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In conduction mode laser welding, the shape of the fusion boundary affects the solidification process, microstructure, and properties of the weld. Although significant progress has been made in the calculations of the shape and size of the fusion zone in recent decades, the conditions for the formation of the wavy fusion boundary are still not well understood. Here we examine the conditions for its formation in terms of important dimensionless numbers. In particular, the computed flow patterns, temperature fields, and molten pool shapes under the flat free surface are examined for various values of Marangoni, Prandtl, Peclet, and dimensionless heat input values. In the absence of electromagnetic force, it is shown that the wavy fusion boundary forms for specific ranges of Marangoni and Prandtl numbers.

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