CaTSM: A Pseudo‐Spectral Thermodynamically Consistent Model of Compressible Flows

Abstract

Abstract We introduce a pseudo‐spectral algorithm that includes full compressible dynamics with the intent of simulating near‐incompressible fluids, CaTSM (Compressible and Thermodynamically consistent Spectral Model). A semi‐implicit scheme is used to model acoustic waves in order to evolve the system efficiently for such fluids. We demonstrate the convergence properties of this numerical code for the case of a shock tube and for Rayleigh‐Taylor instability. A linear equation of state is also presented, which relates the specific volume of the fluid linearly to the potential temperature, salinity, and pressure. This permits the results to be easily compared to a Boussinesq framework in order to assess whether the Boussinesq approximation adequately represents the relevant exchange of energy to the problem of interest. One such application is included, that of the development of a single salt finger, and it is shown that the energetic behavior of the system is comparable to the typical canonical development of the problem for oceanographic parameters. However, for more compressible systems, the results change substantially even for low‐Mach number flows.

Keywords

• compressible fluids
• incompressible fluids
• numerical algorithm
• microscale