Freeze-thaw processes significantly modulate hydraulic and thermal char- acteristics of soil. The changes in the frost and thaw fronts （FTFs） affect the water and energy cycles between the land surface and the atmos...Freeze-thaw processes significantly modulate hydraulic and thermal char- acteristics of soil. The changes in the frost and thaw fronts （FTFs） affect the water and energy cycles between the land surface and the atmosphere. Thus, the frozen soil com- prising permafrost and seasonally frozen soil has important effects on the land surface hydrology in cold regions. In this study, a two-directional freeze and thaw algorithm is incorporated into a thermal diffusion equation for simulating FTFs. A local adaptive variable-grid method is used to discretize the model. Sensitivity tests demonstrate that the method is stable and FTFs can be tracked continuously. The FTFs and soil tempera- ture at the Qinghai-Tibet Plateau D66 site are simulated hourly from September 1, 1997 to September 22, 1998. The results show that the incorporated model performs much better in the soil temperature simulation than the original thermal diffusion equation, showing potential applications of the method in land-surface process modeling.展开更多
We show the existence of Holder continuous periodic weak solutions of the 2D Boussinesq equation with thermal diffusion which satisfy the prescribed kinetic energy.More precisely,for any smooth e(t):[0,1]→R+andε∈(0...We show the existence of Holder continuous periodic weak solutions of the 2D Boussinesq equation with thermal diffusion which satisfy the prescribed kinetic energy.More precisely,for any smooth e(t):[0,1]→R+andε∈(0,110),there exist v∈C 110−ε([0,1]×T2)andθ∈C 1,120−εt 2 C 2,1 x 10−ε([0,1]×T2),which satisfy(1.1)in the sense of distribution and e(t)=ˆT2|v(t,x)|2 dx,∀t∈[0,1].展开更多
基金Project supported by the National Natural Science Foundation of China(Nos.41575096 and91125016)the Strategic Priority Research Program of the Chinese Academy of Sciences(No.XDA05110102)
文摘Freeze-thaw processes significantly modulate hydraulic and thermal char- acteristics of soil. The changes in the frost and thaw fronts （FTFs） affect the water and energy cycles between the land surface and the atmosphere. Thus, the frozen soil com- prising permafrost and seasonally frozen soil has important effects on the land surface hydrology in cold regions. In this study, a two-directional freeze and thaw algorithm is incorporated into a thermal diffusion equation for simulating FTFs. A local adaptive variable-grid method is used to discretize the model. Sensitivity tests demonstrate that the method is stable and FTFs can be tracked continuously. The FTFs and soil tempera- ture at the Qinghai-Tibet Plateau D66 site are simulated hourly from September 1, 1997 to September 22, 1998. The results show that the incorporated model performs much better in the soil temperature simulation than the original thermal diffusion equation, showing potential applications of the method in land-surface process modeling.
基金supported by National Natural Science Foundation of China(Grant No.11971464)supported by National Natural Science Foundation of China(Grant No.11901349)supported by National Natural Science Foundation of China(Grant Nos.11471320 and 11631008)。
文摘We show the existence of Holder continuous periodic weak solutions of the 2D Boussinesq equation with thermal diffusion which satisfy the prescribed kinetic energy.More precisely,for any smooth e(t):[0,1]→R+andε∈(0,110),there exist v∈C 110−ε([0,1]×T2)andθ∈C 1,120−εt 2 C 2,1 x 10−ε([0,1]×T2),which satisfy(1.1)in the sense of distribution and e(t)=ˆT2|v(t,x)|2 dx,∀t∈[0,1].
