The way in which energy propagates away from a two-dimensional oscillatory disturbance in a thermocline is considered theoretically and experimentally. It is shown how the St. Andrew's-cross-wave is modified by reflections and how the cross-wave can develop into thermocline waves. A linear shear flow is then superimposed on the thermocline. Ray theory is used to evaluate the wave shapes and these are compared to finite-difference solutions of the full Navier–Stokes equations.
It is shown how the St Andrew's cross-wave in a density-stratified fluid is modified by a horizontal shear above the level of the source. Ray theory is used to develop the equations for the phase configuration and it is shown that, for the special case when the background natural frequency is constant and the shear is linear, the wave crests are straight lines passing through the source. The waves corresponding to outgoing energy have phase velocities directed towards the horizontal level of the source and the waves which have undergone a reflection have phase velocities directed towards the vertical. It is shown that the ray theory predictions compare well with experiment and with finite-difference calculations.
SUMMARYThe time-dependent hydrodynamic removal of a contaminated uid from a rectangular cavity on the oor of a duct is analysed numerically. Laminar duct ows are considered for Reynolds numbers of 50 and 1600 where the characteristic length is the duct height. Two cases are considered where: (1) the uid density in the cavity is the same as that for the duct uid and (2) the cavity uid has a higher density than the duct uid but the two uids are miscible. The ow is solved by a numerical solution of the timedependent Navier-Stokes equations. Attention is focused on the convective transport of contaminated uid out from the cavity and the e ect of duct ow velocity proÿle on the cleaning process. Passive markers are used in the numerical simulation for the purpose of identifying the contaminated cavity uid. The results show that the ow patterns in the cavity are in uenced by the type of duct ow. From a cleaning perspective, the results suggest that it is easier for the duct ow to penetrate a cavity and to remove contaminated cavity uid when the duct ow is of the Poiseuille type and the aspect ratio is large.
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