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I have a function F that rotates things in order to get the normal direction, perpendicular to the direction obtained by the derivative (rotating by 90 degrees). I also normalize it by dividing by the absolute value of the derivative.
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Here the function h is used to add waves in the horizontal direction.
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In the end I didn't use this approach exactly, since I've simply added the normalized derivative to the x-component, which yields equivalent results. I've also added a bit of a fudge factor multiplying all occurrences of u_0 by 10, which tends to result in less glitches. You can observe this in the function below by using the slider for the variable c.
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