Context : Clumping in the radiation-driven winds of hot , massive stars arises naturally due to the strong , intrinsic instability of line-driving ( the ‘ LDI ’ ) .
But LDI wind models have so far mostly been limited to 1D , mainly because of severe computational challenges regarding calculation of the multi-dimensional radiation force .

Aims : To simulate and examine the dynamics and multi-dimensional nature of wind structure resulting from the LDI .

Methods : We introduce a ‘ pseudo-planar ’ , ‘ box-in-a-wind ’ method that allows us to efficiently compute the line-force in the radial and lateral directions , and then use this approach to carry out 2D radiation-hydrodynamical simulations of the time-dependent wind .

Results : Our 2D simulations show that the LDI first manifests itself by mimicking the typical shell-structure seen in 1D models , but how these shells then quickly break up into complex 2D density and velocity structures , characterized by small-scale density ‘ clumps ’ embedded in larger regions of fast and rarefied gas .
Key results of the simulations are that density-variations in the well-developed wind statistically are quite isotropic and that characteristic length-scales are small ; a typical clump size is \ell _ { cl } / R _ { \ast } \sim 0.01 at 2 R _ { \ast } , thus resulting also in rather low typical clump-masses m _ { cl } \sim 10 ^ { 17 } g. Overall , our results agree well with the theoretical expectation that the characteristic scale for LDI-generated wind-structure is of order the Sobolev length \ell _ { Sob } .
We further confirm some earlier results that lateral ‘ filling-in ’ of radially compressed gas leads to somewhat lower clumping factors in 2D simulations than in comparable 1D models .
We conclude by discussing an extension of our method toward rotating LDI wind models that exhibit an intriguing combination of large- and small-scale structure extending down to the wind base .

Conclusions :