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Energy spectrum functions computed from data of various three-dimensional simulations of forced isotropic turbulence are investigated. The piece-wise parabolic method (PPM) was used to treat flows with Mach number of the order unity. The dissipation is of purely numerical origin. For the dimensionless mean rate of dissipation, we find values in agreement with results from other, mostly incompressible turbulence simulations. The so-called bottleneck phenomenon is also present in the turbulence energy spectra. Although the bottleneck reduces the range of nearly inertial scales considerably, we were able to estimate the value of the Kolmogorov constant. In the statistically stationary regime, C ≈ 1.7 for strictly subsonic turbulence, but also in the presence of shocklets in moderately transonic flows. As compressive components become more significant, however, the value of C appears to decrease. Moreover, we discuss length scales related to numerical dissipation, in particular, an effective numerical length scale ∆ eff , which can be regarded as the characteristic smoothing length of the implicit filter associated with the PPM.

The transient increase in cation permeability observed in duck red cells incubated with norepinephrine has been shown to be a linked, bidirectional, co-transport of sodium plus potassium . This pathway, sensitive to loop diuretics such as furosemide, was found to have a [Na + K] stoichiometry of 1 :1 under all conditions tested . Net sodium efflux was inhibited by increasing external potassium, and net potassium efflux was inhibited by increasing external sodium . Thus, the movement of either cation is coupled to, and can be driven by, the gradient of its co-ion . There is no evidence of trans stimulation of cotransport by either cation . The system also has a specific anion requirement satisfied only by chloride or bromide . Shifting the membrane potential by varying either external chloride (at constant internal chloride) or external potassium (at constant internal potassium in the presence of valinomycin and DIDS [4,4'-diisothiocyano-2,2'-disulfonic acid stilbene]), has no effect on norepinephrine-stimulated net sodium transport . Thus, this co-transport system is unaffected by membrane potential and is therefore electrically neutral . Finally, under the latter conditions-when E,n was held constant near Ex and chloride was not at equilibrium-net sodium extrusion against a substantial electrochemical gradient could be produced by lowering external chloride at high internal concentrations, thereby demonstrating that the anion gradient can also drive co-transport . We conclude, therefore, that chloride participates directly in the co-transport of [Na + K + 2Cl] .

Duck red cells in hypertonic media experience rapid osmotic shrinkage followed by gradual reswelling back toward their original volume. This uptake of salt and water is self limiting and demands a specific ionic composition of the external solution. Although ouabain (10(-4)M) alters the pattern of cation accumulation from predominantly potassium to sodium, it does not affect the rate of the reaction, or the total amount of salt or water taken up. To study the response without the complications of active Na-K transport, ouabain was added to most incubations. All water accumulated by the cells can be accounted for by net salt uptake. Specific external cation requirements for reswelling include: sufficient sodium (more than 23 mM), and elevated potassium (more than 7 mM). In the absence of external potassium cells lose potassium without gaining sodium and continue to shrink instead of reswelling. Adding rubidium to the potassium- free solution promotes an even greater loss of cell potassium, yet causes swelling due to a net uptake of sodium and rubidium followed by chloride. The diuretic furosemide (10(-3)M) inhibits net sodium uptake which depends on potassium (or rubidium), as well as inhibits net sodium uptake which depends on sodium. As a result, cell volume is stabilized in the presence of this drug by inhibition of shrinkage, at low, and of swelling at high external potassium. The response has a high apparent energy of activation (15-20 kcal/mol). We propose that net salt and water movements in hypertonic solutions containing ouabain are mediated by direct coupling or cis-interaction, between sodium and potassium so that the uphill movement of one is driven by the downhill movement of the other in the same direction.

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A B S T R A C T Catecholamines induce net salt and water movements in duck redGen. Physiol. 70:59-79. Otherwise, these two systems share a great many similarities. In both cases, net water and salt movements have a marked dependence on external cation concentrations, are sensitive to furosemide and insensitive to ouabain, and allow the substitution of rubidium for external potassium. In the presence of ouabain, but the absence of external potassium (or rubidium), a furosemide-sensitive net extrusion of sodium against a large electrochemical gradient can be demonstrated. When norepinephrine-treated cells are incubated with ouabain and sufficient external sodium, the furosemide-sensitive, unidirectional influxes of both sodium and rubidium are half-maximally saturated at similar rubidium concentrations; with saturating external rubidium, the same fluxes are half-maximal at comparable levels of external sodium. In the absence of sodium, a catecholamine-stimulated, furosemide-sensitive influx of rubidium persists. In the absence of rubidium, a similar but smaller component of sodium influx can be seen. We interpret these results in terms of a cotransport model for sodium plus potassium which is activated by hypertonicity or norepinephrine. When either ion is absent from the incubation medium, the system promotes an exchange-diffusion type of movement of the co-ion into the cells. In the absence of external potassium, net movement of potassium out of the cell leads to a coupled extrusion of sodium against its electrochemical gradient.

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