Forces from the Sea
Offshore structures must withstand enormous hydrodynamic forces from ocean waves, currents, and storms. For slender cylindrical members — the legs, braces, and risers that form jacket platforms — the Morison equation provides the engineering tool for calculating these forces. Proposed by Morison, O'Brien, Johnson, and Schaaf in 1950, it decomposes the total force into two physically distinct components: drag and inertia.
Drag & Inertia Components
The drag force arises from flow separation and vortex shedding around the cylinder, proportional to the square of water particle velocity. The inertia force comes from the pressure gradient in the accelerating wave field, proportional to the local fluid acceleration. Their relative importance depends on the Keulegan-Carpenter number KC — a low KC means the flow barely moves past the cylinder (inertia dominates), while high KC means extensive vortex shedding (drag dominates).
Design Wave Analysis
Offshore platforms are designed for extreme waves — the 100-year return period wave height is the standard design criterion. In the North Sea, this can exceed 30 meters. Engineers compute wave kinematics using Airy (linear) or Stokes fifth-order theory, then apply the Morison equation at every structural member to determine total base shear and overturning moment. These govern foundation and structural sizing.
Beyond Morison
For large-diameter structures like gravity-based platforms, monopiles for wind turbines, and floating production vessels, the cylinder-to-wavelength ratio exceeds 0.2 and diffraction effects become significant. Here, potential flow panel methods solve the full wave-structure interaction problem. But for the slender-member world of jacket structures, the Morison equation remains the workhorse of offshore engineering seven decades after its publication.