Dynamical similarities and differences between cold fronts and density currents

Victoria Sinclair

University of Helsinki

15.08.2011 Victoria.Sinclair@helsinki.fi www.atm.helsinki.fi/~vsinclai

Some cold fronts can be visually similar to density currents

Tower observations (Shapiro et al 1985)

w and θ

Model simulation of a cold front (dx = 2.5km)

Questions

• What is the force balance across a cold front?

• How does the force balance compare to theoretical predictions?

• Is the force balance across a cold front similar to that across a density current?

– Are cold fronts dynamically related to density currents?

Potential temperature, surface pressure and location of nested domains

3D Idealised experiments with WRF

3D baroclinic life cycle with nested domains

dx = 100km, 20km, 4km

WRF-ARW v3.2, Non-hydrostaticYSU BL scheme over a sea surfaceNo moistureSimulate a cold front and a density current

Drop a cold bubble and allow to spread

dx = 4km

Potential temperature, wind

Scale Analysis for fronts

l α β ACC

along

PGF alon

g

COR

along

ACC

across

PGF across

COR across

100km

1 0.1 1 1 1 0.01 1 1Semi – Geostrophic theory: we can neglect the acceleration only in the across front direction

(Hoskins and Bretherton, 1972)

dx = 100km Force balance across cold front

Green: Wind Vectors Blue: Coriolis ForceRed: Pressure gradient force Black: Resultant acceleration

dx = 4km Force balance across cold front

Green: Wind Vectors Blue: Coriolis ForceRed: Pressure gradient force Black: Resultant accelerationPurple: BL force

Along front forces z=100m

dx =100km dx = 20km dx = 4km

PGF COR

BL ACC

Across front forces z=100m

dx =100km dx = 20km dx = 4km

PGF COR

BL ACC

Cold front vs. Density Current

Blue: Coriolis Force Red: Pressure gradient force Black: Resultant acceleration Purple: BL force

Across front z = 100m dx = 4km

Cold front Density current

Cold front vs. Density Current

Blue: Coriolis Force Red: Pressure gradient force Black: Resultant acceleration Purple: BL force

Along front z = 100m dx = 4km

Cold front Density current

Conclusions

The force balance is resolution dependent

For the cold front at dx = 4km, PGF ≈ Coriolis force in the along front direction PGF >> Coriolis force in the across front direction

In the across front direction, the cold front force balance approaches that of the density current as resolution increases.

In the along front direction the cold front force balance differs to the density current force balance

Across the cold front, the unbalance pressure gradient force is likely due to enhanced horizontal buoyancy gradients.

Cold fronts have a large variety of structures

ΔT= 10K

Δt =5hrs

ΔT= 2K

Δt =30 mins

Temperature Temperature, pressure, rain rate

Density Current force balance

Blue: Coriolis Force Red: Pressure gradient force Black: Resultant acceleration Purple: BL force

z = 1 km dx = 4km

Cold front force balance

Blue: Coriolis Force Red: Pressure gradient force Black: Resultant acceleration Purple: BL force

z = 100m dx = 4km

Cold front force balance

Blue: Coriolis Force Red: Pressure gradient force Black: Resultant acceleration Purple: BL force

z = 1 km dx = 4km

Scale Analysis - revisited

l α β ACC

along

PGF alon

g

COR

along

ACC

across

PGF across

COR across

20 km

7.5

0.5 1 1 0.13 1.8 3.3 1

Use U, V and l from the WRF simulation

Boundary layer processes are not included in Semi Geostrophic theory

Why do the results differ to theory?

Two assumptions

U/VV

115 20 7.5V ms l km 0.5

Scale Analysis - Hoskins and Bretherton (1972)

ACROSS FRONT

ALONG FRONT

Rossby number is assumed to be O(1)

Along front wind is assumed to be much greater than along fronts wind

∆x=100km. No Boundary layer scheme

Green: Wind Vectors Blue: Coriolis ForceRed: Pressure gradient force Black: Resultant acceleration

What do these terms really mean?

u vDiv

x y

0u

t

0u

t

X

U

CF

Increases convergence

Strengthens front0u

t

0u

t

Decreases convergence

Weakens front

What do these terms really mean?

v u

x y

0v

t

0v

t

X

V

CF

Decreases vorticity0v

t

0v

t

Increases vorticity

Effect of resolution of frontal structure

The cross front scale decreases with increasing resolution and the wind shift becomes sharper

Potential temperature and wind barbs at z=100m

Effect of PBL on vertical structure of front

YSU PBL dx = 4kmNo PBL dx = 4kmPotential temperature (2K), system relative wind vectors.

Ascent is shaded. Descent contoured. Scales differ by a factor of 10

Density Current dx=4km.t=1.5 hours, z=100m, YSU BL scheme

Potential temperature and wind vectors

Blue: Coriolis ForceRed: Pressure gradient force Black: Resultant accelerationPurple: BL force