Yeon S. Chang, Xiaobiao Xu, Tamay M. Özgökmen, Eric P. Chassignet, Hartmut Peters, Paul F. Fischer 1

MPO/RSMAS University of Miami

1 Mathematics and Computer Science DivisionArgonne National Laboratory

Gravity current mixing parameterization and calibration of

HYCOM

Objectives

1. To explore how common mixing parameterizations, particularly KPP and TP, perform using an idealized setting and high-resolution nonhydrostatic solution

2. To quantify the differences and limitations of the two schemes, understanding why and how these parameterizations can be modified to produce consistent results.

Outline

1. Numerical test of gravity currents over idealized sloped basin using a OGCM, HYCOM

2. Comparison with 3-D LES (Nek5000) in terms of Entrainment, E(t)

3. Tuning the vertical mixing parameters of KPP and TP

4. Adjustment of parameterization over varying slopes

5. Also testing it as a function of the grid resolution

Nek5000 HYCOM

Configuration of experiments and initial conditions

Distribution of salinity surface, Nek5000

3-D

2-Daveraged in span-wise

T=9350s

7.0

,11*

32

max

c

cshear

Ri

Ri

RiminKK

8.0 if

51

1.008.0

Ri

Ri

RiC

U

wA

E

TP (Hallberg, 2000): developed for overflows based on Ellison and Turner(1959)

KPP (Large et al., 1994, 99): shear-induced, multi-purpose

HYCOM, before tuning

mx 1000 mx 20

KPP scmK /50 2

max : LES studies of upper tropical ocean (e.g., Large, 1998)

TP

0.1AC

HYCOM, before tuning

mx 1000 mx 20

: Lab. Exp. by Ellison and Turner(1959), Turner(1986)

)(

)()()(

0

tl

thth

dX

dhtE

scmK /50,KPP

tuningBefore2

max

0.1,TP

tuningBefore

AC

scmK /2500,KPP

ngAfter tuni2

max

15.0,TP

ngAfter tuni

AC

After tuning

mx 20

KPP scmK /2500 2

max

mx 20

TP 15.0AC

After tuning

mx 1000

KPP scmK /2500 2

max

mx 1000

TP 15.0AC

Why significant modification is necessary to adjust the entrainment curves ?

- Turbulence parameterization should include a dependence on the forcing as well as a dependence on the Ri ; this holds for TP but not for KPP.

KPP: 1. KPP-modeled Mediterranean outflow sinks deeper: insufficient mixing2. Kmax should vary with the strength of the forcing, and a particular value of Kmax cannot hold in bottom gravity current mixing

Maximum turbulence forcing

Peters et al. (1988)

TP:1. Papadakis et al.(2003) : applied TP every 144th steps 2. Turner (1986): small tank (0.1x2 m), large slopes ( >10°) 3. Replacement of bulk Ri inoriginal Turner scheme by

shear Ri in Hallberg(2000)

Test of adjustment to forcing by employing different low-slopes

scmK /50,KPP

tuningBefore2

max

y F b

b

L tyX

x

hz

zFy

dxdydztzyxStzyxuhxXL

tSF0

),'(

000

),,,(),,,(1

)(

11)(

KPP

Salt Flux:

KPP ng,After tuni

TP

Conclusion

1. With appropriate tuning of parameters, both KPP and TP can

be well matched with the nonhydrostatic 3-D solution, and

the results are fairly independent of the horizontal grid

resolution.

2. But there’s substantial difference between KPP and TP

KPP: the amplitude of mixing term is quite dependent on its

peak diffusivity, Kmax, but this given constant cannot

respond to the variation of ambient forcing,

TP: by relating WE to ΔU, TP avoids hard limit for peak

diffusivity, and the implied diffusivity is dependent both

on Ri and on the forcing via ΔU.

3. Further experiments with stratified flows are necessary.