how to apply displacement map to a vertex shader in Webgl?

Question

Hello I have an image of displacement like this. I want to make the surface displace more when the part of image getting darker.

Here is my code in vertex shader. However, it doesn't work. There is no displacement :(. I'm not sure where is the problem

varying vec2 v_uv;
varying vec3 v_normal;
varying vec3 v_position;
uniform sampler2D tex;
uniform sampler2D dis;

void main() {
    float height = texture2D(dis,uv).g;  
    vec3 pos = position + height*normal *10.0;
    gl_Position = projectionMatrix * modelViewMatrix * vec4( pos, 1.0 );
    vec4 pos_1 = (modelViewMatrix * vec4(position,1.0));
    gl_Position = projectionMatrix * pos_1;
    v_position = pos_1.xyz;
    v_normal = normalMatrix * normal;
    v_uv = uv;
}
//in fragment vector
varying vec2 v_uv;
uniform sampler2D tex;
uniform sampler2D dis;
varying vec3 v_normal;
const vec3 lightDirWorld = vec3(0,1,1);

void main()
{
    vec3 nhat = normalize(v_normal);
    vec3 lightDir = normalize(viewMatrix * vec4(lightDirWorld, 0)).xyz;
    float light = dot(nhat, lightDir);
    vec4 color =texture2D(tex, v_uv);
    gl_FragColor = color*vec4(light,light,light,1);
}