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Phares L. Carroll
Department of Mechanical Engineering California Institute of Technology Pasadena, CA 91125, United States

Guillaume Blanquart


Without an energy source, a turbulent velocity field will decay with dynamics dictated by the well-known Karman-Howarth equation. In Direct Numerical Simulation (DNS) studies, turbulent fields are maintained at a state of statistical stationarity (constant Taylor-Reynolds number, Reλ) by supplying such an energy source. The energy source comes in the form of a velocity field forcing method, which involves the addition of a source term to the momentum equation. This momentum source term manifests also in the Karman-Howarth equation, and has a form determined uniquely by the specific forcing method implemented. To ensure the dynamics obtained from the velocity field-forcing methodology are physically correct, their impact on the behavior of the Karman-Howarth equation has been undertaken and attention has been paid to the functional form of the forcing method-imposed source term appended. Two velocity field forcing methods are considered in this study, Lundgren's linear forcing method (Lundgren (2003))) and Alvelius' spectral forcing method (Alvelius (1999)). It was found that the two disparate forcing techniques produce source terms in the Karman-Howarth equation that behave very similarly at small scales, but diverge at the intermediate and large scales. An important consequence of this is that the velocity fields generated by the two methods exhibit comparable statistical and spectral characteristics at these small scales. The contradictory characteristics of the turbulent fields at the large and intermediate scales can be traced similarly back to the differing behavior of the source terms at these scales and their influence on the governing Karman-Howarth equation.