Jiuxing Xing and Alan M. Davies

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Parameterization of orographic related momentum

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Parameterization of orographic related momentum

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Presentation transcript:

Non-hydrostatic effects on internal waves and mixing in the coastal ocean Jiuxing Xing and Alan M. Davies (Proudman Oceanographic Laboratory, Liverpool)

Motivation Understand small scale processes (e.g. solitary waves, convection) Stratified (tidal) flows over the steep topography (e.g., lee waves, flow separation and eddies) Are current coastal ocean models sufficient (e.g., is non-hydrostatic dynamics important)? Jonsmod 2006-Plymouth

Examples of small scale processes: ISWs of elevation on the Oregon shelf Klymak and Moum (2003) Jonsmod 2006-Plymouth

ISWs in the Faeroe-Shetland Channel Hosegood et al (2004) Jonsmod 2006-Plymouth

Stratified tidal flow over sills (Loch Etive, Inall et al, 2004) Jonsmod 2006-Plymouth

Models σ-following coordinate models (e.g., POLCOMS, POM, BOM) Z-coordinate models (e.g., MITgcm) The iterative method for non-hydrostatic pressure: an elliptic equation for the non-hydrostatic pressure Jonsmod 2006-Plymouth

Tests of the MIT model using Lab. exp Tests of the MIT model using Lab. exp. (Internal solitary waves over a slope (Michallet and Ivey 1999) Jonsmod 2006-Plymouth

Internal solitary waves (model results) Jonsmod 2006-Plymouth

Internal solitary waves (lab experiments vs model results) Jonsmod 2006-Plymouth

A dispersive ISW (small-amplitude) Jonsmod 2006-Plymouth

Large amplitude ISWs on a slope Jonsmod 2006-Plymouth

Tidal flow over a sill – lee wave generation and non-hydrostatic effects Idealized model setup M2 tide forced at the seaward boundary Closed landward boundary Resolution: dx=10 to 100m, dz=1m Minimum viscosity (Av=10-3 m2s-1, Ah=10-1 m2s-1, no explicit diffusivity) Initial zero velocity, N=0.01 s-1 Model domain Jonsmod 2006-Plymouth

Interaction of tidal waves with bottom topography: key non-dimensional parameters The key physical parameters: U0, ω0, f, N, h0, L, H. Non-dimensional parameters: U0 /(ω0L) the tidal excursion parameter; h0/H the relative height of the topography; [(ω02 - f 2 )/(N2- ω02)]1/2 the internal wave ray slope; h0 /L the topographic slope; U0 /(Nh0) the Froude number (or h’=Nh0 /U0); Jonsmod 2006-Plymouth

Snapshots of (T,u,w) at 23 mins (4,5,6,7/32 Tm2,non-hydro run) Jonsmod 2006-Plymouth

Snapshots of (T,u,w) at 23 mins (4,5,6,7/32 Tm2,non-hydro run) Jonsmod 2006-Plymouth

Snapshots of Ri number at 4,5,6,7/32T (non-hydrostatic run) Jonsmod 2006-Plymouth

Snapshots of temp & velocity at 4,5,6,7/32T (hydrostatic run) Jonsmod 2006-Plymouth

Temp & velocity at t=2/8T, 3/8T, 4/8T, 5/8T (non-hydrostatic run) Jonsmod 2006-Plymouth

Temp & velocity at t=2/8T, 3/8T, 4/8T, 5/8T (hydrostatic run) Jonsmod 2006-Plymouth

Vertical averaged internal wave energy flux (non-hydrostatic (left) and hydrostatic (right) ) Jonsmod 2006-Plymouth

Non-hydrostatic (top) and hydrostatic pressure Ph and Pnh have a 180o phase shift Jonsmod 2006-Plymouth

In a linear system, Ph & Pnh out phase Jonsmod 2006-Plymouth

nonhydrostatic pressure seafloor value indirect estimate of hydrostatic pressure by matching isopycnals to streamlines seafloor value Jonsmod 2006-Plymouth

Power spectral density (w) at two locations, non-hydrostatic (left) vs hydrostatic (right) (N=0.01) At lower frequency, as predicted by Khatiwala (2003), but not higher frequency. Jonsmod 2006-Plymouth

Power spectral density (w) for a steeper topography (N=0 Power spectral density (w) for a steeper topography (N=0.01), non-hydrostatic (left) vs hydrostatic (right) (N=0.01) Significant departure from recent theory at both lower & higher frequency. Jonsmod 2006-Plymouth

Summary Including non-hydrostatic dynamics in the coastal ocean models is feasible. Model results are encouraging comparing to the laboratory data. Importance of non-hydrostatic dynamics to lee wave generation and breaking; Strong kinetic energy spectral peak at higher (lee wave) frequency near the sill - a challenge to observationlists; Enhanced mixing due to the smaller-scale ripple topography - a challenge to modellers; More work is needed to assess the model quantitatively and quantify wave drag effects on mixing and circulation (3D effects may be important) . Jonsmod 2006-Plymouth