Attempting correct non-hydrostatic flux

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Energy-Pathways-Group · Nov 6, 2024 · c7e199d · c7e199d
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Showing 3 changed files with 53 additions and 13 deletions.
diff --git a/Matlab/WaveVortexModel/@WVTransform/summarizeModeEnergy.m b/Matlab/WaveVortexModel/@WVTransform/summarizeModeEnergy.m
@@ -1,6 +1,9 @@
 function summarizeModeEnergy(self,options)
     % List the most energetic modes
     %
+    % At the moment the +/- waves are simply added together for each mode.
+    % It would be better if they were separate.
+    %
     % - Topic: Energetics
     % - Declaration: summarizeModeEnergy(options)
     % - Parameter n: (optional) number of modes to list

diff --git a/Matlab/WaveVortexModel/NonlinearFluxOperations/WVNonlinearFluxNonhydrostatic.m b/Matlab/WaveVortexModel/NonlinearFluxOperations/WVNonlinearFluxNonhydrostatic.m
@@ -13,6 +13,10 @@
     % - Declaration: WVNonlinearFluxSpatial < [WVNonlinearFluxOperation](/classes/wvnonlinearfluxoperation/)
     properties
         dLnN2 = 0
+        cos_alpha
+        sin_alpha
+        ApmD
+        ApmW
     end
     methods
         function self = WVNonlinearFluxNonhydrostatic(wvt)
@@ -35,13 +39,32 @@
                 self.dLnN2 = shiftdim(wvt.dLnN2,-2);
                 warning('WVTransform not recognized.')
             end
+
+            k = shiftdim(wvt.k,-1);
+            l = shiftdim(wvt.l,-1);
+            kappa = sqrt(k.^2 + l.^2);
+            self.cos_alpha = k./kappa;
+            self.sin_alpha = l./kappa;
+            self.cos_alpha(1) = 0;
+            self.sin_alpha(1) = 0;
+
+            signNorm = -2*(mod(wvt.j,2) == 1)+1; % equivalent to (-1)^j
+            prefactor = -signNorm * sqrt((wvt.g*wvt.Lz)/(2*(wvt.N0*wvt.N0 - wvt.f*wvt.f)));
+            mj = (wvt.j*pi/wvt.Lz);
+            self.ApmD = (mj/2) .* prefactor;
+            self.ApmW = sqrt(-1) * (kappa/2) .* prefactor;
         end
 
-        function varargout = compute(self,wvt,varargin)
+        function [uNL,vNL,wNL,nNL] = spatialFlux(self,wvt)
             uNL = wvt.u .* wvt.diffX(wvt.u)   + wvt.v .* wvt.diffY(wvt.u)   + wvt.w .*  wvt.diffZF(wvt.u);
             vNL = wvt.u .* wvt.diffX(wvt.v)   + wvt.v .* wvt.diffY(wvt.v)   + wvt.w .*  wvt.diffZF(wvt.v);
             wNL = wvt.u .* wvt.diffX(wvt.w)   + wvt.v .* wvt.diffY(wvt.w)   + wvt.w .*  wvt.diffZG(wvt.w);
             nNL = wvt.u .* wvt.diffX(wvt.eta) + wvt.v .* wvt.diffY(wvt.eta) + wvt.w .* (wvt.diffZG(wvt.eta) + wvt.eta .* self.dLnN2);
+        end
+
+        function varargout = compute(self,wvt,varargin)
+
+            [uNL,vNL,wNL,nNL] = self.spatialFlux(wvt);
 
             u_hat = wvt.transformFromSpatialDomainWithFourier(-uNL);
             v_hat = wvt.transformFromSpatialDomainWithFourier(-vNL);
@@ -55,15 +78,16 @@
             zeta_bar = wvt.transformFromSpatialDomainWithFg(iK .* v_hat - iL .* u_hat);
             A0 = wvt.A0Z.*zeta_bar + wvt.A0N.*n_bar;
 
-            delta_bar = wvt.transformWithG_wg(wvt.h_0.*wvt.transformFromSpatialDomainWithFg(iK .* u_hat + iL .* v_hat));
+            delta_bar = self.ApmD .* (wvt.DCT * (self.cos_alpha .* u_hat + self.sin_alpha .* v_hat));
+            w_bar = self.ApmW .* (wvt.DST * w_hat);
             nw_bar = wvt.transformWithG_wg(n_bar - A0);
-            Ap = wvt.ApmD .* delta_bar + wvt.ApmN .* nw_bar;
-            Am = wvt.ApmD .* delta_bar - wvt.ApmN .* nw_bar;
+            Ap = delta_bar + w_bar + wvt.ApmN .* nw_bar;
+            Am = delta_bar + w_bar - wvt.ApmN .* nw_bar;
 
             Ap(:,1) = wvt.transformFromSpatialDomainWithFio(u_hat(:,1) - sqrt(-1)*v_hat(:,1))/2;
             Am(:,1) = conj(Ap(:,1));
 
-            phase = exp(-wvt.iOmega*(t-wvt.t0));
+            phase = exp(-wvt.iOmega*(wvt.t-wvt.t0));
             Ap = Ap .* phase;
             Am = Am .* conj(phase);
 

diff --git a/Matlab/WaveVortexModel/UnitTests/MiscTests/NonlinearFluxScratch.m b/Matlab/WaveVortexModel/UnitTests/MiscTests/NonlinearFluxScratch.m
@@ -4,7 +4,7 @@
 % removed the aliased wavenumbers. This means that all modes should be
 % resolved in the nonlinear flux.
 
-Lxyz = [500, 500, 500];
+Lxyz = [500, 500, 250];
 Nxyz = [8 8 9];
 latitude = 33;
 
@@ -20,6 +20,7 @@
 % wvt.initWithRandomFlow('geostrophic','mda','inertial',uvMax=0.1);
 % wvt.initWithRandomFlow('mda',uvMax=0.1);
 wvt.initWithRandomFlow('wave',uvMax=0.1);
+% wvt.initWithRandomFlow('wave',uvMax=0.00001);
 % wvt.initWithRandomFlow(uvMax=0.1);
 % wvt.initWithWaveModes(kMode=1,lMode=1,j=2,phi=0,u=0.05,sign=1);
 % wvt.addWaveModes(kMode=1,lMode=1,j=1,phi=0,u=0.05,sign=-1);
@@ -33,6 +34,13 @@
 wvt.addWaveModes(kMode=1,lMode=1,j=1,phi=0,u=0.05,sign=1);
 wvt.addWaveModes(kMode=1,lMode=0,j=1,phi=0,u=0.05,sign=1);
 
+% Renormalize so that each wave-mode has the same total energy
+renorm = 1./sqrt(wvt.Apm_TE_factor.*abs(wvt.Ap).^2);
+renorm(isinf(renorm))=0;
+wvt.Ap = wvt.Ap .* renorm;
+
+% For this test, the vertical momentum contributions sum to zero
+
 antialiasMask = zeros(wvt.spectralMatrixSize);
 antialiasMask(wvt.Kh > 2*max(abs(wvt.k))/3) = 1;
 antialiasMask(wvt.J > 2*max(abs(wvt.j))/3) = 1;
@@ -51,19 +59,24 @@
 
 fprintf('\nNon-hydrostatic:\n')
 % wvt.initWithUVEta(wvt.u,wvt.v,wvt.eta);
+wvt.nonlinearFluxOperation = WVNonlinearFluxNonhydrostatic(wvt);
 [Fp,Fm,F0] = wvt.nonlinearFlux();
 [Ep,Em,E0] = wvt.energyFluxFromNonlinearFlux(Fp,Fm,F0,deltaT=0);
 fprintf('(Ep,Em,E0) = (%g, %g, %g), total %g\n', sum(Ep(:)), sum(Em(:)), sum(E0(:)), sum(Ep(:))+sum(Em(:))+sum(E0(:)));
 
 fprintf('Ep:\n')
-displayFluxEnergy(wvt_hs,Ep)
-% fprintf('Em:\n')
-% displayFluxEnergy(wvt_hs,Em)
+displayFluxEnergy(wvt,Ep)
+fprintf('Em:\n')
+displayFluxEnergy(wvt,Em)
 % fprintf('E0:\n')
-% displayFluxEnergy(wvt_hs,E0)
+% displayFluxEnergy(wvt,E0)
 
 % (wvt.totalEnergy-wvt.totalEnergySpatiallyIntegrated)/wvt.totalEnergy
 
+% Not sure if this is helpful or meaningful.
+% [uNL,vNL,wNL,nNL] = wvt.nonlinearFluxOperation.spatialFlux(wvt);
+% energy = sum(shiftdim(wvt.z_int,-2).*mean(mean( wvt.u.*uNL + wvt.v.*vNL + wvt.w.*wNL + shiftdim(wvt.N2,-2).*wvt.eta.*nNL, 1 ),2 ) )/2
+
 %%
 fprintf('\nHydrostatic:\n')
 wvt_hs.initWithUVEta(wvt.u,wvt.v,wvt.eta);
@@ -74,8 +87,8 @@
 
 fprintf('Ep:\n')
 displayFluxEnergy(wvt_hs,Ep)
-% fprintf('Em:\n')
-% displayFluxEnergy(wvt_hs,Em)
+fprintf('Em:\n')
+displayFluxEnergy(wvt_hs,Em)
 % fprintf('E0:\n')
 % displayFluxEnergy(wvt_hs,E0)
 
@@ -99,7 +112,7 @@
 %%
 function displayFluxEnergy(wvt,E)
 [~,indices] = sort(abs(E(:)),'descend');
-for iMode=1:10
+for iMode=1:5
     [kMode,lMode,jMode] = wvt.modeNumberFromIndex(indices(iMode));
     fprintf('(%d,%d,%d) with energy %g\n',kMode,lMode,jMode,E(indices(iMode)));
 end