<p>Three typical weld surface morphologies will be formed during the process of ultra-narrow gap welding with plate tungsten cathode arc constricted by insulating solid wall, which are symmetrical concave type, symmetrical convex type, and unilateral concave type. Based on the fluid dynamics equations and Maxwell’s equations, a three-dimensional mathematical model of plate tungsten cathode arc constricted by insulating solid wall under different weld surface morphologies in ultra-narrow gap is established. Then the arc current density field, Lorentz force field, flow field, and temperature field are obtained by iterative solution of the governing equations. The results show that the morphology of the weld surface will change the arc discharge gap in the ultra-narrow gap, so that the diversion effect of the arc to the groove bottom and corner will change. The stronger the diversion effect of the arc to the groove bottom and corner is, the more obvious the expansion of the current density field, Lorentz force field and temperature field at the groove bottom and corner is, while the arc jet was weakened. On the contrary, the weakening of the diversion effect of the arc to the groove bottom and corner will cause the current density field, Lorentz force field and temperature field to shrink. And then, the arc jet will be strengthened. The diversion effect of three weld surface morphologies from strong to weak is symmetrical concave type, unilateral concave type, and symmetrical convex type.</p>