The self-propulsion of a deformable body in a perfect fluid

It is shown that a deformable body can move persistently from rest through a perfect fluid without having to produce vorticity in the fluid

Brownian motion in thin sheets of viscous fluid

The drag on a cylindrical particle moving in a thin sheet of viscous fluid is calculated. It is supposed that the sheet is embedded in fluid of much lower viscosity. A finite steady drag is obtained, which depends logarithmically on the ratio of the viscosities. The Einstein relation is used to determine the diffusion coefficient for Brownian motion of the particle, with application to the movement of molecules in biological membranes. In addition, the Brownian motion is calculated using the Langevin equation, and a logarithmically time-dependent diffusivity is obtained for the case when the embedding fluid has zero viscosity

Long wavelength bifurcation of gravity waves on deep water

Conditions are found for the appearance of non-uniform progressive waves of permanent form from a long-wave modulation of a finite-amplitude Stokes wave on deep water. The waveheight at which the modulated waves can occur is a very slowly decreasing function of the modulation wavelength for values up to 150 times the original wavelength. Some qualitative remarks are made about the problem of determining the stability of the new waves

The large-scale structure of homogeneous turbulence

A field of homogeneous turbulence generated at an initial instant by a distribution of random impulsive forces is considered. The statistical properties of the forces are assumed to be such that the integral moments of the cumulants of the force system all exist. The motion generated has the property that at the initial instant E(kappa) = Ckappa^2 + o(kappa^2) where E(k) is the energy spectrum function, k is the wave-number magnitude, and C is a positive number which is not in general zero. The corresponding forms of the velocity covariance spectral tensor and correlation tensor are determined. It is found that the terms in the velocity covariance Rij(r) are O(r^−3) for large values of the separation magnitude r. An argument based on the conservation of momentum is used to show that C is a dynamical invariant and that the forms of the velocity covariance at large separation and the spectral tensor at small wave number are likewise invariant. For isotropic turbulence, the Loitsianski integral diverges but the integral $$\int_0^{\infty} r^2R(r)dr = \frac{1}{2}\pi C$$ exists and is invariant

Dynamics of vorticity

Remarks are made about the status of research on the role of vorticity in fluid dynamics and some unsolved problems of current interest are described

Approach of a vortex pair to a rigid free surface in viscous fluid

The motion in a viscous incompressible fluid of a vortex pair toward a rigid plane wall on which slip is allowed is considered. It is shown that the centroids of vorticity do not approach the wall monotonically, and there is some rebound at a rate depending upon the viscosity and initial separation of the vortices

The number of waves on unstable vortex rings

An explanation is proposed for the dependence on Reynolds number and other parameters of the number of waves which appear on vortex rings formed by pushing fluid out of a tube. It is shown that the number of waves can be sensitive to the vorticity distribution in the core of the ring. The process of ring formation is discussed and it is concluded that peaked vorticity distributions, limited by viscosity, will occur. Quantitative estimates of the number of waves are made. Agreement with observation is satisfactory

Dependence on Reynolds number of high-order moments of velocity derivatives in isotropic turbulence

The results of a heuristic model of the fine scale structure of homogeneous turbulence are presented. Predictions are made about the way in which flatness and skewness factors of arbitrary order depend upon the Reynolds number of the turbulence

The approach of a vortex pair to a plane surface in inviscid fluid

It is shown that a symmetrical vortex pair consisting of equal and opposite vortices approaching a plane wall at right angles must approach the monotonically in the absence of viscous effects. An approximate calculation is carried out for uniform vortices in which the vortices are assumed to be deformed into ellipses whose axis ratio is determined by the local rate of strain according to the results of Moore & Saffman (1971)

Spatial quantum noise in singly resonant second-harmonic generation

We study the spatial distribution of quantum noise in singly resonant second-harmonic generation. Calculations are performed below threshold for spatial modulational instability. For parameters for which the intracavity fields are modulationally stable the spatial spectrum shows maximum squeezing at k=0, whereas under conditions of modulational instability we find maximum squeezing at finite wave number |k|=kc, where kc corresponds to the classical critical wave number