We examine the inviscid flow generated around a body moving impulsively from rest with a constant velocity U in a constant density gradient, ∇ρ0, which is assumed to be weak in the sense ε=a[mid ]∇ρ0[mid ] /ρ0[Lt ]1, where a is the length scale of the body. In the absence of a density gradient (ε=0), the flow is irrotational and no force acts on the body. When 0<ε[Lt ]1, vorticity is generated by a baroclinic torque and vortex stretching, which introduce a rotational component into the flow. The aim is to calculate both the flow around the body and the force acting on it.

When a two-dimensional body moves perpendicularly to the density gradient U·∇ρ0=0, the density and velocity field are both steady in the body's frame of reference and the vorticity field decays with distance from the body. When a three-dimensional body moves perpendicularly to the density gradient, the vorticity field is regular in the main flow region, [Dscr ]M, but is singular in a thin inner region [Dscr ]I located adjacent to the body and to the downstream-attached streamline, and the flow is characterized by trailing horseshoe vortices. When the body moves parallel to the density gradient U×∇ρ0=0, the density field is unsteady in the body's frame of reference; however to leading order the flow is steady in the region [Dscr ]M moving with the body for Ut/a[Gt ]1. In the thin region [Dscr ]I of thickness O(aε), the density gradient and vorticity are singular. When U×∇ρ0=0 this singularity leads to a downstream ‘jet’ with velocities of O(−(U·∇ρ0) Ua/(ρ0U)) on the downstream attached streamline(s). In the far field the flow is characterized by a sink of strength CM[Vscr ] (U·∇ρ0) /2ρ0, located at the origin, where CM is the added-mass coefficient of the body and [Vscr ] is the body's volume.

The forces acting on a body moving steadily in a weak density gradient are calculated by considering the steady relative velocity field in region [Dscr ]M and evaluating the momentum flux far from the body. When U·∇ρ0=0, a lift force, CL[Vscr ] (U·∇ρ0)×U, pushes the body towards the denser fluid, where the lift coefficient is CL=CM/2 for a three-dimensional body, that is axisymmetric about U, and is CL=(CM+1)/2 for a two-dimensional body. The direction of the lift force is unchanged when U is reversed. A general expression for the forces on bodies moving in a weak shear and perpendicularly to a density gradient is calculated. When U×∇ρ0=0, a drag force −CD[Vscr ] (U·∇ρ0)U retards the body as it moves into denser fluid, where the drag coefficient is CD=CM/2, for both two- and three-dimensional axisymmetric bodies. The direction of the drag force changes sign when U is reversed. There are two contributions to the drag calculation from the far field; the first is from the wake ‘jet’ on the attached streamline(s) caused by the rotational component of the flow and this leads to an accelerating force. The second and larger contribution arises from a downstream density variation, caused by the distortion of the isopycnal surfaces by the primary irrotational flow, and this leads to a drag force.

When cylinders or spheres move with a velocity U at arbitrary orientation to the density gradient, it is shown that they are acted on by a linear combination of lift and drag forces. Calculations of their trajectories show that they initially slow down or accelerate on a length scale of order ρ0/[mid ]∇ρ0[mid ] (independent of [Vscr ] and U) as they move into regions of increasing or decreasing density, but in general they turn and ultimately move parallel to the density gradient in the direction of increasing density gradient.