### 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 |
---|---|

Article number | 126604 |

Journal | Physics of Fluids |

Volume | 30 |

Issue number | 12 |

DOIs | |

Publication status | Published - 2018 Dec 1 |

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### All Science Journal Classification (ASJC) codes

- Condensed Matter Physics

### Cite this

*Physics of Fluids*,

*30*(12), [126604]. https://doi.org/10.1063/1.5053444

}

*Physics of Fluids*, vol. 30, no. 12, 126604. https://doi.org/10.1063/1.5053444

**Theoretical investigation of nonhydrostatic effects on convectively forced flows : Propagating and evanescent gravity-wave modes.** / Seo, Jaemyeong Mango; Baik, Jong Jin; Chun, Hye-Yeong.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Theoretical investigation of nonhydrostatic effects on convectively forced flows

T2 - Propagating and evanescent gravity-wave modes

AU - Seo, Jaemyeong Mango

AU - Baik, Jong Jin

AU - Chun, Hye-Yeong

PY - 2018/12/1

Y1 - 2018/12/1

N2 - 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 kc = 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 kc 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.

AB - 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 kc = 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 kc 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.

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U2 - 10.1063/1.5053444

DO - 10.1063/1.5053444

M3 - Article

AN - SCOPUS:85059513258

VL - 30

JO - Physics of Fluids

JF - Physics of Fluids

SN - 1070-6631

IS - 12

M1 - 126604

ER -