We study the shape of spiral curves in an annulus which is governed by curvature flow equations with a driving force term. We establish that as the model parameter $\mu$ (which is the coefficient of the curvature) approaches $\infty$, the profile of the spiral curve tends to a line segment, while as $\mu$ approaches $0^{+}$, the limiting profile of the spiral curve is the involute of the inner circle of the annulus and the associated limiting rotational speed is the ratio of a constant $c$, which is the propagation speed of the planar wave, to the inner radius of the annulus. Hence the model parameter $\mu$ can be viewed as a twisted parameter. Finally, the spiral curve under consideration is shown to be with sign-changing curvature and exponentially stable.

我们研究了由驱动力项与曲率流方程控制的环面中螺旋曲线的形状。我们将其确定为模型参数$\mu$ （即曲率系数）方法 $\infty$，螺旋曲线的轮廓倾向于一条线段，而当 $\mu$ 方法 $0^{+}$，螺旋曲线的极限轮廓是环的内圆的渐开线，而相关的极限旋转速度是常数的比率 $C$，即平面波到环的内半径的传播速度。因此模型参数$\mu$可以视为扭曲参数。最后，所考虑的螺旋曲线显示出具有符号改变的曲率并且呈指数稳定。