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The critical-velocity behavior of oscillatory superfluid Helium-4 flowthrough a 2-micrometer by 2-micrometer aperture in a 0.1-micrometer-thick foilhas been studied from 0.36 K to 2.10 K at frequencies from less than 50 Hz upto above 1880 Hz. The pressure remained less than 0.5 bar. In early runs duringwhich the frequency remained below 400 Hz, the critical velocity was anearly-linearly decreasing function of increasing temperature throughout theregion of temperature studied. In runs at the lowest frequencies, isolated 2 Piphase slips could be observed at the onset of dissipation. In runs withfrequencies higher than 400 Hz, downward curvature was observed in the decreaseof critical velocity with increasing temperature. In addition, above 500 Hz analteration in supercritical behavior was seen at the lower temperatures,involving the appearance of large energy-loss events. These irregular eventstypically lasted a few tens of half-cycles of oscillation and could involvehundreds of times more energy loss than would have occurred in a singlecomplete 2 Pi phase slip at maximum flow. The temperatures at which thisaltered behavior was observed rose with frequency, from ~ 0.6 K and below, at500 Hz, to ~ 1.0 K and below, at 1880 Hz.Comment: 35 pages, 13 figures, prequel to cond-mat/050203

The Frequency Dependence of Critical-Velocity Behavior in the Oscillatory Flow of Superfluid 4He Through a 2 × 2-μm Aperture in a Thin Foil