A fully observer-covariant view of Fluid Mehanics with some applications.

In this talk we present a formulation of the equations of motion of simple fluids that applies to generic observers. In this formulation, the state of the flow is described by sections of the cotangent bundle over the manifold that describes the space occupied by the fluid, whose evolution is given by the Lie derivative. Thus, we avoid the need to introduce an extra structure, the Levi-Civita connection. We initially formulate the equations for a class of observers that include the canonical inertial observers. Later, we invoke the principle of covariance to show how the formulation naturally extends to arbitrary observers. Time permitting, we will give consider a few applications, such as a generalized Orr-Sommerfeld equation and inertial equatorial waves on a wobbly planet.