Mediaspace scheduled maintenance: Aug 25, 2026 07:00 - 12:00 AM. During this time, videos will be temporarily unavailable. Check status updates.

Lecture

Kalman-Hauad-Morning Relation

Description

This lecture focuses on deriving the Kalman-Hauad-Morning relation in the context of stationary turbulence with a forcing term. The instructor explains the importance of homogeneity and isotropy assumptions, as well as the implications of stationarity for the velocity field and forcing term. Through detailed mathematical derivations, the lecture explores the third order structure function and its divergence, leading to the derivation of the common Howard-Mohnen relation for homogeneous but not isotropic cases.

Official source

Ontological neighbourhood

Physics

Mechanics: Fluid mechanics

Related concepts (14)

Navier–Stokes equations

The Navier–Stokes equations (nævˈjeː_stəʊks ) are partial differential equations which describe the motion of viscous fluid substances, named after French engineer and physicist Claude-Louis Navier and Irish physicist and mathematician George Gabriel Stokes. They were developed over several decades of progressively building the theories, from 1822 (Navier) to 1842-1850 (Stokes). The Navier–Stokes equations mathematically express momentum balance and conservation of mass for Newtonian fluids.

Potential flow

In fluid dynamics, potential flow (or ideal flow) describes the velocity field as the gradient of a scalar function: the velocity potential. As a result, a potential flow is characterized by an irrotational velocity field, which is a valid approximation for several applications. The irrotationality of a potential flow is due to the curl of the gradient of a scalar always being equal to zero. In the case of an incompressible flow the velocity potential satisfies Laplace's equation, and potential theory is applicable.

Mathematical proof

A mathematical proof is a deductive argument for a mathematical statement, showing that the stated assumptions logically guarantee the conclusion. The argument may use other previously established statements, such as theorems; but every proof can, in principle, be constructed using only certain basic or original assumptions known as axioms, along with the accepted rules of inference. Proofs are examples of exhaustive deductive reasoning which establish logical certainty, to be distinguished from empirical arguments or non-exhaustive inductive reasoning which establish "reasonable expectation".

Laminar flow

In fluid dynamics, laminar flow (ˈlæmənər) is characterized by fluid particles following smooth paths in layers, with each layer moving smoothly past the adjacent layers with little or no mixing. At low velocities, the fluid tends to flow without lateral mixing, and adjacent layers slide past one another like playing cards. There are no cross-currents perpendicular to the direction of flow, nor eddies or swirls of fluids. In laminar flow, the motion of the particles of the fluid is very orderly with particles close to a solid surface moving in straight lines parallel to that surface.

Stokes flow

Stokes flow (named after George Gabriel Stokes), also named creeping flow or creeping motion, is a type of fluid flow where advective inertial forces are small compared with viscous forces. The Reynolds number is low, i.e. . This is a typical situation in flows where the fluid velocities are very slow, the viscosities are very large, or the length-scales of the flow are very small. Creeping flow was first studied to understand lubrication. In nature, this type of flow occurs in the swimming of microorganisms and sperm.

Related lectures (32)

Inviscid Flows: Understanding Fluid Dynamics

Explores inviscid flows, Reynolds number importance, linear deformations, and volume change in fluid dynamics.

Turbulence Concepts: Reynolds Decomposition and Closure Problem

Explores Reynolds decomposition, closure problem, and turbulence modeling challenges.

Understanding Turbulence

By the instructor Tobias Schneider explores the fundamental aspects of turbulence and its significance in various scientific disciplines.

Fluid Mechanics in Biomechanics

Introduces fluid mechanics in biomechanics, covering Eulerian description, momentum conservation, Navier-Stokes equations, and practical simulations.

Turbulent Flow Modeling