the flow unstable in case of spin up. • Low Rossby number can make the flow unstable in case of spin down ( centrifugal instability ) • Rossby number and flow direction along a slope has significant impact along the flow.
Future work
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.
•
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 with a different bottom topography. 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.
Experimental Results Evolution of azimuthal velocity with time ( Ro # 0.2) r=0.37 0.2
u/U0
0.1
V1 U1 V2 U2 V3 U3 V4 U4
0.1
v/V0
0
0 Time Series Ro=0.2, r=0.37
0.1 U/U0 & V/U0
0.1 0.2 0.3
0.2 0.3
0.5
0.5
0.6
0.6
0.7
2
3
4
5
6 t/T
7
8
Spin up Ro # 0.2
9
10
11
0.4
0.4
0.7 1
r=0.37
0.2
0.8 2
3
4
5
6
t/T
7
Spin up Ro #0.2
8
9
10
11
Evolution of azimuthal velocity with time r=0.5 0.2
u/U0
0.1
0 0.1
0.2
0.2
U/U0 &V/U0
Time Series Ro=0.2, r=0.5
0.1
0.3 0.4
0.3
0.5
0.6
0.6
0.7
0.7 2
3
4
5
6 t/T
7
8
9
10
11
0.4
0.5
0.8 1
V1 U1 V2 U2 V3 U3 V4 U4
0.1
v/V0
0
r=0.5
0.2
0.8 2
Spin Up Ro #0.2
3
4
5
6
t/T
7
8
9
10
11
Evolution of azimuthal velocity with time r=0.65 0.2
u/U0
0.1
Time Series Ro=0.2, r=0.65
0 0.1
0.2
0.2
U/U0 & V/U0
0.1
0.3 0.4
0.3
0.5
0.6
0.6
0.7
0.7 2
3
4
5
6 t/T
7
8
9
10
11
0.4
0.5
0.8 1
V1 U1 V2 U2 V3 U3 V4 U4
0.1
v/V0
0
radius = 0.65
0.2
0.8 2
Spin Up Ro #0.2
3
4
5
6
t/T
7
8
9
10
11
Evolution of azimuthal velocity with time r = 0.77 radius =0.77 0.2
u/U0
0.1
0.2 0.1
v/V0
0
Time Series Ro=0.2, r=0.77
0
0.1
0.2
0.2
U/U0 & V/U0
0.1
0.3
0.3
0.4
0.4 0.5
0.5
0.6
0.6
0.7
0.7
0.8 1
V1 U1 V2 U2 V3 U3 V4 U4
2
3
4
5
6 t/T
7
8
9
10
11
0.8 2
Spin up , Ro # 0.2
3
4
5
6
t/T
7
8
9
10
11
Evolution of Azimuthal velocity with time (Spin Down) r = 0.37 1.2
u/U0
V1 U1 V2 U2 V3 U3 V4 U4
1.2 1
U/U0 & V/U0
0.8 0.6 0.4 0.2
0.8 0.6
0.4 0.2
0 0.2 1
radius =0.37
1.4
v/V0
1 Time Series Ro=0.2, r=0.37
0
2
3
4
5
6 t/T
7
8
9
10
11
0.2 2
3
Spin Down, Ro # 0.2
4
5
6
t/T
7
8
9
10
11
Evolution of Azimuthal velocity with time r = 0.5 1.4
u/U0
1.2
1
1
0.8 0.6 0.4
0.8 0.6
0.4 0.2
0.2
0 0.2
0 0.2 0
V1 U1 V2 U2 V3 U3 V4 U4
1.4
v/V0
U/U0 & V/U0
Time Series Ro=0.2, r=0.5
1.2
radius =0.5
1.6
2
4
6
8
10 t/T
12
14
16
18
20
0.4 2
3
Spin Down, Ro # 0.2
4
5
6
t/T
7
8
9
10
11
Evolution of Azimuthal velocity with time r= 0.65 1.4
u/U0
V1 U1 V2 U2 V3 U3 V4 U4
1.6
v/V0
1
1.4
0.8
1.2
0.6 0.4 0.2
1 0.8
0.6 0.4
0
0.2
0.2 0.4 0
radius = 0.65
1.8
U/U0 & V/U0
Time Series Ro=0.2, r=0.65
1.2
0 2
4
6
8
10 t/T
12
14
16
18
20
0.2 2
3
Spin Down, Ro # 0.2
4
5
6
t/T
7
8
9
10
11
Evolution of Azimuthal velocity with time r= 0.77 1.4
u/U0
radius = 0.77
1.8
V1 U1 V2 U2 V3 U3 V4 U4
1.6
v/V0
1.4
1
1.2
0.8
U/U0 & V/U0
Time Series Ro=0.2, r=0.77
1.2
0.6 0.4
1 0.8
0.6 0.4
0.2
0.2
0 0.2 1
0 2
3
4
5
6 t/T
7
8
9
10
11
0.2 2
3
Spin Down, Ro# o.2
4
5
6
t/T
7
8
9
10
11
Radial velocity profile for azimuthal velocity Radial velocity profile for U, Ro# 0.2
0.1 0
0.5
0.1
0.4
0.3
t/T=2 t/T=5 t/T=8 t/T=10
0.3 U/U0
t/T=2 t/T=5 t/T=8 t/T=10
0.2 U/U0
Radial velocity profile for U, Ro# 0.2
0.6
0.2
0.4 0.1
0.5
0
0.6 0.7 0.35
0.4
0.45
0.5
0.55
0.6 r/R
0.65
0.7
Spin Up , Ro # 0.2
0.75
0.8
0.85
0.1 0.35
0.4
0.45
0.5
0.55
0.6 r/R
0.65
0.7
Spin Down , Ro # 0.2
0.75
0.8
0.85
Radial velocity profile for radial velocity Radial velocity profile for V, Ro# 0.2
0.12
t/T=2 t/T=5 t/T=8 t/T=10
0.1
V/U0
0.08
0
0.06
0.02
0.04
0.04
0.02
V/U0
0.06 0.08
0 0.02 0.35
Radial velocity profile for V, Ro# 0.2
0.02
0.1 0.4
0.45
0.5
0.55
0.6 r/R
0.65
0.7
0.75
0.8
0.85
0.12
t/T=2 t/T=5 t/T=8 t/T=10
0.14
Spin Down, Ro # 0.2
0.16 0.35
0.4
0.45
0.5
0.55
0.6 r/R
0.65
Spin Up, Ro # 0.2
0.7
0.75
0.8
0.85
Radial velocity (U) from four runs :Spin Up Run 1:t/T=5 Run 3:t/T=5 Run 2:t/T=5 Run 4:t/T=5
Radial velocity profiles for U at 2 rotations for four Runs 0
Run 1:t/T=2 Run 2:t/T=2 Run 3:t/T=2 Run 4:t/T=2
0.1
Radial velocity profiles for U at 5 rotations for four Runs
0 0.1 0.2
0.3
0.3
U/U0
U/U0
0.2
0.4
0.4
0.5
0.5
0.6
0.6
0.35
0.4
0.45
0.5
0.55
0.6 r/R
0.65
0.7
0.75
0.8
0.35
0.85
0.4
0.45
2 rotation Run 1:t/T=8 Run 3:t/T=8 Run 2:t/T=8 Run 4:t/T=8
0.55
0.6 r/R
0.65
0.7
0.75
0.8
0.85
5 rotation Run 1:t/T=10 Run 3:t/T=10 Run 2:t/T=10 Run 4:t/T=10
Radial velocity profiles for U at 8 rotations for four Runs
0
Radial velocity profiles for U at 10 rotations for four Runs
0 0.1
0.2
0.2
0.3
0.3
U/U0
U/U0
0.1
0.4
0.4
0.5
0.5
0.6
0.6
0.35
0.5
0.4
0.45
0.5
0.55
0.6 r/R
8 rotation
0.65
0.7
0.75
0.8
0.35
0.85
Ro #0.2
0.4
0.45
0.5
0.55
0.6 r/R
0.65
10 rotation
0.7
0.75
0.8
0.85
Run 1:t/T=2 Run 3:t/T=2 Run 2:t/T=2 Run 4:t/T=2
Radial velocity (U) from four runs :Spin Down Radial velocity profiles for U at 2 rotations for four Runs
Radial velocity profiles for U at 5 rotations for four Runs
0.5 0.5
0.4
0.4
0.1
0.2 0.1
0
0
0.1
0.4
0.45
0.5
0.55
0.6 r/R
0.65
0.7
0.75
0.8
0.85
0.1
0.35
0.4
0.45
0.5
2 rotation Run 1:t/T=8 Run 2:t/T=8 Run 3:t/T=8 Run 4:t/T=8
0.5 0.4
0.6 r/R
0.65
0.7
0.75
0.8
0.85
Radial velocity profiles for U at 10 rotations for four Runs Run 1:t/T=10 Run 2:t/T=10 Run 3:t/T=10 Run 4:t/T=10
0.5 0.4
0.3
0.3
0.2
U/U0
U/U0
0.55
5 rotation
Radial velocity profiles for U at 8 rotations for four Runs
0.1
0.2 0.1
0
0
0.1
0.35
0.3
0.2
U/U0
U/U0
0.3
0.35
Run 1:t/T=5 Run 2:t/T=5 Run 3:t/T=5 Run 4:t/T=5
0.4
0.45
0.5
0.55
0.6 r/R
8 rotation
0.65
0.7
0.75
0.8
0.85
0.1
0.35
Ro #0.2
0.4
0.45
0.5
0.55
0.6 r/R
0.65
10 rotation
0.7
0.75
0.8
0.85
Evolution of azimuthal velocity with time ( Ro # 0.15) r = 0.37 U1 V1 U3 V3 U2 V2 U4 V4 0.2
u/U0
Time Series Ro=0.15, r=0.37
0.1
0.1
v/V0
0
0
0.1 U/ U0 & V/U0
0.1
0.2
0.2
0.3
0.3
0.4
0.4
0.5
0.5
0.6
0.6 1
radius =0.3
0.2
2
3
4
5
6 t/T
7
8
9
10
11
2
Spin Up : Ro # 0.15
3
4
5
6
t/T
7
8
9
10
11
Evolution of azimuthal velocity with time r = 0.5 0.2
u/U0
0.1
V1 U1 V2 U2 V3 U3 V4 U4
0.1
v/V0
0
0.1
0.1 U/U0 & V/U0
Time Series Ro=0.15, r=0.5
0
0.2
0.2
0.3
0.3
0.4
0.4
0.5
0.5
0.6
0.6
0.7 1
radius= 0.5
0.2
2
3
4
5
6 t/T
7
8
9
10
11
0.7 2
3
Spin Up : Ro # 0.15
4
5
6
t/T
7
8
9
10
11
Evolution of azimuthal velocity with time r =0.65 0.2
u/U0
0.1
0.1
0.1 U/U0 & V/U0
0
Time Series Ro=0.15, r=0.65
0.1
v/V0
0
0.2
0.2
0.3
0.3
0.4
0.4
0.5
0.5
0.6 0.7 1
radius =0.65
0.2
0.6 2
3
4
5
6 t/T
7
8
9
10
11
0.7 2
Spin Up : Ro # 0.15
3
4
5
6
t/T
7
8
9
10
V1 U1 V2 U2 V3 U3 V4 U4
11
Evolution of azimuthal velocity with time r = 0.77 0.1
u/U0
0.1
v/V0
0
radius =0.77
0.2
Time Series Ro=0.15, r=0.77
0 0.1
0.1 0.2 0.3
0.3
0.4
0.4
0.5
0.5 0.6 1
V1 U1 V2 U2 V3 U3 V4 U4
U/U0 & V/U0
0.2
0.6
2
3
4
5
6 t/T
7
8
9
10
11
2
3
Spin Up : Ro # 0.15
4
5
6
t/T
7
8
9
10
11
Evolution of Azimuthal velocity with time (Spin Down) r = 0.37 0.4
u/U0
0.2
0.2 0.1 0
0.1
0
0.1
0.1
0.2
0.2 0.3 1
V1 U1 V2 U2 V3 U3 V4 U4
0.3
Ro=0.15, r=0.37
Time Series Ro=0.15, r=0.37
v/V0
0.3
Time series for different Run
0.4
0.3 2
3
4
5
6 t/T
7
8
9
10
11
0.4 2
3
4
Spin Down : Ro # 0.15
5
6
t/T
7
8
9
10
11
Evolution of Azimuthal velocity with time r = 0.5 0.5
u/U0
0.3
0.3
0.2
0.2
0.1 0
0
0.1
0.2
0.2 2
3
4
5
6 t/T
7
8
9
10
11
0.1
0.1
0.3 1
V1 U1 V2 U2 V3 U3 V4 U4
0.4
v/V0
Ro=0.15, r=0.5
Time Series Ro=0.15, r=0.5
0.4
Time series for different Run
0.5
0.3 2
3
Spin Down : Ro # 0.15
4
5
6
t/T
7
8
9
10
11
Evolution of Azimuthal velocity with time r = 0.65 0.6
u/U0 v/V0
0.4
0.3
0.3 0.2 0.1
0.2
0
0.1
0.1 2
3
4
5
6 t/T
7
8
9
10
11
0.1
0
0.2 1
V1 U1 V2 U2 V3 U3 V4 U4
0.4
Ro=0.15, r=0.65
Time Series Ro=0.15, r=0.65
0.5
Time series for different Run
0.5
0.2 2
3
Spin Down : Ro # 0.15
4
5
6
t/T
7
8
9
10
11
Evolution of Azimuthal velocity with time r = 0.77 0.6
u/U0
0.4
0.4
0.3
0.3
0.2 0.1
0.1 0
0.1
0.1 2
3
4
5
6 t/T
7
8
9
10
11
0.2
0
0.2 1
V1 U1 V2 U2 V3 U3 V4 U4
0.5
v/V 0
Ro=0.15, r=0.77
Time Series Ro=0.15, r=0.77
0.5
Time series for different Run
0.6
0.2 2
3
Spin Down : Ro # 0.15
4
5
6
t/T
7
8
9
10
11
Radial velocity profile for azimuthal velocity ( Ro # 0.15) Radial velocity profile for U, Ro# 0.15
0
0.5
0.2
0.4
0.3
0.3
t/T=2 t/T=5 t/T=8 t/T=10
U/U0
U/U0
0.1
0.4
0.2
0.5
0.1 t/T=2 t/T=5 t/T=8 t/T=10
0.6 0.7 0.35
Radial velocity profile for U, Ro# 0.15
0.6
0.4
0.45
0.5
0.55
0.6 r/R
0.65
Spin Up
0.7
0.75
0.8
0.85
0 0.1 0.35
0.4
0.45
0.5
0.55
0.6 r/R
0.65
Spin Down
0.7
0.75
0.8
0.85
Radial velocity profile for radial velocity ( Ro # 0.15) Radial velocity profile for V, Ro# 0.15
0.14
t/T=2 t/T=5 t/T=8 t/T=10
0.12 0.1
0.04
0.02 0
0.06 V/V0
V/V0
t/T=2 t/T=5 t/T=8 t/T=10
0.06
0.08
0.04
0.02 0.04
0.02
0.06
0
0.08
0.02 0.04 0.35
Radial velocity profile for V, Ro# 0.15
0.08
0.1 0.4
0.45
0.5
0.55
0.6 r/R
0.65
Spin Up
0.7
0.75
0.8
0.85
0.12 0.35
0.4
0.45
0.5
0.55
0.6 r/R
0.65
Spin Down
0.7
0.75
0.8
0.85
Radial velocity (U) from four runs :Spin Up Radial velocity profiles for U at 2 rotations for four Runs 0
0.1
Radial velocity profiles for U at 5 rotations for four Runs
Run 1:t/T=2 Run 2:t/T=2 Run 3:t/T=2 Run 4:t/T=2
0
Run 1:t/T=5 Run 2:t/T=5 Run 3:t/T=5 Run 4:t/T=5
0.1
0.2
U/U0
0.2
U/U0
0.3
0.3
0.4
0.4
0.5
0.5
0.6 0.6 0.35
0.4
0.45
0.5
0.55
0.6 r/R
0.65
0.7
0.75
0.8
0.35
0.85
0.4
0.45
0.5
2 Rotation
0.6 r/R
0.65
0.7
Radial velocity profiles for U at 8 rotations for four Runs Run 1:t/T=8 Run 2:t/T=8 Run 3:t/T=8 Run 4:t/T=8
0.1
Run 1:t/T=10 Run 2:t/T=10 Run 3:t/T=10 Run 4:t/T=10
U/U0
U/U0
0.3
0.4
0.4
0.5
0.5
0.6
0.6 0.55
0.6 r/R
0.65
8 Rotation
0.7
0.75
0.8
0.1
0.3
0.5
0.85
0
0.2
0.45
0.8
Radial velocity profiles for U at 10 rotations for four Runs
0.2
0.4
0.75
5 Rotation
0
0.35
0.55
0.35
0.85
Ro # 0.15
0.4
0.45
0.5
0.55
0.6 r/R
0.65
10 Rotation
0.7
0.75
0.8
0.85
Radial velocity (U) from four runs :Spin Down Radial velocity profiles for U at 2 rotations for four Runs
0.6
Run 1:t/T=2 Run 2:t/T=2 Run 3:t/T=2 Run 4:t/T=2
0.5 0.4
Run 1:t/T=5 Run 2:t/T=5 Run 3:t/T=5 Run 4:t/T=5
0.5 0.4 0.3 U/U0
0.3 U/U0
Radial velocity profiles for U at 5 rotations for four Runs
0.6
0.2
0.2
0.1
0.1
0
0
0.1
0.1
0.2 0.35
0.4
0.45
0.5
0.55
0.6 r/R
0.65
0.7
0.75
0.8
0.2 0.35
0.85
0.4
0.45
Radial velocity profiles for U at 8 rotations for four Runs Run 1:t/T=8 Run 2:t/T=8 Run 3:t/T=8 Run 4:t/T=8
0.5 0.4
0.65
0.7
0.75
0.8
0.85
Run 1:t/T=10 Run 2:t/T=10 Run 3:t/T=10 Run 4:t/T=10
0.5 0.4
0.3 U/U0
U/U0
0.6 r/R
Radial velocity profiles for U at 10 rotations for four Runs
0.6
0.3 0.2
0.2
0.1
0.1
0
0
0.1
0.1
0.2 0.35
0.55
5 Rotation
2 Rotation 0.6
0.5
0.4
0.45
0.5
0.55
0.6 r/R
0.65
8 Rotation
0.7
0.75
0.8
0.2 0.35
0.85
Ro # 0.15
0.4
0.45
0.5
0.55
0.6 r/R
10 Rotation
0.65
0.7
0.75
0.8
0.85
Evolution of azimuthal velocity with time ( Ro # 0.4) r =0.37 r =0.5 0.2
V/U0
0.4
U/U0
0.2
Time Series Ro=0.4, r=0.37
0
V/U0
Time Series Ro=0.4, r=0.5
0.2 0.4
U/U0
0
0.2 0.4
0.6
0.6
0.8
0.8
1
1 1.2 0
1
2
3
4
5 t/T
6
7
8
9
10
Spin Up
1.2 0
1
2
3
4
5 t/T
6
7
8
9
10
Evolution of azimuthal velocity with time r= 0.65
r= 0.77
0.4
V/U0
0.4
U/U0
V/U0
0.2
0
Time Series Ro=0.4, r=0.65
Time Series Ro=0.4, r=0.65
0.2
0.2
U/U0
0
0.2
0.4
0.4
0.6
0.6
0.8
0.8
1 1.2 0
1 1
2
3
4
5 t/T
6
7
8
9
10
1.2 0
1
2
Spin Up ( Ro #0.4)
3
4
5 t/T
6
7
8
9
10
Evolution of Azimuthal velocity with time (Spin Down) r = 0.37
r = 0.5
0.8
V/U0
0.7
1.2
U/U0
0.6
V/U0 U/U0
Time Series Ro=0.4, r=0.37
1
0.5 Time Series Ro=0.4, r=0.5
0.8
0.4 0.3
0.6
0.2
0.4
0.1 0
0.2
0.1 0.2 0
0 2
4
6
8
t/T
10
12
14
16
18
0.2 0
Ro # 0.4
2
4
6
8
t/T
10
12
14
16
18
Evolution of Azimuthal velocity with time r = 0.65
r = 0.77
1
V/U0 U/U0
V/U0
0.8
U/U0
0.6
0.6
0.4
0.4
0.2
0.2 0
0
0.2
0.2 0.4 0
1
Time Series Ro=0.4, r=0.65
0.8 Time Series Ro=0.4, r=0.65
2
4
6
8
t/T
10
12
14
16
18
0.4 0
2
Spin Down ( Ro #0.4)
4
6
8
t/T
10
12
14
16
18
Radial velocity profile for azimuthal velocity ( Ro # 0.4) Radial velocity profile for U,Ro #0.4
0.2 0
Radial velocity profile for U,Ro #0.4
0.9
t/T=2 t/T=5 t/T=8 t/T=10
t/T=2 t/T=5 t/T=8 t/T=10
0.8 0.7
0.6
0.2
0.5
U/U0
U/U0
0.4 0.6
0.4 0.3 0.2
0.8
0.1 1 1.2 0.35
0
0.4
0.45
0.5
0.55
0.6 r/R
Spin Up
0.65
0.7
0.75
0.8
0.85
0.1 0.35
0.4
0.45
0.5
0.55
0.6 r/R
Spin Down
0.65
0.7
0.75
0.8
0.85
Radial velocity profile for radial velocity ( Ro # 0.4) Radial velocity profile for V,Ro #0.4
0.3
t/T=2 t/T=5 t/T=8 t/T=10
0.25
Radial velocity profile for V,Ro #0.4
0
t/T=2 t/T=5 t/T=8 t/T=10
0.02 0.04
0.2
0.06
V/U0
V/U0
0.15 0.1
0.08 0.1 0.12
0.05
0.14
0 0.05 0.35
0.16
0.4
0.45
0.5
0.55
0.6 r/R
0.65
Spin Up
0.7
0.75
0.8
0.85
0.18 0.35
0.4
0.45
0.5
0.55
0.6 r/R
0.65
0.7
Spin Down
0.75
0.8
0.85
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 • Flows in the shallow water spin up and spin down faster then the flow in the deep water. • There is a evidence of periodic flow blocking for spin up at high Rossby number. • High Rossby number can make the flow unstable in case of spin up. • Low Rossby number can make the flow unstable in case of spin down ( centrifugal instability ) • Rossby number and flow direction along a slope has significant impact along the flow.
Future work
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