## What is eulerian framework?

The Eulerian specification of the flow field is a way of looking at fluid motion that focuses on specific locations in the space through which the fluid flows as time passes. This can be visualized by sitting on the bank of a river and watching the water pass the fixed location.

## What is material derivative in fluid mechanics?

In continuum mechanics, the material derivative describes the time rate of change of some physical quantity (like heat or momentum) of a material element that is subjected to a space-and-time-dependent macroscopic velocity field.

**What is boussinesq hypothesis in turbulence modeling?**

Boussinesq’s hypothesis is that the turbulent stresses are related to the mean velocity gradients in almost the same way that the viscous stresses are related to the complete velocity gradients.

### What is Lagrange approach?

A Lagrangian approach is usually taken for modeling transport of oil at surface and subsurface. A total current load can be used in the formulation of models as a summation of all environmental loadings from wind, wave, currents and turbulent diffusivity.

### What is meant by substantial derivative?

Substantial derivative is an important concept in fluid mechanics which describes the change of fluid elements by physical properties such as temperature, density, and velocity components of flowing fluid along its trajectory [61].

**What is the eddy viscosity hypothesis?**

The eddy viscosity hypothesis is a core element of a mathematical model that describes turbulent flow next to a solid wall that is based on a macroscopic description of turbulent flow. In fact, the theory of boundary resistance in channel flow was historically developed using the eddy viscosity concept.

## What is Reynolds stress tensor?

In fluid dynamics, the Reynolds stress is the component of the total stress tensor in a fluid obtained from the averaging operation over the Navier–Stokes equations to account for turbulent fluctuations in fluid momentum.

## What is Boussinesq analysis?

The Boussinesq solution for the distribution of stresses in a half-space resulting from surface loads is largely used in geotechnical and road engineering. It is based on the assumption of a linear–elastic homogeneous isotropic half-space for the soil media.

**What is the difference between Lagrangian and Hamiltonian?**

The key difference between Lagrangian and Hamiltonian mechanics is that Lagrangian mechanics describe the difference between kinetic and potential energies, whereas Hamiltonian mechanics describe the sum of kinetic and potential energies.

### What is difference between steady and unsteady flow?

steady: A steady flow is one in which the conditions (velocity, pressure and cross- section) may differ from point to point but DO NOT change with time. unsteady: If at any point in the fluid, the conditions change with time, the flow is described as unsteady.

### What is the formula of the substantial derivative?

Δf = ∂f ∂t Δt + ∂f ∂x1 Δx1 + ∂f ∂x2 Δx2 + ∂f ∂x3 Δx3 (1.331) Page 3 120 Since the differential df is the limit of Δf as all changes of variable go to zero, we can take the limit of equation 1.331 to obtain df in terms of dx1, dx2, and dx3.

**How is the substantial derivative of velocity vector denoted?**

1. How is the substantial derivative of velocity vector denoted? Explanation: \frac{D\vec{V}}{Dt} is the substantial derivative.