# Corrections

## Viscous scale of turbulence (misprint on p. 63)

The viscous scale is defined by the requirement that the Reynolds number is of order unity:

The kinematic viscosity is the mean free path times the thermal molecular velocity (comparable to the speed of sound). Therefore, the viscous scale is much larger than the mean free path as long as the velocity difference on the viscous scale is much smaller than the speed of sound. This is practically always the case for turbulence in liquids and gases. For example, in atmosheric turbulence, the external scale L can be in hundreds of meteres with velocity v(L) in tens of meters per second, but the viscous scale l is usually less than a millimiter so that

## Sound barrier

In Sect. 2.3.5 the solution of (2.47) in the hyperbolic case must have B->1/B.

## Solution of the Problem 3.7

In the middle of p. 151 it must be (3.29) instead of (3.5). Note also that not all features of the phase portrait are shown in the left panel of Fig. 4.3.

## Solution of the problem 1.11

Since Omega was given as 10 revolutions per second then the angular frequency is 2 pi times 10. To get the estimates for the force, accelerations etc, one needs extra factor 2 pi ≈ 6.3.

## Solution 1.14

In the Basic Solution the formula for the explosive velocity growth is missing:v(t)=v(0)/(1-r0Agt/B)2.

## Section 1.3.2 Moving sphere

There is a sign "-" missing in the formula for the potential in the figure on p. 23 and in the formula for the force (1.25). On p. 24, the last term in pressure must have 1/2 factor and the next sentence must be "the force is minus the pressure integral over surface".

## Rayleigh stability criterium

On page 8 there is a misprint in the last formula of the section 1.1.3: there is an extra factor r^4 there (thanks to Guillermo Casas for pointing this out).

## Problem 1.15 in the Russian edition

The frame speed must be V/\cos\theta. The velocity at infinity is V rather than u.

## Potential vorticity on p. 14

In the last derivation on p. 14 the last term in the first and second lines must be multiplied by omega:

## Pint and point

On page 11 must be "point" instead of "pint".