Instanton calculus in shell models of turbulence

Daumont1, Dombre, Gilson

  • 1Centre de Recherches sur les Tres Basses Temperatures-CNRS, Laboratoire Conventionne Avec l'Universite Joseph Fourier, Boiinsertion markte Postale 166, 38042 Grenoble Cedex 9, France and Ecole Normale Superieure de Lyon, Laboratoire.

Related Concept Videos

Clausius-Clapeyron Equation02:35

Clausius-Clapeyron Equation

The equilibrium between a liquid and its vapor depends on the temperature of the system; a rise in temperature causes a corresponding rise in the vapor pressure of its liquid. The Clausius-Clapeyron equation gives the quantitative relation between a substance’s vapor pressure (P) and its temperature (T); it predicts the rate at which vapor pressure increases per unit increase in temperature.
Impulse-Momentum Theorem00:49

Impulse-Momentum Theorem

The total change in the motion of an object is proportional to the total force vector acting on it and the time over which it acts. This product is called impulse, a vector quantity with the same direction as the total force acting on the object.
By writing Newton's second law of motion in terms of the momentum of an object and the external force acting on it, and simultaneously using the definition of the impulse vector, it can be shown that the total impulse on an object is equal to its net...
The Clausius–Clapeyron Equation01:29

The Clausius–Clapeyron Equation

The Clausius-Clapeyron equation is a fundamental principle in physical chemistry and thermodynamics that describes the relationship between a substance's vapor pressure and temperature. Named after Rudolf Clausius and Benoît Paul Émile Clapeyron, the equation is integral in predicting a substance's behavior under different temperature conditions.The Clausius-Clapeyron equation allows us to calculate how the pressure at which a liquid boils (its vapor pressure) changes as the temperature changes.
Viscosity of Fluid01:19

Viscosity of Fluid

Viscosity measures the resistance a fluid offers to flow and deformation. It results from internal friction between layers of fluid moving relative to one another. Dynamic viscosity, denoted by the Greek letter mu (μ), quantifies the force needed to move one fluid layer over another. For Newtonian fluids like water and air, the relationship between the shearing stress and the rate of shearing strain is linear, meaning their viscosity remains constant regardless of the applied stress.
Navier–Stokes Equations01:28

Navier–Stokes Equations

For incompressible Newtonian fluids, where density remains constant, stresses show a linear relationship with the deformation rate, defined by normal and shear stresses. Normal stresses depend on the pressure exerted on the fluid and the rate of deformation in specific directions, which determines how fluid flows under varying pressures. Shear stresses, on the other hand, act tangentially across fluid layers. They explain how adjacent fluid layers slide relative to one another, connecting...
Dimensionless Groups in Fluid Mechanics01:15

Dimensionless Groups in Fluid Mechanics

Dimensionless groups in fluid mechanics provide simplified ratios that help analyze fluid behavior without relying on specific units. The Reynolds number (Re), which represents the ratio of inertial to viscous forces, distinguishes between laminar and turbulent flows, making it essential in the design of pipelines and aerodynamic surfaces. The Froude number (Fr), the ratio of inertial to gravitational forces, is particularly useful in predicting wave formation and hydraulic jumps in...