The prevalent theories have considered electromagnetic and electrostatic plasma waves and instabilities in the presence of only flow shear. As a result, these theories have predicted only excitation (destabilization) of instabilities which has lead to the well-known hypothesis that `flow shear is the origin of many space and laboratory oscillations and instabilities.' However, here we propose a model of plasma oscillations and instabilities in the presence of a more realistic flow profile including both flow shear and flow curvature. Now, with the inclusion of flow curvature the stability picture is changed drastically. The flow curvature, contrary to the flow shear, can actually `stabilize' the waves which is rather opposite to the well-know hypothesis of the generation of electromagnetic and electrostatic fluctuations by the velocity shear. The new model of plasma waves and oscillations in the presence of both flow shear and curvature, being more realistic, will have wider applications in fluid dynamics and space physics.