THE TWO-DIMENSIONAL FLOW OF AN INVISCID DENSITY-STRATIFIED LIQUID PAST A SLENDER BODY.
BOEING SCIENTIFIC RESEARCH LABS SEATTLE WASH FLIGHT SCIENCES LAB
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Under the assumption of small velocity perturbations the linearized equation governing the two-dimensional flow of a density-stratified fluid is developed. The density is assumed to vary exponentially with depth which simplifies the equations and permits consideration of a fluid of infinite extent vertically as well as horizontally. The approximate derivation used emphasizes the physical aspects of the situation, employing the eccentricity of the center of gravity of a fluid element and the resulting torque which is developed even in the absence of viscosity. Particular attention is given to the case where gravity forces greatly exceed accelerative forces. For this case the expression for a dipole is developed and corrected to eliminate infinite energy from the upstream field. It is shown how the dipole is used to construct slender bodies, and expressions for the wave drag of slender bodies are given. The attempt is to further clarify some of the simpler aspects of stratified-fluid flow. Author
- Fluid Mechanics