Step 1: Understand the profile types.
The profiles S\(_1\), S\(_2\), and S\(_3\) describe different types of flow profiles based on the slope change. S\(_3\) is typically the profile that occurs when the slope changes from steeper to less steep.
Step 2: Identify the correct profile.
The correct profile for a change from a steeper slope to a less steep slope is S\(_3\).
Final Answer: (A) S\(_3\)
