Rotating planar gravity currents at moderate Rossby numbers: Fully resolved simulations and shallow-water modelling
The flow of a gravity current of finite volume and density ρ 1 released from rest from a rectangular lock (of height h 0 ) into an ambient fluid of density ρ 1 (< ρ 1 ) in a system rotating with Ω about the vertical z is investigated by means of fully resolved direct numerical simulations (DNS) and...
| Authors: | ; ; ; |
|---|---|
| Format: | Article |
| Status: | Published version |
| Publication date: | 2019 |
| Country: | Argentina |
| Institution: | Consejo Nacional de Investigaciones Científicas y Técnicas |
| Repository: | CONICET Digital (CONICET) |
| Language: | English |
| OAI Identifier: | oai:ri.conicet.gov.ar:11336/116767 |
| Online Access: | http://hdl.handle.net/11336/116767 |
| Access Level: | Open access |
| Keyword: | GRAVITY CURRENTS ROTATING FLOWS https://purl.org/becyt/ford/2.3 https://purl.org/becyt/ford/2 |
| _version_ | 1878403014712098816 |
|---|---|
| author | Salinas, Jorge Sebastián |
| author2 | Bonometti, Thomas Ungarish, Marius Cantero, Mariano Ignacio |
| author2_role | author author author |
| author_browse | Bonometti, Thomas Cantero, Mariano Ignacio Salinas, Jorge Sebastián Ungarish, Marius |
| author_facet | Salinas, Jorge Sebastián Bonometti, Thomas Ungarish, Marius Cantero, Mariano Ignacio |
| author_role | author |
| collection | CONICET Digital (CONICET) |
| description | The flow of a gravity current of finite volume and density ρ 1 released from rest from a rectangular lock (of height h 0 ) into an ambient fluid of density ρ 1 (< ρ 1 ) in a system rotating with Ω about the vertical z is investigated by means of fully resolved direct numerical simulations (DNS) and a theoretical model (based on shallow-water and Ekman layer spin-up theories, including mixing). The motion of the dense fluid includes several stages: propagation in the x-direction accompanied by Coriolis acceleration/deflection in the -y-direction, which produces a quasi-steady wedge-shaped structure with significant anticyclonic velocity v, followed by a spin-up reduction of v accompanied by a slow x drift, and oscillation. The theoretical model aims to provide useful insights and approximations concerning the formation time and shape of wedge, and the subsequent spin-up effect. The main parameter is the Coriolis number, C = Ωh 0 /(g′h 0 ) 1/2 , where g′ =(ρ 1 /ρ 0 -1)g is the reduced gravity. The DNS results are focused on a range of relatively small Coriolis numbers, 0.1 ≤ C ≤ 0.25 (i.e. Rossby number Ro = 1=(2C) in the range 2 ≤ Ro ≤ 5), and a large range of Schmidt numbers 1≤Sc<∞; the Reynolds number is large in all cases. The current spreads out in the x direction until it is arrested by the Coriolis effect (in ∼1/4 revolution of the system). A complex motion develops about this state. First, we record oscillations on the inertial time scale 1/Ω (which are a part of the geostrophic adjustment), accompanied by vortices at the interface. Second, we note the spread of the wedge on a significantly longer time scale; this is an indirect spin-up effect - mixing and entrainment reduce the lateral (angular) velocity, which in turn decreases the Coriolis support to the ∂h/∂x slope of the wedge shape. Contrary to non-rotating gravity currents, the front does not remain sharp as it is subject to (i) local stretching along the streamwise direction and (ii) convective mixing due to Kelvin-Helmholtz vortices generated by shear along the spanwise direction and stemming from Coriolis effects. The theoretical model predicts that the length of the wedge scales as C -2/3 (in contrast to the Rossby radius ∈1/C which is relevant for large C; and in contrast to C -1/2 for the axisymmetric lens). |
| eu_rights_str_mv | openAccess |
| format | article |
| id | AR_2d4efa3e9c8f2777e302dfd8bf86cb1f |
| identifier_str_mv | Salinas, Jorge Sebastián; Bonometti, Thomas; Ungarish, Marius; Cantero, Mariano Ignacio; Rotating planar gravity currents at moderate Rossby numbers: Fully resolved simulations and shallow-water modelling; Cambridge University Press; Journal of Fluid Mechanics; 867; 5-2019; 114-145 0022-1120 CONICET Digital CONICET |
| institution | Consejo Nacional de Investigaciones Científicas y Técnicas |
| instname_str | Consejo Nacional de Investigaciones Científicas y Técnicas |
| language | eng |
| network_acronym_str | AR |
| network_name_str | Argentina |
| oai_identifier_str | oai:ri.conicet.gov.ar:11336/116767 |
| publishDate | 2019 |
| publishDateSort | 2019 |
| publisher | Cambridge University Press |
| publisherStr | Cambridge University Press |
| reponame_str | CONICET Digital (CONICET) |
| spelling | Rotating planar gravity currents at moderate Rossby numbers: Fully resolved simulations and shallow-water modelling Salinas, Jorge Sebastián Bonometti, Thomas Ungarish, Marius Cantero, Mariano Ignacio GRAVITY CURRENTS ROTATING FLOWS https://purl.org/becyt/ford/2.3 https://purl.org/becyt/ford/2 The flow of a gravity current of finite volume and density ρ 1 released from rest from a rectangular lock (of height h 0 ) into an ambient fluid of density ρ 1 (< ρ 1 ) in a system rotating with Ω about the vertical z is investigated by means of fully resolved direct numerical simulations (DNS) and a theoretical model (based on shallow-water and Ekman layer spin-up theories, including mixing). The motion of the dense fluid includes several stages: propagation in the x-direction accompanied by Coriolis acceleration/deflection in the -y-direction, which produces a quasi-steady wedge-shaped structure with significant anticyclonic velocity v, followed by a spin-up reduction of v accompanied by a slow x drift, and oscillation. The theoretical model aims to provide useful insights and approximations concerning the formation time and shape of wedge, and the subsequent spin-up effect. The main parameter is the Coriolis number, C = Ωh 0 /(g′h 0 ) 1/2 , where g′ =(ρ 1 /ρ 0 -1)g is the reduced gravity. The DNS results are focused on a range of relatively small Coriolis numbers, 0.1 ≤ C ≤ 0.25 (i.e. Rossby number Ro = 1=(2C) in the range 2 ≤ Ro ≤ 5), and a large range of Schmidt numbers 1≤Sc<∞; the Reynolds number is large in all cases. The current spreads out in the x direction until it is arrested by the Coriolis effect (in ∼1/4 revolution of the system). A complex motion develops about this state. First, we record oscillations on the inertial time scale 1/Ω (which are a part of the geostrophic adjustment), accompanied by vortices at the interface. Second, we note the spread of the wedge on a significantly longer time scale; this is an indirect spin-up effect - mixing and entrainment reduce the lateral (angular) velocity, which in turn decreases the Coriolis support to the ∂h/∂x slope of the wedge shape. Contrary to non-rotating gravity currents, the front does not remain sharp as it is subject to (i) local stretching along the streamwise direction and (ii) convective mixing due to Kelvin-Helmholtz vortices generated by shear along the spanwise direction and stemming from Coriolis effects. The theoretical model predicts that the length of the wedge scales as C -2/3 (in contrast to the Rossby radius ∈1/C which is relevant for large C; and in contrast to C -1/2 for the axisymmetric lens). Fil: Salinas, Jorge Sebastián. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; Argentina. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina. Comisión Nacional de Energía Atómica. Gerencia del Área de Energía Nuclear. Instituto Balseiro; Argentina Fil: Bonometti, Thomas. Centre National de la Recherche Scientifique; Francia. Université de Toulouse. Institut de Mécanique des Fluides de Toulouse; Francia Fil: Ungarish, Marius. Technion - Israel Institute of Technology; Israel Fil: Cantero, Mariano Ignacio. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Patagonia Norte; Argentina. Comisión Nacional de Energía Atómica. Centro Atómico Bariloche; Argentina. Comisión Nacional de Energía Atómica. Gerencia del Área de Energía Nuclear. Instituto Balseiro; Argentina Cambridge University Press http://hdl.handle.net/11336/116767 Salinas, Jorge Sebastián; Bonometti, Thomas; Ungarish, Marius; Cantero, Mariano Ignacio; Rotating planar gravity currents at moderate Rossby numbers: Fully resolved simulations and shallow-water modelling; Cambridge University Press; Journal of Fluid Mechanics; 867; 5-2019; 114-145 0022-1120 CONICET Digital CONICET |
| spellingShingle | Rotating planar gravity currents at moderate Rossby numbers: Fully resolved simulations and shallow-water modelling Salinas, Jorge Sebastián GRAVITY CURRENTS ROTATING FLOWS https://purl.org/becyt/ford/2.3 https://purl.org/becyt/ford/2 |
| status_str | publishedVersion |
| title | Rotating planar gravity currents at moderate Rossby numbers: Fully resolved simulations and shallow-water modelling |
| title_full | Rotating planar gravity currents at moderate Rossby numbers: Fully resolved simulations and shallow-water modelling |
| title_fullStr | Rotating planar gravity currents at moderate Rossby numbers: Fully resolved simulations and shallow-water modelling |
| title_full_unstemmed | Rotating planar gravity currents at moderate Rossby numbers: Fully resolved simulations and shallow-water modelling |
| title_short | Rotating planar gravity currents at moderate Rossby numbers: Fully resolved simulations and shallow-water modelling |
| title_sort | Rotating planar gravity currents at moderate Rossby numbers: Fully resolved simulations and shallow-water modelling |
| topic | GRAVITY CURRENTS ROTATING FLOWS https://purl.org/becyt/ford/2.3 https://purl.org/becyt/ford/2 |
| topic_facet | GRAVITY CURRENTS ROTATING FLOWS https://purl.org/becyt/ford/2.3 https://purl.org/becyt/ford/2 |
| url | http://hdl.handle.net/11336/116767 |