## Abstract

Nonhydrostatic effects on convectively forced mesoscale flows are theoretically investigated using a linearized, two-dimensional, steady-state, nonrotating, Boussinesq airflow system with prescribed convective forcing. The nondimensionalized airflow system contains the nonhydrostaticity factor β = U/Na, where U is the basic-state wind speed, N is the basic-state buoyancy frequency, and a is the half-width of the convective forcing. In an inviscid-limit system, the solution for vertical velocity is classified into the propagating mode (k ≤ β^{-1}, where k is the nondimensional horizontal wavenumber) and the evanescent mode (k > β^{-1}). As β increases, an alternating wavy pattern of updrafts and downdrafts appears downstream of the convective forcing with a nondimensional horizontal wavelength of 2πβ corresponding to the nondimensional critical horizontal wavenumber k_{c} = β^{-1}. The momentum flux analysis shows that the alternating updrafts and downdrafts are almost horizontally propagating gravity waves of the propagating mode whose k is slightly smaller than k_{c} and that these gravity waves strengthen the momentum flux above the convective forcing. In a viscous system, the solution for vertical velocity has propagating and decaying components simultaneously that cannot be explicitly separated. Here, the propagating mode and two evanescent modes are defined by comparing the magnitudes of the nondimensional vertical wavenumber and decay rate. For large viscous coefficients, the k-range of the propagating mode becomes narrow and the alternating updrafts and downdrafts are dissipated. As β increases, the propagating mode, which strengthens the momentum flux above the convective forcing, is effectively dissipated even with a small viscous coefficient.

Original language | English |
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Article number | 126604 |

Journal | Physics of Fluids |

Volume | 30 |

Issue number | 12 |

DOIs | |

Publication status | Published - 2018 Dec 1 |

### Bibliographical note

Funding Information:The authors are grateful to two anonymous reviewers for providing valuable comments on this study. This work was funded by the Korea Meteorological Administration Research and Development Program under Grant No. KMIPA 2015-5100 and by the Small Grant for Exploratory Research (SGER) program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science and ICT (MSIT) (No. 2018R1D1A1A02086007).

Publisher Copyright:

© 2018 Author(s).

## All Science Journal Classification (ASJC) codes

- Computational Mechanics
- Condensed Matter Physics
- Mechanics of Materials
- Mechanical Engineering
- Fluid Flow and Transfer Processes