How to make a fluid carpet effect

For each vertex : use the vertex position as a reference in the wave, add a timer value, now evaluate sine value. Here is an example using sine and perlin (perlin looks more 'random', and can be evaluated with 2 variables). In a new scene, create a plane and attach the script. In play mode, modify the public inspector variables.

 using UnityEngine;
 using System.Collections;
 
 public class PerlinPlane : MonoBehaviour 
 {
     public float speed = 2f;
     public float scaleY = 1f;
     public float freqX = 0.2f;
     public float freqZ = 3.6f;
     
     private float timer = 0f;
     private Mesh mesh;
     private Vector3[] originalVerts;
     
     void Start()
     {
         mesh = GetComponent< MeshFilter >().mesh;
         originalVerts = new Vector3[ mesh.vertices.Length ];
         System.Array.Copy( mesh.vertices, originalVerts, mesh.vertices.Length );
     }
 
     void Update()
     {
         Vector3[] verts = new Vector3[ originalVerts.Length ];
         
         for ( int i = 0; i < originalVerts.Length; i++ ) 
         {
             verts[ i ] = new Vector3( originalVerts[i].x, 0, originalVerts[i].z );
             
             //verts[ i ].y = Mathf.Sin( originalVerts[i].x * freqX + timer ) * scaleY;
             verts[ i ].y = ( Mathf.PerlinNoise( originalVerts[i].x * freqX + timer, originalVerts[i].z * freqZ + timer ) * 2f - 1f ) * scaleY;
         }
         
         mesh.vertices = verts;
         mesh.RecalculateBounds();
         
         timer += speed * Time.deltaTime;
     }
 }