On the Generalized Ertel-Rossby Invariant

A new invariant called the generalized Ertel Rossby invariant （GER） was developed in this study. The new invariant is given by the dot product of the generalized vorticity and the generalized velocity. The generalized vortieity is the absolute vorticity minus the cross product of the gradient of Lagrangian--time integrated temperature and the gradient of entropy. The generalized velocity is the absolute velocity minus the sum of the gradient of Lagrangian-time integrated kinetic potential and the Lagrangian time integrated temperature multiplied by the gradient of entropy. In addition to the traditional potential vorticity, the GER invariant may provide another useful tool to study the atmospheric dynamic processes for weather phenomena ranging from large scales to small scales.

Some exact solutions of the oscillatory motion of a generalized second grade fluid in an annular region of two cylinders

The velocity field and the associated shear stress corresponding to the longitudinal oscillatory flow of a generalized second grade fluid, between two infinite coaxial circular cylinders, are determined by means of the Laplace and Hankel transforms. Initially, the fluid and cylinders are at rest and at t = 0＋ both cylinders suddenly begin to oscillate along their common axis with simple harmonic motions having angular frequencies Ω1 and Ω2. The solutions that have been obtained are presented under integral and series forms in terms of the generalized G and R functions and satisfy the governing differential equation and all imposed initial and boundary conditions. The respective solutions for the motion between the cylinders, when one of them is at rest, can be obtained from our general solutions. Furthermore, the corresponding solutions for the similar flow of ordinary second grade fluid and Newtonian fluid are also obtained as limiting cases of our general solutions. At the end, the effect of different parameters on the flow of ordinary second grade and generalized second grade fluid are investigated graphically by plotting velocity profiles.

Exact solution for the rotational flow of a generalized second grade fluid in a circular cylinder

This paper deals with the rotational flow of a generalized second grade fluid, within a circular cylinder, due to a torsional shear stress. The fractional calculus approach in the constitutive relationship model of a second grade fluid is introduced. The velocity field and the resulting shear stress are determined by means of the Laplace and finite Hankel transforms to satisfy all imposed initial and boundary conditions. The solutions corresponding to second grade fluids as well as those for Newtonian fluids are obtained as limiting cases of our general solutions. The influence of the fractional coefficient on the velocity of the fluid is also analyzed by graphical illustrations.

ANALYSIS AND SIMULATION ON THE MECHANISM OF A NOVEL DUAL-WAVE SHOCK TEST MACHINE

For qualifying the anti-shock performance of shipboard equipments and simulating actual underwater explosion environments, a novel dual-wave shock test machine is proposed to increase testing capability of shock test machines as well as to meet certain shock testing specification. The machine can generate a double-pulse acceleration shock for test articles according to specification defined in BV043/85. On the basis of the impact theory, a nonlinear dynamic model of the hydraulically-actuated test machine is established with thorough analysis on its mechanism which involves conversion of gas potential energy and dissipation of kinetic energy. Simulation results have demonstrated that the machine can produce a double-pulse acceleration shock in the time domain or a desired shock response spectrum in the frequency domain, which sets a theoretical base for the construction of the proposed machine.

MOVING VELOCITIES OF PRECURSOR SOLITON GENERATION IN TWO-LAYER FLOW

Based on the AfKdV equation of Xu et al.([1]), a theory on the velocities of the precursor soliton generation in two-layer flow over topography is presented in the present paper. Moving velocities of precursor solitons, of the first zero-crossing of the tailing wavetrain and of the flow behind the topography are found theoretically. It is shown that for a given topography, when its moving velocities are at the resonant points, we have the following rules: the ratio of the moving velocity of the precursor solitons to that of the first zero-crossing of the tailing wavetrain equals -4/3. At the same time, the ratio of the width of generating region of the precursor solitons to that of the depressed water region equals also -4/3. The theoretical results are examined by means of numerical calculation. The comparison between the theoretical and numerical results are found in good agreement. For different stratified parameters of two-layer how, the velocities of the precursor soliton generation are also predicted in terms of the present theoretical results.