Nonlinear Scale Interactions and Energy Pathways in the Ocean

Transcription

1 Nonlinear Scale Interactions and Energy Pathways in the Ocean 1,2 Hussein Aluie, 1 Matthew Hecht & 3 Geoff Vallis 1 LANL, the 2 New Mexico Consortium and 3 U of Exeter with support from LANL s Institute for Geophysics, Planetary Physics and Signatures and Center for Nonlinear Studies

2 Ocean Circulation Multiscale Flow: O(10 4 ) km -- O(1) mm Source: NASA

3 Ocean Circulation Multiscale Flow: O(10 4 ) km -- O(1) mm Inhomogeneous and Anisotropic Source: NASA

4 Ocean Circulation Multiscale Flow: O(10 4 ) km -- O(1) mm Inhomogeneous and Anisotropic Mean Kinetic energy (KE) is concentrated in narrow intense currents. Source: NASA

5 Ocean Circulation Multiscale Flow: O(10 4 ) km -- O(1) mm Inhomogeneous and Anisotropic Mean Kinetic energy (KE) is concentrated in narrow intense currents. but much of the KE in the ocean resides in mesoscale eddies of size ~100 km Source: NASA

6 Ocean Circulation Multiscale Flow: O(10 4 ) km -- O(1) mm Inhomogeneous and Anisotropic Mean Kinetic energy (KE) is concentrated in narrow intense currents. but much of the KE in the ocean resides in mesoscale eddies of size ~100 km Source: NASA The Problem What is the flow of energy between different spatial scales, different forms?

7 Ocean Circulation Nonlinear Processes & Structures Baroclinic Instability Wind Barotropic Instability? Watts Mesoscale Eddies? Mean Flow Rossby Waves Bottom Drag Source: NASA Internal Waves?? Internal Waves The Problem What is the flow of energy between different spatial scales, different forms (how big are these arrows)?

8 Traditional Approach Source: NASA

9 Our Approach Coarse-graining (Filtering) Leonard (1974), Germano (1992), Eyink (1994), Piomelli et al. (1991), Liu et al (1994), Chen, Ecke, Eyink (2003),

10 Large-scale energy budget Cascade of Energy Energy flux

11 Large-scale energy budget Cascade of Energy Every point and every instant Energy flux Variable scale

12 Large-scale energy budget Measuring Energy Transfer

13 Measuring Energy Transfer Large-scale energy budget Subgrid scale (SGS) flux

14 Measuring Energy Transfer Large-scale energy budget Subgrid scale (SGS) flux Frisch (1995), used by Scott & Wang (2005), Tulloch, Marshall, Hill and Smith (2011) sweeping energy in space between structures

15 Measuring Energy Transfer Large-scale energy budget Subgrid scale (SGS) flux Frisch (1995), used by Scott & Wang (2005), Tulloch, Marshall, Hill and Smith (2011) Lindborg (2006), Mininni, et al. (2008) sweeping energy in space between structures

16 Measuring Energy Transfer Any measure of the energy exchange must satisfy: 1. Galilean Invariance 2. Florida Gulf Stream

17 Measuring Energy Transfer Any measure of the energy exchange must satisfy: 1. Galilean Invariance 2. Florida Gulf Stream

18 Measuring Energy Transfer Any measure of the energy exchange must satisfy: 1. Galilean Invariance 2. SGS definition Frisch (1995) definition

19 Measuring Energy Transfer Any measure of the energy exchange must satisfy: 1. Galilean Invariance 2. Frisch (1995) definition SGS definition V0 Simulation Domain

20 Measuring Energy Transfer Any measure of the energy exchange must satisfy: 1. Galilean Invariance 2. SGS definition After boosting Frisch (1995) definition After boosting

21 Measuring Energy Transfer Any measure of the energy exchange must satisfy: Vanish in the absence of subscale fluctuations

22 Measuring Energy Transfer Any measure of the energy exchange must satisfy: Vanish in the absence of subscale fluctuations SGS definition Lindborg (2006) definition

23 North Europe SGS definition Africa South North Europe Frisch definition Africa South

24 North Europe SGS definition = +0.9 W/km 2 /m Africa South North Europe Africa Frisch definition = W/km 2 /m South

25 North Europe SGS definition = +0.9 W/km 2 /m South North South Africa Europe Africa = -197 W/km 2 /m Frisch definition = W/km 2 /m = +319 W/km 2 /m

26 North Europe Africa South North Europe Africa South

27 In summary Traditional homogeneous/isotropic turbulence tools break down in the Ocean. Spectral Transfer and Flux can be qualitatively wrong. Guided by basic physical principles (Galilean invariance,.), the SGS approach to coarse-graining provides a robust means to measure energy transfer at different locations in the Ocean.

28 In summary Traditional homogeneous/isotropic turbulence tools break down in the Ocean. Spectral Transfer and Flux can be qualitatively wrong. Guided by basic physical principles (Galilean invariance,.), the SGS approach to coarse-graining provides a robust means to measure energy transfer at different locations in the Ocean. Were ready to publish last summer, before we realized we weren t

29 In summary Traditional homogeneous/isotropic turbulence tools break down in the Ocean. Spectral Transfer and Flux can be qualitatively wrong. Guided by basic physical principles (Galilean invariance,.), the SGS approach to coarse-graining provides a robust means to measure energy transfer at different locations in the Ocean. Were ready to publish last summer, before we realized we weren t Since then, have worked through issues of calculating energy transfer on the sphere (scale-dependent commutation of vector operations and filter).