Mixing in Cold water Domes and at Sills Alan M. Davies and Jiuxing Xing Proudman Oceanographic Laboratory, Liverpool, UK

Dome Problem Wind forced internal waves in cold water bottom dome. Mixing within thermocline. Internal mixing. Role of Vorticity at dome front in producing internal wave Role of wind forcing frequency. Super and Sub- inertial features

Non-Linear effects on Inertial Oscillations Unbounded Ocean Eqts Effect of external shear is to change Amp. + Freq. of I.O. Frontal Shear Changes I.O. amp./Freq at depth so conv/divg. Gives internal wave at level of thermocline. Freq. int. wave above inertial propogates away, if below trapped

Super-inertial wind forcing

Wavelength λf from Dispersion Relation ωf = forcing frequency So λf/Leff gives nodal structure where Leff is “effective length” of dome

Sub-inertial wind forcing

CONCLUSIONS 1.Non-linear effects associated with along frontal flows produce near-inertial internal waves in presence of wind forcing 2.Super-inertial internal waves propagate away from generation region (front) 3.Sub-inertial are trapped and enhance mixing in frontal region 4.In a cold water bottom dome, super-inertial internal waves are trapped as standing waves, can modify GM spectrum 5.Response in centre of dome different from 1D model, must account for internal wave 6.Sub-inertial wave confined to front, and response in centre of dome as in 1D model

TIDAL MIXING AT SILLS Idealized Loch Etive Recent measurements Inall et al Non-hydrostatic model High resolution Idealized M2 forcing + idealized T profile Example of internal mixing of tidal origin

Initial Conditions

Influence of small scale topog. Lee wave characteristics influenced by Buoyancy frequency Velocity over sill….. Froude Number Fourier transform of topog. So How small scale effect mixing ?????

CONCLUSIONS….. Sill Internal tide little mixing Lee Wave not advected back over sill Lee Wave major source of mixing Lee wave distribution influenced by non- hydro. nature of model Lee wave spectrum/mixing influenced by small scale topog. + Horizontal Visc. Assumptions in b.b.l. also infulence lee wave hence mixing

Future Role surface stratification / fresh water, wind mixing Detailed distribution of Topog. Sill b.b.l effects Lateral + across sill form drag Horizontal + Vertical tke schemes (LES) Role non-linearity (u du/dx ) Internal tides vz. Lee waves control on mixing

Model Skill Assessment Model Validation in highly variable undersampled domain. Spectral Decompostion.. Hans van Haren Detailed measurement critical small scale topog. and stratification. Tidal corrected dissipation rates and mixing + filtered lee wave advection effects Role of lab. Expts + upscale.