One of the 7 Clay Mathematics Institute $1 million Millennium Problems concerns existence and regularity of solutions to the Navier-Stokes equations. The problem was formulated in 2000 and I discussed certain very problematic aspects of the formulation in the following articles from 2008: On the Uniqueness of Weak Solutions of the Navier-Stokes Equations Is the Clay Navier-Stokes Problem Wellposed? also addressed […]

# Category archives for **fluid mechanics**

The milestone of computing the drag of car by solving the Navier-Stokes equations was passed in 2011 with the work reported in Adaptive Simulation of Turbulent Flow Past a Full Car Model, by N. Jansson, J. Hoffman and M. Nazarov: With about 10 million mesh points a C_D of 0.38 was computed, to be compared […]

To give perspective to the New Theory of Flight presented on the web site The Secret of Flight, let us see how the Old Theory of Flight is presented in the classical text Fundamentals of Aerodynamics by John D. Anderson. We quote from and comment on the essential Chapter 4 Incompressible Flow Over Airfoils: 2d Flow around […]

Ludwig Prandtl sentencing fluid mechanics to 100 years of uncomputability. The Paralyzing Dictate by the Father Ludwig Prandtl (1875 – 1953) took on the role of Father of Modern Fluid Mechanics by breaking away from the paradigm of classical fluid mechanics formed by Euler and d’Alembert in the mid 18th century based on describing slightly […]

The Father of Modern Aerodynamics inspecting the Ho III 1938 Rhön Contest Challenger. 1. The Legacy of Prandtl Ludwig Prandtl (1875-1953) is named Father of Modern Aerodynamics and Founder of Modern Fluid Mechanics. Wikipedia tells the story: (full story) In 1904 he delivered a groundbreaking paper On Motion of Fluids Flow with Very Little Viscosity in which he described the boundary […]

New Theory of Flight presented on The Secret of Flight is based on an analysis of computational solutions of the Navier-Stokes equations with slip boundary condition showing that the rotational slip separation pattern at the trailing edge (shown in the picture above) has an important role for […]

Here is a little Christmas and New Year puzzle to all readers of The World as Computation: There is a strong connection between turbulence black body radiation expansion of the Universe driven by dark energy the European economical crisis which all share the phenomenon of local collapse balanced by global expansion as explained in Computational […]

Is it possible to explain by energy conservation the apparent expansion of the Universe with galaxies seemingly repelling each other, as a compensation for the potential energy lost in the formation of galaxies by gravitational implosion? In short: Local implosion balanced by global explosion. Let us explore this natural and simple idea. Let us thus […]

My collection of Google Knols named My Book of Knolshas now been moved to this site as a collection of articles under the following headlines: philosophy of science mathematics mathematics/science education Newtonian mechanics fluid mechanics thermodynamics quantum mechanics theory of relativity global climate economy applications software I plan to update the articles on their new home.

# Modern Mathematics Education

Need of Reform

A reform of mathematics education is necessary to make it conform to the modern information society based on computational mathematics.

# Why Phelps’ Dolphin Kick Works

The secret of the feet of Michael Phelps

We give a scientific explanation of why the Dolphin Kick of Michael Phelps is so efficient.

# Hyperreality in Physics

simulation without origin

The French post-modern philosopher Baudrillard identifies hyperreality as simulation without real origin

(such as Disneyland), and claims that existing hyperreality can replace non-existing reality. We suggest a parallel in physics as equations without exact solutions including Lagrange’s equations of particle mechanics, Euler’s equations of fluid mechanics and Schrödinger’s equation of quantum mechanics, for which only approximate computational solutions exist. Hyperreal physics in the form of computational simulations similarly replaces non-existing physics.

# Why Birds Can Fly

The secret of bird flight

We explain gliding and flapping flight of birds based on computing turbulent solutions of the Navier-Stokes equations. We show that classical explanations are incorrect.

# Why a Topspin Tennis Ball Curves Down

and why a backspin table tennis ball also curves down

We present, based on computing turbulent solutions of the Navier-Stokes equations, a new explanation of the Magnus effect causing a topspin tennis ball to curve down and a backspin curve up. We also explain the reverse Magnus effect causing a backspin table tennis ball to curve down. We show that the classical explanation of the Magnus effect based on potential flow with circulation is non-physical and thus incorrect.