Context: Clumping in the radiation-driven winds of hot, massive stars arisesnaturally 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 ofsevere computational challenges regarding calculation of the multi-dimensionalradiation force. Aims: To simulate and examine the dynamics andmulti-dimensional nature of wind structure resulting from the LDI. Methods: Weintroduce a `pseudo-planar', `box-in-a-wind' method that allows us toefficiently compute the line-force in the radial and lateral directions, andthen use this approach to carry out 2D radiation-hydrodynamical simulations ofthe time-dependent wind. Results: Our 2D simulations show that the LDI firstmanifests itself by mimicking the typical shell-structure seen in 1D models,but how these shells then quickly break up into complex 2D density and velocitystructures, characterized by small-scale density `clumps' embedded in largerregions of fast and rarefied gas. Key results of the simulations are thatdensity-variations in the well-developed wind statistically are quite isotropicand that characteristic length-scales are small; a typical clump size is ~0.01Rat 2R, thus resulting also in rather low typical clump-masses ~10^17 g.Overall, our results agree well with the theoretical expectation that thecharacteristic scale for LDI-generated wind-structure is of order the Sobolevlength. We further confirm some earlier results that lateral `filling-in' ofradially compressed gas leads to somewhat lower clumping factors in 2Dsimulations than in comparable 1D models. We conclude by discussing anextension of our method toward rotating LDI wind models that exhibit anintriguing combination of large- and small-scale structure extending down tothe wind base.
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