Measurements of layer depth during baroclinic instability in a two-layer flow

This study investigates the baroclinic instability of a two-layer rotating fluid system. The instability is generated by releasing a cylinder of buoyant fluid at the surface of ambient fluid. The buoyant fluid is dyed so that its depth may be determined from its optical thickness. The system first adjusts until the horizontal density gradient is balanced by a flow along the front, and the adjusted state is then unstable to azimuthal waves. Contours of constant upper layer depth are examined, and the perturbation at each azimuthal wavenumber is determined. The initial wavenumber is well modelled by simple quasi-geostrophic theory. There is a clear high wavenumber cutoff, and a transfer of energy to larger scales with time.     

On the electrical discharge in d.c. and high frequency fields simultaneously

Summary When a d.c. and a h.f. field are perpendicularly superposed in a electrical discharge (p 10–10^–4 mm Hg), three types of discharge can exist, classified from the standpoint of d.c. conduction: (1) d.c. glow type, d.c.-dominant discharge with additional ionization by h.f. field; (2) space chargelimited type, the same as the conduction in the floating double probe in a plasma produced by h.f. field; (3) an intermediate stage between the first and second types, herein referred to as transition type. According to our analysis of the transition type at low pressure, the value of in high electric fields can be deduced from the measurement.     

Momentum and energy balances for dispersed two-phase flow

Summary The equations of motion and the mechanical energy balances for two-phase flow systems are derived by integration over a volume containing a large number of elements of the dispersed phase.List of symbols A, A boundary of volumes V, V - dA, dA surface element of A, A - A _s boundary of particles in V - dA _s surface element of A _s - F force per unit volume of the system - g –gz=gravity vector - g acceleration by gravity - I unit tensor - p pressure - Q dissipation in the continuous phase - Q _s dissipation in the dispersed phase - R compression work in the continuous phase - R _s compression work in the dispersed phase - t time - u velocity of continuous phase - u _s velocity of dispersed phase - u magnitude of u - u _s magnitude of u _s - V volume in the two-phase system - V part of V occupied by the continuous phase - W work done by F - z vertical coordinate - local volume fraction of the dispersed phase - pI–=stress tensor of the continuous phase - _s turbulent particle stress tensor - density of the continuous phase - _s density of the dispersed phase - shearing-stress tensor of the continuous phase - _s turbulent particle shearing-stress tensor - nabla operator - u, u _s velocity gradient tensor - substantial derivative (Shell Internationale Research Maatschappij N.V.)(Bataafse Internationale Petroleum Maatschappij N.V.)     

Transient flow near a rotating disk

Summary The solution of the time dependent flow due to the impulsive starting of a single infinite disk from rest is obtained numerically for the entire history of the transient. The primary tangential velocity exhibits a single overshoot of its steady value while the growth of the secondary flows is monotonic. The overshoot is seen to be a direct consequence of the lag in the development of the secondary flows. An analytical solution is obtained for a related linearized problem: The angular velocity of an infinite disk, initially rotating with an infinite environment, is perturbed. The oscillatory decays to the steady state, which occur in both unbounded and bounded linearized analyses, are discussed in relation to the overshoot in the impulsively started disk problem.     

The swirling radial free jet

Summary A general similarity solution suggested by Watson for the problem of the laminar, radial, free-jet with swirl has been previously discussed by Riley who also calculated the order to which the solution was valid. That problem is considered in more detail here and higher order terms are given. It is shown that a perturbation scheme for the stream function consisting of a series of inverse powers of and which uses the asymptotic similarity solution as the basic solution is inadequate, and a modification to the series so as to include terms like ⁿ (ln ) ^m must be adopted in order to satisfy the boundary conditions. It is also shown that the general similarity solution may be obtained from the asymptotic series representing the general case with swirl for certain special values of the free constants and also for the no-swirl or free-jet problem. The asymptotic series is given to order ^–13 for the case of swirl and to order ^–29 when there is no swirl.     

Ferrite-loaded cavity resonators

The problem of the determination of the free oscillation modes of a cavity resonator completely filled with magnetized ferrite is considered. A first order formulation, which takes into account the equation of motion of the magnetization vector together with Maxwell's equations, is used. By expanding the field vectors in terms of solenoidal and irrotational eigenfunctions of the corresponding empty resonator, a matrix eigenvalue problem in classical form is obtained. The general formulation is specialized to the particular case of a circularly cylindrical resonator filled with transversely magnetized ferrite. A numerical analysis for the determination of resonance frequencies and field configurations is carried out.Work partially supported by Consiglio Nazionale delle Ricerche of Italy.     

A rotating field mhd hydrostatic thrust bearing

It is found that the load capacity of a magnetohydrodynamic thrust bearing with a rotating disk can be increased by rotating the axial magnetic field at a suitable speed in a direction opposite to that of the disk rotation. This method of improving the bearing performance is considered to be efficient if the Hartmann number is not too large. Thus for a given load, the size and weight of the magnet to be used in a thrust bearing with rotating field can be reduced considerably.Nomenclature a radius of plenum recess - b outside disk radius - B ₀ magnetic induction of applied axial magnetic field - hE ₀ ^1/2/a ^1/2, nondimensionalized electric field - E ₀ radial electric field at r=a - E _r radial electric field - h half of lubricant film thickness - M (B ₀ ² h ²/)^1/2, Hartmann number - P pressure - P _e pressure at r=b - P ₀ pressure at r=a - Q volume flow rate of lubricant - Q ₀ volume flow rate of a nonrotating bearing in the absence of applied magnetic field - r radial coordinate - u, v fluid velocity components in radial and circumferential directions, respectively - W load capacity of bearing - W ₀ load capacity of a nonrotating bearing in the absence of a magnetic field having a flow rate which the same bearing would have at Hartmann number M - z axial coordinate - azimuthal coordinate - coefficient of viscosity of lubricant - _e magnetic permeability - fluid density - electrical conductivity - angular velocity of rotating disk - _C critical disk velocity at which W=0 - _M angular velocity of axial magnetic field - optimum angular velocity of magnetic field On leave of absence from Department of Aero-Space Engineering, University of Notre Dame, Notre Dame (Ind.), U.S.A.     

A sensitive and rapid bridge for the study of magnetic susceptibilities at frequencies from 200 to 106 Hz

Summary A new piece of equipment is described for measuring / ₀ and / ₀ as a function of field (0 to 4250 Oe), temperature (1.2°K to room temperature) and frequency (200 Hz to 1 MHz). It is about ten times more sensitive than the Hartshorn bridge used in Leiden²⁾ and it is more convenient to operate as the measuring procedure is automatic after initial adjustments have been made. The main component is a bridge circuit of four inductors, built as closely similar to each other as possible. The output from the bridge goes to two phase sensitive detectors which monitor the two outputs, one inphase, one /2 out of phase, of the bridge. A heterodyne system is used where the input signal to the bridge is obtained by mixing the output from a variable frequency oscillator with that from a 1.5 MHz oscillator and taking the difference frequency, which is phase locked to a master oscillator. The output from the bridge, after preamplification, is mixed with a second output from the variable oscillator and the difference taken again. This gives a 1.5 MHz signal modulated by the magnetic effects in the bridge which is used in the two phase-sensitive detectors. Their output is recorded on an x–y writer. The bridge needs only be balanced to an output of about 50 mV because the sample is moved between two coils and the difference voltage is measured. The use of the same equipment to measure relaxation times longer than 100 ms is also described.Communication No. 349a from The Kamerlingh Onnes Laboratorium, Leiden, The Netherlands     

Torsional oscillations of an infinite plate in an elastico-viscous fluid

Summary The equations of motion of an infinite plate performing torsional oscillations in Walters elastico-viscous liquid B have been solved by expanding the velocity profile in powers of the amplitude of oscillation of the plate. The first order solution consists of a transverse velocity and the second-order solution gives a radial-axial flow composed of a steady part and a fluctuating part. The steady part of the radial flow does not vanish outside the boundary layer and hence the equations are solved by another approximate method for the steady part of the flow. The effects of the non-Newtonian term is to increase the non-dimensional boundary layer to start with and subsequently to decrease it and to increase the shearing stress at the plate. The steady radial and the steady axial velocities fall short of the inelastic flow in the beginning but later on their values lie above.     

Shape Oscillations of Rising Bubbles

The paper details results from an experimental study on bubbles rising in still tap water. Shape and motion parameters of the bubbles were measured using a combination of high speed cinematography and digital image processing. The Reynolds numbers of the bubbles studied ranged from about 700 to 1300, with the bubbles exhibiting all the familiar shape and motion characteristics: oblate spheroids becoming wobbly, and spiralling or zig-zagging motion becoming rocking as the bubble size increased. Time series of the bubble major axes revealed regular oscillations in the bubble shape. In most cases three frequencies could be readily identified, corresponding to those of vortex shedding from the bubble and two modes of ellipsoidal harmonics (modes 2,0 and 2,2). Comparison of time series of bubble shape and motion indicated a strong interaction between the shape oscillations of mode 2,0 and bubble motion. As the bubble size increased the frequency of both shape oscillation modes approached that of the vortex shedding, which remained constant at about 12 Hz for all of our experiments. The frequencies become equal for bubbles larger than in our study, at a Reynolds number of about 3000. Using data from the literature we found that the vortex shedding appears to become locked-in on the mode 2,0 shape oscillation.