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| Main Authors: | , , , |
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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2604.26290 |
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| _version_ | 1866917445523996672 |
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| author | Tiwari, Harshit Singh, Dhananjay Verma, Mahendra K. Ranjan, Rajesh |
| author_facet | Tiwari, Harshit Singh, Dhananjay Verma, Mahendra K. Ranjan, Rajesh |
| contents | Supersonic turbulence is vital to astrophysical and high-speed engineering flows, yet its energy transfer mechanisms remain poorly understood. We present high-resolution ($1024^3$) direct numerical simulations (DNS) of forced compressible turbulence across a range of turbulent Mach numbers ($M_t = 0.2$ to $3.0$). Using the GPU-accelerated solver \texttt{DHARA} with a seventh-order, low-dissipation Targeted Essentially Non-Oscillatory (TENO) scheme, we resolve both fine-scale eddies and sharp shock fronts. Our results reveal a fundamental shift in the energy cascade in the supersonic regime. As $M_t$ increases, the rotational kinetic energy spectrum steepens from a Kolmogorov-like $k^{-5/3}$ scaling toward a Burgers-like $k^{-2}$ scaling. Conversely, the compressive energy spectrum becomes shallower, deviating from Burgers scaling. We show that these spectral modifications are driven by a dominant cross-scale transfer of energy from solenoidal to compressive modes within the inertial range, alongside significant contributions from pressure dilatation. Scaling laws for the root-mean-square compressive velocity ($U_C$) and compressive energy flux ($Π_C$) are found to mirror classical Burgers turbulence. Finally, we show that while energy injection rates depend on forcing type rather than Mach number, increased $M_t$ leads to decreased rotational dissipation and increased compressive dissipation and pressure dilatation. These findings elucidate intermodal energy cascade mechanisms, advancing our understanding of energy transfers in supersonic turbulence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_26290 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Scaling in Supersonic Turbulence: Energy Spectra and Fluxes using High-Fidelity Direct Numerical Simulations Tiwari, Harshit Singh, Dhananjay Verma, Mahendra K. Ranjan, Rajesh Fluid Dynamics Computational Physics Supersonic turbulence is vital to astrophysical and high-speed engineering flows, yet its energy transfer mechanisms remain poorly understood. We present high-resolution ($1024^3$) direct numerical simulations (DNS) of forced compressible turbulence across a range of turbulent Mach numbers ($M_t = 0.2$ to $3.0$). Using the GPU-accelerated solver \texttt{DHARA} with a seventh-order, low-dissipation Targeted Essentially Non-Oscillatory (TENO) scheme, we resolve both fine-scale eddies and sharp shock fronts. Our results reveal a fundamental shift in the energy cascade in the supersonic regime. As $M_t$ increases, the rotational kinetic energy spectrum steepens from a Kolmogorov-like $k^{-5/3}$ scaling toward a Burgers-like $k^{-2}$ scaling. Conversely, the compressive energy spectrum becomes shallower, deviating from Burgers scaling. We show that these spectral modifications are driven by a dominant cross-scale transfer of energy from solenoidal to compressive modes within the inertial range, alongside significant contributions from pressure dilatation. Scaling laws for the root-mean-square compressive velocity ($U_C$) and compressive energy flux ($Π_C$) are found to mirror classical Burgers turbulence. Finally, we show that while energy injection rates depend on forcing type rather than Mach number, increased $M_t$ leads to decreased rotational dissipation and increased compressive dissipation and pressure dilatation. These findings elucidate intermodal energy cascade mechanisms, advancing our understanding of energy transfers in supersonic turbulence. |
| title | Scaling in Supersonic Turbulence: Energy Spectra and Fluxes using High-Fidelity Direct Numerical Simulations |
| topic | Fluid Dynamics Computational Physics |
| url | https://arxiv.org/abs/2604.26290 |