Examples of calculation methods for flow and mixing in stratified fluids

TLDR

The paper reviews mathematical models for predicting flow and mixing in stratified lakes and reservoirs, focusing on turbulence models that simulate momentum, heat, and mass transport in averaged‑equation statistical methods. It surveys prediction methods ranging from one‑dimensional integral approaches to direct Navier‑Stokes simulations, including turbulence models from Prandtl mixing‑length theory to second‑order closure schemes. Illustrative examples demonstrate the predictive capabilities of these methods across diverse stratified flow situations.

Abstract

Certain mathematical models for predicting the flow and mixing processes in stratified fluids are reviewed, with particular focus on stratified lakes and reservoirs. The various types of prediction methods are introduced briefly, from one‐dimensional integral methods to direct simulations of the Navier‐Stokes equations. The paper concentrates on turbulence models for simulating the turbulent momentum, heat, and mass transport terms appearing in the statistical methods employing averaged equations. Models ranging from the simple Prandtl mixing length theory to second‐order‐closure schemes are discussed. To illustrate the predictive capabilities of the methods, examples are presented of applications of the method covered to a variety of stratified flow situations.