A simple vertex displacement script that uses sine on two axis to emulate a wave-like behaviour.

WaveMesh.cs

//A simple vertex displacement script that uses sine on two axis to emulate a wave-like behaviour. 
public class WaveMesh : MonoBehaviour
{
    public MeshFilter meshFilter;
    public float amplitude = 0.5f;
    public float xLength = 0.5f;
    public float zLength = 0.5f;
    public float speed = 1.0f;
    //Only affect the vertices above this heigth in local space
    public float affectedVerticesHeightTreshold;
    //Offset vertices below this height with this:
    public float unaffectedVerticesOffset;

    private float[] originalHeight;
    private Mesh targetMesh;

    public void StoreMeshInfo()
    {
        targetMesh = meshFilter.mesh;
        originalHeight = new float[targetMesh.vertexCount];
        for (int i = 0; i < originalHeight.Length; i++)
        {
            originalHeight[i] = targetMesh.vertices[i].y;
        }
    }

    public void UpdateMesh()
    {
        Vector3[] vertices = targetMesh.vertices;

        for (int i = 0; i < vertices.Length; i++)
        {
            if (originalHeight[i] > affectedVerticesHeightTreshold)
            {
                vertices[i].y = Mathf.Sin((Time.time * speed) + (vertices[i].x * xLength) + (vertices[i].z * zLength) + originalHeight[i]) * amplitude;
            }
            else
            {
                vertices[i].y = -amplitude-unaffectedVerticesOffset;
            }
        }

        targetMesh.vertices = vertices;
        targetMesh.RecalculateNormals();
    }
}