The Linear and Non-linear Evolution Mechanism of The Linear and Non-linear Evolution Mechanism of Mesoscale Vortex Disturbances in Winter Over Mesoscale Vortex Disturbances in Winter Over

Western Japan SeaWestern Japan SeaYasumitsu MAEJIMA and Keita IGA

(Ocean Research Institute, The University of Tokyo)1.　 Introduction

In winter over Japan Sea, meso-alpha-scale and meso-beta-scale vortex disturbances are often formed along Convergent Cloud Band. Many previous studies about the vortex disturbances have been conducted. They suggested that meso-alpha-scale disturbances are generated by baroclinic instability, and meso-beta-scale disturbances by barotropic instability. However, in these studies, they specified the kind of instability from observations and the linear stability analysis was performed for basic field which includes only the focused instability. In such basic fields which excludes other instabilities, we cannot discuss what kinds of disturbances dominate.In order to address this problem, we consider a basic field which include both baroclinic and barotropic instabilities, and calculate linear stability and time evolution. We will discuss what kind of disturbances become dominant depending on the features of the basic field.

2. Linear stability analysisObservational studies showed that the Convergent Cloud Band had a frontal structure with the horizontal and vertical shear. By calculating the linear stability of a basic field modeled on such a frontal structure, we will elucidate the generation mechanism of the unstable mode and investigate the dominant unstable mode depending on the change of the characteristics of the basic field. We solved the following eigen value problem:　　　　　　　　　　　　　　　　　　(The basic field in the reference case, frontal transition layer is 1000m, potential temperature difference on ground surface is 10K and stability of atmosphere is )

01

2

2

2

22

y

q

zSykcU

(A) Meso-alpha-scale unstable mode

(B) Meso-beta-scale unstable mode

The meso-alpha-scale unstable mode is generated by baroclinic instability

The meso-beta-scale unstable mode is generated by barotropic instability

* Constant phase lines are tilted to left seeing from the side of warm air in basic field.

* The energy conversion term from available potential energy to eddy kinetic energy is dominant.

* Constant phase lines are tilted to right in horizontal shear zone in basic field ,which means eddy momentum flux is positive.

* The energy conversion term from zonal kinetic energy to eddy kinetic energy is dominant.

We calculated eigen value problem for various parameters of basic field : frontal transition layer, stability of atmosphere.

2-1. Reference case 2-2. The response of parameters to growth rate

(i)　 Dependence on thickness of frontal transition layer

* Growth rate becomes larger as transition layer becomes thinner.* Meso-beta-scale unstable modes dominate when the layer is thin.

(ii)　 Dependence on stability of atmosphere

* Meso-alpha-sacle unstable modes dominate when stability of atmosphere is small.* Growth rate of meso-beta-scale unstable mode is almost same.

Meso-alpha-scale wave length~600km

Meso-beta-scale wave length~70km

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When the transition layer is thin, meso-beta-scale unstable mode is generated in middle layer.

The fastest growing mode when the transition layer is 300m

The transition layer is 500m

The transition layer is 300m

Meso-alpha-scale wave length~620km

Meso-beta-scale wave length~70km

Meso-beta-scale wave length~70km

Meso-alpha-scale wave length~480km

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Meso-beta-scale wave length~125km

A visible image of Japanese geostationary satellite(MASAT-1R) at 05UTC 31 January, 2005

Meso-beta-scale wave length~150km

3. Contribution of instabilities to the generation and development of vortex disturbances

In order to investigate the contribution of the instabilities to the generation and development of vortex disturbances, we calculate time evolution of the basic field by using non-hydrostatic numerical model, and compare the vortex disturbances in the numerical model with the unstable mode in the linear theory.

3-1. Model configuration

Non-hydrostatic numerical model “CReSS” (Tsuboki and Sakakubara 2006)

* Horizontal resolution : 3km, Vertical resolution : 200m * Prediction variables : 3-dimensional velocity, pressure and potential temperature* Boundary condition : Periodic boundary conditions (in longitudinal direction) * 4th order numerical diffusion term is included. Open boundary conditions (in meridional direction) Rigid wall boundary (in vertical direction)

3-2. Time evolution of the basic field

(i) Reference case

The basic field is same as the reference case in linear stability analysis,but for (ref. section 2-1).

Horizontal wind and pressure anomaly

Longitudinal-vertical cross section at t=151200s (42h)

(ii)　 Dependence on thickness of frontal transition layer

(iii)　 Dependence on stability of atmosphere

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* Meso-beta-scale vortex disturbances are generated (t=21600s).* The generation height is close to the unstable mode in linear theory.* After t=108000s(30h), meso-alpha-scale vortex disturbance is formed.

* Meso-beta-scale vortex disturbances are not formed.* Meso-alpha-scale vortex disturbances (λ~500km) are generated within 12hours.* The wave length and growth rate of meso-alpha-scale vortex disturbances reasonably agree with that of linear theory.

(The color shade show pressure anomaly [in hPa] and black arrow horizontal velocity vectors [in m/s])

* The isobaric lines are tilted to westward.

* Warm advection exists in front of the trough and cold advection in rear of the trough.

The generation mechanism is baroclinic instability

The transition layer of basic field is 300m. (ref. section 2-2(i))

The stability of atmosphere of basic field is . (ref. section 2-2(ii))

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* Growth rate of the meso-alpha-scale vortex disturbance (λ~600km) is slightly larger than reference case. * The wave length of meso-alpha-scale vortex disturbances reasonably agree with that of linear theory.

4. Further studies

* Why the meso-beta-scale vortex disturbances have the shallow layer of 2km and below?* To investigate the role for developing mesoscale vortex disturbances in latent heat flux from sea surface and SST gradient.