Shear Rate Of Flow Near Magnetopause

Shear rate of flow near magnetopause is related to the degree of energy transfer near magnetopause. Flow shear is a fundamental condition of Kelvin-Helmholtz instability and an important condition of many transient reconnections. Many numerical simulations near magnetopause have to use shear rate of flow as an important input parameter. However, up to now it is hypothetical and not realistic. By simultaneous multipoint observations of Cluster, using methods of linear interpolation and barycentric coordinates, we have determined shear rate of flow near magnetopause, an observational spatial parameter that can not be obtained until Cluster. The method we have adopted here can be used widely to determine shear rate of flow at any location. Observational spatial distribution of shear rate of flow at magnetopause, magnetosphere and magnetosheath nearby at different regions of magnetopause has been analyzed. We focus on 3 regions of magnetopause: dusk side of magnetopause with x > 0, dawn side of magnetopause with x < 0, and dusk side of magnetopause with x < 0 to investigate the spatial distribution of shear rate of flow. The main analysis results are below:1. Comparison of shear rates of different velocity components near magnetopause:(1)At dusk side of magnetopause with x > 0, among 6 cases, in 4 cases shear rate of Vz component is larger than shear rates of other velocity components, while shear rates of other velocity components are nearly equal; in 2 cases shear rates of different velocity components show little difference.(2)At dawn side of magnetopause with x < 0, in all cases (6 cases) shear rate of Vz component is larger than shear rates of other velocity components, while shear rates of other velocity components are nearly equal.(3)At dusk side of magnetopause with x < 0, among 7 cases, in 5 cases e 2 ?? Vz is larger than other shear rates while other shear rates are nearly equal; in 2 cases shear rates of different velocity components show little difference.2. Comparison of shear rate of flow at magnetosphere and at magnetosheath near magnetopause:(1)At dusk side of magnetopause with x > 0, among 6 cases, in 4 cases shear rate of flow at magnetosphere is larger than shear rate of flow at magnetosheath near magnetopause; in 2 cases shear rates of flow at magnetosphere and at magnetosheath near magnetopause are nearly equal.(2)At dawn side of magnetopause with x < 0, in all cases (6 cases) shear rate of flow at magnetosphere is larger than shear rate of flow at magnetosheath near magnetopause.(3) At dusk side of magnetopause with x < 0, small shear rates show little difference between at magnetosphere and at magnetosheath, while relatively larger shear rate e2·▽V_z is different between at magnetosphere and at magnetosheath. Among 7 cases, in 5 cases e2·▽V_z at magnetosphere is larger than e2·▽V_z at magntosheath; in 2 cases e2·▽V_z at magnetosheath is larger than e2·▽V_z at magnetosphere.3. The derived shear rate of flow near magnetopause can be large or can be small.(1) At dusk side of magnetopause with x > 0, among 6 cases there are 1 case with large shear rate and 5 cases with small shear rates.(2)At dawn side of magnetopause with x < 0, among 6 cases there are 3 cases with large shear rates and 3 cases with small shear rates.(3) At dusk side of magnetopause with x < 0, in all 7 cases shear rates are small.Generally, shear rate of flow near magnetopause is small in most cases, with the spatial velocity difference of dozens of km/s over the distance of 1000 km. Shear rate of Vz component at magnetosphere near magnetopause is larger. Shear rates of Vz component along dawn-dusk direction are nearly equal at dusk side of magnetopause with x > 0 and at dawn side of magnetopause with x < 0, larger than at dusk side of magnetopause with x < 0. The derived shear rate of flow near magnetopause could be large in a few cases.The influence of solar wind condition on shear rate of flow near magnetopause seems not obvious.