Ephemeral shared volume in docker

I'm looking for a way to share an arbitrary directory in one Docker container with another, but without persisting the volumes between container creations.

The use case is sharing static assets between a web application and a web server like nginx. Both containers are built by an image. The web application's Dockerfile copies the static assets to a directory like /var/www/public when it's built. I want to avoid persisting the volume because the static assets are updated when the web application is built.

I've attempted this with a docker-compose.yml that looks like the following, but unfortunately this persists the volume and when a container is recreated with the new image, the contents of the shared volume aren't updated.

version: '3.5'

services:
  web:
    image: bswinnerton/nyc-restaurant-grades
    networks:
      - backend
    volumes:
      - www_data:/var/www/app/
  nginx:
    image: nginx
    depends_on:
      - web
    volumes:
      - ./nginx.conf:/etc/nginx/conf.d/default.conf:ro
      - www_data:/var/www/app/
    networks:
      - backend

volumes:
  www_data:

networks:
  backend:

And the web application's Dockerfile looks something like this:

FROM ruby:2.5.1

# Install dependencies
RUN apt-get update -qq && apt-get install -y build-essential libpq-dev nodejs

# Set working directory, where the commands will be ran:
RUN mkdir -p /var/www/app
WORKDIR /var/www/app

# Adding gems
COPY Gemfile Gemfile
COPY Gemfile.lock Gemfile.lock
RUN bundle install --jobs 20 --retry 5

# Adding project files
COPY . .

# Precompile assets
RUN bundle exec rails assets:precompile

CMD [ "bundle", "exec", "puma", "-C", "config/puma.rb" ]

I considered using a tmpfs mount, but it appears they cannot be shared between containers.